Journal articles: 'Robust model fitting'

1

Welsh, A. H., and A. F. Ruckstuhl. "Robust fitting of the binomial model." Annals of Statistics 29, no. 4 (August 2001): 1117–36. http://dx.doi.org/10.1214/aos/1013699996.

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Wang, Hanzi, and David Suter. "Using symmetry in robust model fitting." Pattern Recognition Letters 24, no. 16 (December 2003): 2953–66. http://dx.doi.org/10.1016/s0167-8655(03)00156-9.

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Medley, Daniela O., Carlos Santiago, and Jacinto C. Nascimento. "Deep Active Shape Model for Robust Object Fitting." IEEE Transactions on Image Processing 29 (2020): 2380–94. http://dx.doi.org/10.1109/tip.2019.2948728.

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Pham, Trung T., Tat-Jun Chin, Jin Yu, and David Suter. "The Random Cluster Model for Robust Geometric Fitting." IEEE Transactions on Pattern Analysis and Machine Intelligence 36, no. 8 (August 2014): 1658–71. http://dx.doi.org/10.1109/tpami.2013.2296310.

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Song, Weixing, Weixin Yao, and Yanru Xing. "Robust mixture regression model fitting by Laplace distribution." Computational Statistics & Data Analysis 71 (March 2014): 128–37. http://dx.doi.org/10.1016/j.csda.2013.06.022.

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Wang, Yiru, Yinlong Liu, Xuechen Li, Chen Wang, Manning Wang, and Zhijian Song. "GORFLM: Globally Optimal Robust Fitting for Linear Model." Signal Processing: Image Communication 84 (May 2020): 115834. http://dx.doi.org/10.1016/j.image.2020.115834.

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Wimmer, M., F. Stulp, S. Pietzsch, and B. Radig. "Learning Local Objective Functions for Robust Face Model Fitting." IEEE Transactions on Pattern Analysis and Machine Intelligence 30, no. 8 (August 2008): 1357–70. http://dx.doi.org/10.1109/tpami.2007.70793.

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Tennakoon, Ruwan, Alireza Sadri, Reza Hoseinnezhad, and Alireza Bab-Hadiashar. "Effective Sampling: Fast Segmentation Using Robust Geometric Model Fitting." IEEE Transactions on Image Processing 27, no. 9 (September 2018): 4182–94. http://dx.doi.org/10.1109/tip.2018.2834821.

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Tennakoon, Ruwan B., Alireza Bab-Hadiashar, Zhenwei Cao, Reza Hoseinnezhad, and David Suter. "Robust Model Fitting Using Higher Than Minimal Subset Sampling." IEEE Transactions on Pattern Analysis and Machine Intelligence 38, no. 2 (February 1, 2016): 350–62. http://dx.doi.org/10.1109/tpami.2015.2448103.

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Yang, Jingjing, and David W. Scott. "Robust fitting of a Weibull model with optional censoring." Computational Statistics & Data Analysis 67 (November 2013): 149–61. http://dx.doi.org/10.1016/j.csda.2013.05.009.

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Heinrich, Stuart B. "Efficient and robust model fitting with unknown noise scale." Image and Vision Computing 31, no. 10 (October 2013): 735–47. http://dx.doi.org/10.1016/j.imavis.2013.07.003.

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Lin, Shuyuan, Hailing Luo, Yan Yan, Guobao Xiao, and Hanzi Wang. "Co-Clustering on Bipartite Graphs for Robust Model Fitting." IEEE Transactions on Image Processing 31 (2022): 6605–20. http://dx.doi.org/10.1109/tip.2022.3214073.

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Zhang, Zongliang, Jonathan Li, Yulan Guo, Xin Li, Yangbin Lin, Guobao Xiao, and Cheng Wang. "Robust procedural model fitting with a new geometric similarity estimator." Pattern Recognition 85 (January 2019): 120–31. http://dx.doi.org/10.1016/j.patcog.2018.07.027.

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Cheng, Chia-Ming, and Shang-Hong Lai. "A consensus sampling technique for fast and robust model fitting." Pattern Recognition 42, no. 7 (July 2009): 1318–29. http://dx.doi.org/10.1016/j.patcog.2009.01.007.

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Chen, Y., and J. E. Paloheimo. "A robust regression analysis of recruitment in fisheries." Canadian Journal of Fisheries and Aquatic Sciences 52, no. 5 (May 1, 1995): 993–1006. http://dx.doi.org/10.1139/f95-098.

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Variations in environmental variables and (or) errors in measuring stock and recruitment often result in large and heterogeneous variations in fitting fish stock–recruitment (SR) data to a regression model. This makes the commonly used least squares (LS) method inappropriate in estimating the SR relationship. Hence, we propose the following procedure: (i) identify possible outliers in fitting data to a given SR model using the least median of the squared orthogonal distance that is not sensitive to atypical values and requires no assumption on distribution of errors and (ii) apply the LS method to the SR data with defined outliers being down weighted. We showed by simulation that the SR parameters of the Ricker model could be estimated with smaller estimation errors and biases using the proposed procedures than with the traditional LS approach. Examination of four sets of published field data leads us to suggest fitting fish SR data to suitable models using the proposed estimation method and interpreting the results with the assistance of knowledge on the relevant environmental variables and measurement errors. However, our interpretation should be viewed as a working hypothesis requiring special studies to clarify the causal links between environmental variables and recruitment.

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Xia, Ye-Mao, Xin-Yuan Song, and Sik-Yum Lee. "Robust model fitting for the non linear structural equation model under normal theory." British Journal of Mathematical and Statistical Psychology 62, no. 3 (November 2009): 529–68. http://dx.doi.org/10.1348/000711008x345966.

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Greco, Luca, Giovanni Saraceno, and Claudio Agostinelli. "Robust Fitting of a Wrapped Normal Model to Multivariate Circular Data and Outlier Detection." Stats 4, no. 2 (June 1, 2021): 454–71. http://dx.doi.org/10.3390/stats4020028.

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In this work, we deal with a robust fitting of a wrapped normal model to multivariate circular data. Robust estimation is supposed to mitigate the adverse effects of outliers on inference. Furthermore, the use of a proper robust method leads to the definition of effective outlier detection rules. Robust fitting is achieved by a suitable modification of a classification-expectation-maximization algorithm that has been developed to perform a maximum likelihood estimation of the parameters of a multivariate wrapped normal distribution. The modification concerns the use of complete-data estimating equations that involve a set of data dependent weights aimed to downweight the effect of possible outliers. Several robust techniques are considered to define weights. The finite sample behavior of the resulting proposed methods is investigated by some numerical studies and real data examples.

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Wang, Hanzi, Guobao Xiao, Yan Yan, and David Suter. "Searching for Representative Modes on Hypergraphs for Robust Geometric Model Fitting." IEEE Transactions on Pattern Analysis and Machine Intelligence 41, no. 3 (March 1, 2019): 697–711. http://dx.doi.org/10.1109/tpami.2018.2803173.

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Yan, Yan, Min Liu, Si Chen, and Fan Xiao. "A novel robust model fitting approach towards multiple-structure data segmentation." Neurocomputing 239 (May 2017): 181–93. http://dx.doi.org/10.1016/j.neucom.2017.02.015.

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Xiao, Guobao, Hanzi Wang, Yan Yan, and Liming Zhang. "Robust geometric model fitting based on iterative Hypergraph Construction and Partition." Neurocomputing 336 (April 2019): 56–66. http://dx.doi.org/10.1016/j.neucom.2018.03.085.

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Lai, Taotao, Hamido Fujita, Changcai Yang, Qiming Li, and Riqing Chen. "Robust Model Fitting Based on Greedy Search and Specified Inlier Threshold." IEEE Transactions on Industrial Electronics 66, no. 10 (October 2019): 7956–66. http://dx.doi.org/10.1109/tie.2018.2881950.

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Lai, Taotao, Riqing Chen, Changcai Yang, Qiming Li, Hamido Fujita, Alireza Sadri, and Hanzi Wang. "Efficient Robust Model Fitting for Multistructure Data Using Global Greedy Search." IEEE Transactions on Cybernetics 50, no. 7 (July 2020): 3294–306. http://dx.doi.org/10.1109/tcyb.2019.2900096.

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Van Gysel, M., P. Lemberge, and P. Van Espen. "Implementation of a spectrum fitting procedure using a robust peak model." X-Ray Spectrometry 32, no. 6 (2003): 434–41. http://dx.doi.org/10.1002/xrs.666.

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Payandeh, Bijan, and Yonghe Wang. "A site-index model remodified." Canadian Journal of Forest Research 24, no. 1 (January 1, 1994): 197–98. http://dx.doi.org/10.1139/x94-028.

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A previously reported site index model with unconstrained parameter estimates may not be amenable to extrapolation. A modification is presented that is more robust and has no apparent shortcomings. Results of fitting both models to white spruce (Piceaglauca (Moench) Voss) and aspen (Populustremuloides Michx.) data sets are presented and discussed.

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Breda, Iris, Polychronis Papaderos, Jean Michel Gomes, and Stergios Amarantidis. "A new fitting concept for the robust determination of Sérsic model parameters." Astronomy & Astrophysics 632 (December 2019): A128. http://dx.doi.org/10.1051/0004-6361/201935144.

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Context. The Sérsic law (SL) offers a versatile, widely used functional form for the structural characterization of galaxies near and far. Whereas fitting this three-parameter function to galaxies with a genuine SL luminosity distribution (e.g., several local early-type galaxies–ETGs) yields a robust determination of the Sérsic exponent η and effective surface brightness μeff, this is not necessarily the case for galaxies whose surface brightness profiles (SBPs) appreciably deviate, either in their centers or over an extended radius interval, from the SL (e.g., ETGs with a “depleted” core and nucleated dwarf ellipticals, or most late-type galaxies-LTGs). In this general case of “imperfect” SL profiles, the best-fitting solution may significantly depend on the radius (or surface brightness) interval fit, the photometric passbands considered and the specifics of the fitting procedure (photometric uncertainties of SBP data points or image pixels, and corrections for point spread function (PSF) convolution effects). Such uncertainties may then affect, in a non-easily predictable manner, automated structural studies of large heterogeneous galaxy samples and introduce a scatter, if not a bias, in galaxy scaling relations and their evolution across redshift (z). Aims. Our goal is to devise a fitting concept that permits a robust determination of the equivalent SL model for the general case of galaxies with imperfect SL profiles. Methods. The distinctive feature of the concept proposed here (iFIT) is that the fit is not constrained through standard χ2 minimization between an observed SBP and the SL model of it, but instead through the search for the best match between the observationally determined and theoretically expected radial variation of the mean surface brightness and light growth curve. This approach ensures quick convergence to a unique solution for both perfect and imperfect Sérsic profiles, even shallow and resolution-degraded SBPs. iFIT allows for correction of PSF convolution effects, offering the user the option of choosing between a Moffat, Gaussian, or user-supplied PSF. iFIT, which is a standalone FORTRAN code, can be applied to any SBP that is provided in ASCII format and it has the capability of convenient graphical storage of its output. The iFIT distribution package is supplemented with an auxiliary SBP derivation tool in python. Results. iFIT has been extensively tested on synthetic data with a Sérsic index 0.3 ≤ η ≤ 4.2 and an effective radius 1 ≤ Reff (″)≤20. Applied to non PSF-convolved data, iFIT can infer the Sérsic exponent η with an absolute error of ≤ 0.2 even for shallow SBPs. As for PSF-degraded data, iFIT can recover the input SL model parameters with a satisfactorily accuracy almost over the entire considered parameter space as long as FWHM(PSF) ≤ Reff. This study also includes examples of applications of iFIT to ETGs and local low-mass starburst galaxies. These tests confirm that iFIT shows little sensitivity on PSF corrections and SBP limiting surface brightness, and that subtraction of the best-fitting SL model in two different bands generally yields a good match to the observed radial color profile. Conclusions. It is pointed out that the publicly available iFIT offers an efficient tool for the non-supervised structural characterization of large galaxy samples, as those expected to become available with Euclid and LSST.

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Ma, Mingyang, Silong Peng, and Xiyuan Hu. "A lighting robust fitting approach of 3D morphable model for face reconstruction." Visual Computer 32, no. 10 (September 21, 2015): 1223–38. http://dx.doi.org/10.1007/s00371-015-1158-z.

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Wong, Hoi Sim, Tat-Jun Chin, Jin Yu, and David Suter. "A simultaneous sample-and-filter strategy for robust multi-structure model fitting." Computer Vision and Image Understanding 117, no. 12 (December 2013): 1755–69. http://dx.doi.org/10.1016/j.cviu.2013.08.007.

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Wang, Hanzi, and David Suter. "MDPE: A Very Robust Estimator for Model Fitting and Range Image Segmentation." International Journal of Computer Vision 59, no. 2 (September 2004): 139–66. http://dx.doi.org/10.1023/b:visi.0000022287.61260.b0.

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WANG, HAI-JUN, and MING LIU. "ACTIVE CONTOURS DRIVEN BY LOCAL GAUSSIAN DISTRIBUTION FITTING ENERGY BASED ON LOCAL ENTROPY." International Journal of Pattern Recognition and Artificial Intelligence 27, no. 06 (September 2013): 1355008. http://dx.doi.org/10.1142/s0218001413550082.

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This paper presents a scheme of improvement on the local Gaussian distribution fitting energy (LGDF) model in terms of robustness to initialization and noise. The LGDF energy is redefined as a weighted energy integral. The weights are defined based on local entropy deriving from a gray level distribution of local image, which enables the proposed model to be robust to the initialization. Experimental results prove that the proposed model is more robustness to noise than the original LGDF model, local binary fitting (LBF) model and local image fitting (LIF) model.

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Yang, Yixin, Xin Lü, Jian Ma, and Han Qiao. "A Robust Factor Analysis Model for Dichotomous Data." Journal of Systems Science and Information 2, no. 5 (October 25, 2014): 437–50. http://dx.doi.org/10.1515/jssi-2014-0437.

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AbstractFactor analysis is widely used in psychology, sociology and economics, as an analytically tractable method of reducing the dimensionality of the data in multivariate statistical analysis. The classical factor analysis model in which the unobserved factor scores and errors are assumed to follow the normal distributions is often criticized because of its lack of robustness. This paper introduces a new robust factor analysis model for dichotomous data by using robust distributions such as multivariatet-distribution. After comparing the fitting results of the normal factor analysis model and the robust factor analysis model for dichotomous data, it can been seen that the robust factor analysis model can get more accurate analysis results in some cases, which indicates this model expands the application range and practical value of the factor analysis model.

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Guo, Zhimin, Yangyang Tian, and Wandeng Mao. "A Robust Faster R-CNN Model with Feature Enhancement for Rust Detection of Transmission Line Fitting." Sensors 22, no. 20 (October 19, 2022): 7961. http://dx.doi.org/10.3390/s22207961.

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Rust of transmission line fittings is a major hidden risk to transmission safety. Since the fittings located at high altitude are inconvenient to detect and maintain, machine vision techniques have been introduced to realize the intelligent rust detection with the help of unmanned aerial vehicles (UAV). Due to the small size of fittings and disturbance of complex environmental background, however, there are often cases of missing detection and false detection. To improve the detection reliability and robustness, this paper proposes a new robust Faster R-CNN model with feature enhancement mechanism for the rust detection of transmission line fitting. Different from current methods that improve feature representation in front end, this paper adopts an idea of back-end feature enhancement. First, the residual network ResNet-101 is introduced as the backbone network to extract rich discriminative information from the UAV images. Second, a new feature enhancement mechanism is added after the region of interest (ROI) pooling layer. Through calculating the similarity between each region proposal and the others, the feature weights of the region proposals containing target object can be enhanced via the overlaying of the object’s representation. The weight of the disturbance terms can then be relatively reduced. Empirical evaluation is conducted on some real-world UAV monitoring images. The comparative results demonstrate the effectiveness of the proposed model in terms of detection precision and recall rate, with the average precision of rust detection 97.07%, indicating that the proposed method can provide an reliable and robust solution for the rust detection.

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Shertzer, Kyle W., and Michael H. Prager. "Least median of squares: a suitable objective function for stock assessment models?" Canadian Journal of Fisheries and Aquatic Sciences 59, no. 9 (September 1, 2002): 1474–81. http://dx.doi.org/10.1139/f02-112.

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Robust fitting methods, intended for data sets possibly contaminated with invalid observations, are gaining increased use in analysis of fishery data. In particular, the method of least median of squares (LMS) has attracted attention. Its hallmark is high statistical resistance, which makes it immune to up to 50% contamination in the data. However, the same property makes it inefficient and can cause faulty fitting of typical fishery data. The LMS fit can be in conflict with important sections of a time series, a problem we illustrate by fitting a biomass dynamic (surplus production) model to simulated and actual fishery data. Additionally, we illustrate that LMS parameter estimates can be highly sensitive to small perturbations in the data. Other robust methods, like the method of least absolute values (LAV), appear less prone to such problems. A key reference on LMS recommends using the method as part of an exploratory procedure to identify outliers, rather than as an objective function for final model fitting. We concur with that recommendation.

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Birnbaum, Michael H., and Bonny Quan. "Note on Birnbaum and Wan (2020): True and error model analysis is robust with respect to certain violations of the MARTER model." Judgment and Decision Making 15, no. 5 (September 2020): 861–62. http://dx.doi.org/10.1017/s193029750000797x.

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AbstractThe Markov True and Error (MARTER) model (Birnbaum & Wan, 2020) has three components: a risky decision making model with one or more parameters, a Markov model that describes stochastic variation of parameters over time, and a true and error (TE) model that describes probabilistic relations between true preferences and overt responses. In this study, we simulated data according to 57 generating models that either did or did not satisfy the assumptions of the True and Error fitting model, that either did or did not satisfy the error independence assumptions, that either did or did not satisfy transitivity, and that had various patterns of error rates. A key assumption in the TE fitting model is that a person’s true preferences do not change in the short time within a session; that is, preference reversals between two responses by the same person to two presentations of the same choice problem in the same brief session are due to random error. In a set of 48 simulations, data generating models either satisfied this assumption or they implemented a systematic violation, in which true preferences could change within sessions. We used the true and error (TE) fitting model to analyze the simulated data, and we found that it did a good job of distinguishing transitive from intransitive models and in estimating parameters not only when the generating model satisfied the model assumptions, but also when model assumptions were violated in this way. When the generating model violated the assumptions, statistical tests of the TE fitting models correctly detected the violations. Even when the data contained violations of the TE model, the parameter estimates representing probabilities of true preference patterns were surprisingly accurate, except for error rates, which were inflated by model violations. In a second set of simulations, the generating model either had error rates that were or were not independent of true preferences and transitivity either was or was not satisfied. It was found again that the TE analysis was able to detect the violations of the fitting model, and the analysis correctly identified whether the data had been generated by a transitive or intransitive process; however, in this case, estimated incidence of a preference pattern was reduced if that preference pattern had a higher error rate. Overall, the violations could be detected and did not affect the ability of the TE analysis to discriminate between transitive and intransitive processes.

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Martin, R. Douglas, and Daniel Z. Xia. "Efficient bias robust regression for time series factor models." Journal of Asset Management 23, no. 3 (March 14, 2022): 215–34. http://dx.doi.org/10.1057/s41260-022-00258-0.

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AbstractWe introduce a robust regression estimator for time series factor models called the mOpt estimator. This estimator minimizes the maximum bias due to outlier generating distribution deviations from a standard normal errors distribution model, and at the same time has a high normal distribution efficiency. We demonstrate the efficacy of the mOpt estimator in comparison with the non-robust least squares (LS) estimator in applications to both single factor and multifactor time series models. For the case of single factor CAPM models we compared mOpt and LS estimates for cross sections of liquid stocks from the CRSP database in each contiguous two-year interval from 1963 to 1980. The results show that absolute differences between the two estimates greater than 0.3 occur for about 18% of the stocks, and differences greater than 0.5 occur for about 7.5% of the stocks. Our application of the mOpt estimator to multifactor models focuses on fitting the Fama-French 3-factor and the Fama-French-Carhart 4-factor models to weekly stock returns for the year 2008, using both the robust t-statistics associated with the mOpt estimates and a new statistical test for differences between the mOpt and LS coefficients. The results demonstrate the efficacy of the mOpt estimator in providing better model fits than the LS estimates, which are adversely influenced by outliers. Finally, since model selection is an important aspect of time series factor model fitting, we introduce a new robust prediction errors based model selection criterion called the Robust Final Prediction Error (RFPE), which makes natural use of the mOpt regression estimator. When applied to the 4-factor model, the RFPE finds as the best subset model the one that contains the Market, SMB and MOM factors, not the three Fama-French factors Market, SMB and HML. We anticipate that RFPE will prove to be quite useful for model selection of time series factor models.

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Tan, K. C., and Y. Li. "Evolutionary L∞ identification and model reduction for robust control." Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering 214, no. 3 (May 1, 2000): 231–38. http://dx.doi.org/10.1243/0959651001540591.

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An evolutionary approach for modern robust control oriented system identification and model reduction in the frequency domain is proposed. The technique provides both an optimized nominal model and a ‘worst-case’ additive or multiplicative uncertainty bounding function which is compatible with robust control design methodologies. In addition, the evolutionary approach is applicable to both continuous- and discrete-time systems without the need for linear parametrization or a confined problem domain for deterministic convex optimization. The proposed method is validated against a laboratory multiple-input multiple-output (MIMO) test rig and benchmark problems, which show a higher fitting accuracy and provides a tighter L∞ error bound than existing methods in the literature do.

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Silalahi, Divo Dharma, Habshah Midi, Jayanthi Arasan, Mohd Shafie Mustafa, and Jean-Pierre Caliman. "Automated Fitting Process Using Robust Reliable Weighted Average on Near Infrared Spectral Data Analysis." Symmetry 12, no. 12 (December 17, 2020): 2099. http://dx.doi.org/10.3390/sym12122099.

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With the complexity of Near Infrared (NIR) spectral data, the selection of the optimal number of Partial Least Squares (PLS) components in the fitted Partial Least Squares Regression (PLSR) model is very important. Selecting a small number of PLS components leads to under fitting, whereas selecting a large number of PLS components results in over fitting. Several methods exist in the selection procedure, and each yields a different result. However, so far no one has been able to determine the more superior method. In addition, the current methods are susceptible to the presence of outliers and High Leverage Points (HLP) in a dataset. In this study, a new automated fitting process method on PLSR model is introduced. The method is called the Robust Reliable Weighted Average—PLS (RRWA-PLS), and it is less sensitive to the optimum number of PLS components. The RRWA-PLS uses the weighted average strategy from multiple PLSR models generated by the different complexities of the PLS components. The method assigns robust procedures in the weighing schemes as an improvement to the existing Weighted Average—PLS (WA-PLS) method. The weighing schemes in the proposed method are resistant to outliers and HLP and thus, preserve the contribution of the most relevant variables in the fitted model. The evaluation was done by utilizing artificial data with the Monte Carlo simulation and NIR spectral data of oil palm (Elaeis guineensis Jacq.) fruit mesocarp. Based on the results, the method claims to have shown its superiority in the improvement of the weight and variable selection procedures in the WA-PLS. It is also resistant to the influence of outliers and HLP in the dataset. The RRWA-PLS method provides a promising robust solution for the automated fitting process in the PLSR model as unlike the classical PLS, it does not require the selection of an optimal number of PLS components.

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Gong, Yu Sheng, Qian Han, and Li Ping Zhang. "Research into the Model of GNSS Leveling Polynomial Surface Fitting Based on MATLAB." Applied Mechanics and Materials 90-93 (September 2011): 2907–12. http://dx.doi.org/10.4028/www.scientific.net/amm.90-93.2907.

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To make full use of geodetic height results measured by GNSS and improve the accuracy that GNSS geodetic height convert to normal height, method of polynomial surface fitting has been selected in this article to research into fitting of the elevation. In the first place, for least squares estimation do not have the ability of resisting gross error, robust estimation is introduced to data preprocessing, which has solve the problem of distortion model effectively and then combines with specific engineering to make comparison and to analyze accuracy of polynomial surface fitting data of different orders. MATLAB has been used in programming design in the whole process, which has realized automatic processing of data.

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Shi, Dexin, Christine DiStefano, Xiaying Zheng, Ren Liu, and Zhehan Jiang. "Fitting latent growth models with small sample sizes and non-normal missing data." International Journal of Behavioral Development 45, no. 2 (January 7, 2021): 179–92. http://dx.doi.org/10.1177/0165025420979365.

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This study investigates the performance of robust maximum likelihood (ML) estimators when fitting and evaluating small sample latent growth models with non-normal missing data. Results showed that the robust ML methods could be used to account for non-normality even when the sample size is very small (e.g., N < 100). Among the robust ML estimators, “MLR” was the optimal choice, as it was found to be robust to both non-normality and missing data while also yielding more accurate standard error estimates and growth parameter coverage. However, the choice “MLMV” produced the most accurate p values for the χ2 test statistic under conditions studied. Regarding the goodness of fit indices, as sample size decreased, all three fit indices studied (i.e., comparative fit index, root mean square error of approximation, and standardized root mean square residual) exhibited worse fit. When the sample size was very small (e.g., N < 60), the fit indices would imply that a proposed model fit poorly, when this might not be actually the case in the population.

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Li, Guang Rui. "A Robust Star Acquisition Algorithm Based on Facet Model." Advanced Materials Research 532-533 (June 2012): 1747–51. http://dx.doi.org/10.4028/www.scientific.net/amr.532-533.1747.

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An efficient and robust star acquisition algorithm based on facet fitting is presented to improve the performance of star sensors. The location of star central pixels can be determined by searching extremum intensity pixels among the point spread function (PSF) of stars, which is well fitted by the cubic facet model. According to extremum theory, the second derivative operators are pre-calculated and the searching process can be completed using convolution operations thrice. Simultaneously, cluster formation is also a time consuming routine, which is accomplished using specific maximum and minimum threshold to speed up it. A variety of experiments are carried out to validate the performance of proposed algorithm, moreover, the performance evaluation index M is presented. The results clearly show that the proposed algorithm makes a great progress than the vector method in time expense and accuracy under intense noise conditions.

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Zhang, Hui-Guo, Chang-Lin Mei, and He-Ling Wang. "Robust SiZer Approach for Varying Coefficient Models." Mathematical Problems in Engineering 2013 (2013): 1–13. http://dx.doi.org/10.1155/2013/547874.

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Varying coefficient models have widely been applied to many practical fields for exploring dynamic patterns of the regression relationships. In this study, we propose a robust scenario of SiZer (significant zero crossing of derivatives) inference approach based on the local least absolute deviation fitting procedure and the bootstrap confidence interval to uncover the statistically significant features of the coefficient functions in a varying coefficient model under different smoothing scales. The simulation study shows that the proposed SiZer approach is quite robust to outliers and performs well in finding the significant features of the coefficient functions. Furthermore, a real environmental data set is analyzed to demonstrate the application of the proposed approach.

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Brazauskas, Vytaras, and Robert Serfling. "Favorable Estimators for Fitting Pareto Models: A Study Using Goodness-of-fit Measures with Actual Data." ASTIN Bulletin 33, no. 02 (November 2003): 365–81. http://dx.doi.org/10.2143/ast.33.2.503698.

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Several recent papers treated robust and efficient estimation of tail index parameters for (equivalent) Pareto and truncated exponential models, for large and small samples. New robust estimators of “generalized median” (GM) and “trimmed mean” (T) type were introduced and shown to provide more favorable trade-offs between efficiency and robustness than several well-established estimators, including those corresponding to methods of maximum likelihood, quantiles, and percentile matching. Here we investigate performance of the above mentioned estimators on real data and establish — via the use of goodness-of-fit measures — that favorable theoretical properties of the GM and T type estimators translate into an excellent practical performance. Further, we arrive at guidelines for Pareto model diagnostics, testing, and selection of particular robust estimators in practice. Model fits provided by the estimators are ranked and compared on the basis of Kolmogorov-Smirnov, Cramér-von Mises, and Anderson-Darling statistics.

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Brazauskas, Vytaras, and Robert Serfling. "Favorable Estimators for Fitting Pareto Models: A Study Using Goodness-of-fit Measures with Actual Data." ASTIN Bulletin 33, no. 2 (November 2003): 365–81. http://dx.doi.org/10.1017/s0515036100013519.

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Several recent papers treated robust and efficient estimation of tail index parameters for (equivalent) Pareto and truncated exponential models, for large and small samples. New robust estimators of “generalized median” (GM) and “trimmed mean” (T) type were introduced and shown to provide more favorable trade-offs between efficiency and robustness than several well-established estimators, including those corresponding to methods of maximum likelihood, quantiles, and percentile matching. Here we investigate performance of the above mentioned estimators on real data and establish — via the use of goodness-of-fit measures — that favorable theoretical properties of the GM and T type estimators translate into an excellent practical performance. Further, we arrive at guidelines for Pareto model diagnostics, testing, and selection of particular robust estimators in practice. Model fits provided by the estimators are ranked and compared on the basis of Kolmogorov-Smirnov, Cramér-von Mises, and Anderson-Darling statistics.

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Zhao, Qian, Vytaras Brazauskas, and Jugal Ghorai. "ROBUST AND EFFICIENT FITTING OF SEVERITY MODELS AND THE METHOD OF WINSORIZED MOMENTS." ASTIN Bulletin 48, no. 1 (November 2, 2017): 275–309. http://dx.doi.org/10.1017/asb.2017.30.

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AbstractContinuous parametric distributions are useful tools for modeling and pricing insurance risks, measuring income inequality in economics, investigating reliability of engineering systems, and in many other areas of application. In this paper, we propose and develop a new method for estimation of their parameters—the method of Winsorized moments (MWM)—which is conceptually similar to the method of trimmed moments (MTM) and thus is robust and computationally efficient. Both approaches yield explicit formulas of parameter estimators for log-location-scale families and their variants, which are commonly used to model claim severity. Large-sample properties of the new estimators are provided and corroborated through simulations. Their performance is also compared to that of MTM and the maximum likelihood estimators (MLE). In addition, the effect of model choice and parameter estimation method on risk pricing is illustrated using actual data that represent hurricane damages in the United States from 1925 to 1995. In particular, the estimated pure premiums for an insurance layer are computed when the lognormal and log-logistic models are fitted to the data using the MWM, MTM and MLE methods.

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Zeng, Yinuo, Wendi Bao, Liying Tao, Die Hu, Zonglin Yang, Liren Yang, and Delong Shang. "Regularized Spectral Spike Response Model: A Neuron Model for Robust Parameter Reduction." Brain Sciences 12, no. 8 (July 29, 2022): 1008. http://dx.doi.org/10.3390/brainsci12081008.

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The modeling procedure of current biological neuron models is hindered by either hyperparameter optimization or overparameterization, which limits their application to a variety of biologically realistic tasks. This article proposes a novel neuron model called the Regularized Spectral Spike Response Model (RSSRM) to address these issues. The selection of hyperparameters is avoided by the model structure and fitting strategy, while the number of parameters is constrained by regularization techniques. Twenty firing simulation experiments indicate the superiority of RSSRM. In particular, after pruning more than 99% of its parameters, RSSRM with 100 parameters achieves an RMSE of 5.632 in membrane potential prediction, a VRD of 47.219, and an F1-score of 0.95 in spike train forecasting with correct timing (±1.4 ms), which are 25%, 99%, 55%, and 24% better than the average of other neuron models with the same number of parameters in RMSE, VRD, F1-score, and correct timing, respectively. Moreover, RSSRM with 100 parameters achieves a memory use of 10 KB and a runtime of 1 ms during inference, which is more efficient than the Izhikevich model.

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Rahman, Md Siddiqur, and Jafar A. Khan. "Building a Robust Linear Model with Backward Elimination Procedure." Dhaka University Journal of Science 62, no. 2 (February 8, 2015): 87–93. http://dx.doi.org/10.3329/dujs.v62i2.21971.

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For building a linear prediction model, Backward Elimination (BE) is a computationally suitable stepwise procedure for sequencing the candidate predictors. This method yields poor results when data contain outliers and other contaminations. Robust model selection procedures, on the other hand, are not computationally efficient or scalable to large dimensions, because they require the fitting of a large number of submodels. Robust version of BE is proposed in this study, which is computationally very suitable and scalable to large high-dimensional data sets. Since BE can be expressed in terms of sample correlations, simple robustifications are obtained by replacing these correlations by their robust counterparts. A pairwise approach is used to construct the robust correlation matrix -- not only because of its computational advantages over the d-dimensional approach, but also because the pairwise approach is more consistent with the idea of step-by-step algorithms. The performance of the proposed robust method is much better than standard BE. DOI: http://dx.doi.org/10.3329/dujs.v62i2.21971 Dhaka Univ. J. Sci. 62(2): 87-93, 2014 (July)

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Vasilopoulos, Yannis, Eliška Skořepová, and Miroslav Šoóš. "COMF: Comprehensive Model-Fitting Method for Simulating Isothermal and Single-Step Solid-State Reactions." Crystals 10, no. 2 (February 24, 2020): 139. http://dx.doi.org/10.3390/cryst10020139.

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It is well known that the implementation of the conventional model-fitting (CMF) method leads to several indistinguishable ‘best’ candidate models (BCMs) for a single-step isothermal solid-state reaction (ISSR), meaning that subjective selection becomes unavoidable. Here, we developed a more robust comprehensive model-fitting method (COMF) which, while maintaining the mathematical simplicity of CMF, utilizes a ranking criterion that enables automatic and unambiguous determination of the BCM. For each model evaluated, COMF, like CMF, fits the integral reaction rate, but, unlike CMF, it also fits the experimental conversion fraction and reaction speed. From this, three different determination coefficients are calculated and combined to rank the considered models. To validate COMF, we used two sets of experimental kinetic data from the literature regarding the isothermal desolvation of pharmaceutical solvates: (i) tetrahydrofuran solvates of sulfameter, and (ii) methanol solvates of ciclesonide. Our results suggest that from an algorithmic perspective, COMF could become the model-fitting method of choice for ISSRs making the selection of BCM easier and more reliable.

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Gutiérrez-Vargas, Álvaro A., Michel Meulders, and Martina Vandebroek. "randregret: A command for fitting random regret minimization models using Stata." Stata Journal: Promoting communications on statistics and Stata 21, no. 3 (September 2021): 626–58. http://dx.doi.org/10.1177/1536867x211045538.

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In this article, we describe the randregret command, which implements a variety of random regret minimization (RRM) models. The command allows the user to apply the classic RRM model introduced in Chorus (2010, European Journal of Transport and Infrastructure Research 10: 181–196), the generalized RRM model introduced in Chorus (2014, Transportation Research, Part B 68: 224–238), and also the µRRM and pure RRM models, both introduced in van Cranenburgh, Guevara, and Chorus (2015, Transportation Research, Part A 74: 91–109). We illustrate the use of the randregret command by using stated choice data on route preferences. The command offers robust and cluster standarderror correction using analytical expressions of the score functions. It also offers likelihood-ratio tests that can be used to assess the relevance of a given model specification. Finally, users can obtain the predicted probabilities from each model by using the randregretpred command.

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Gutiérrez-Vargas, Álvaro A., Michel Meulders, and Martina Vandebroek. "randregret: A command for fitting random regret minimization models using Stata." Stata Journal: Promoting communications on statistics and Stata 21, no. 3 (September 2021): 626–58. http://dx.doi.org/10.1177/1536867x211045538.

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In this article, we describe the randregret command, which implements a variety of random regret minimization (RRM) models. The command allows the user to apply the classic RRM model introduced in Chorus (2010, European Journal of Transport and Infrastructure Research 10: 181–196), the generalized RRM model introduced in Chorus (2014, Transportation Research, Part B 68: 224–238), and also the µRRM and pure RRM models, both introduced in van Cranenburgh, Guevara, and Chorus (2015, Transportation Research, Part A 74: 91–109). We illustrate the use of the randregret command by using stated choice data on route preferences. The command offers robust and cluster standarderror correction using analytical expressions of the score functions. It also offers likelihood-ratio tests that can be used to assess the relevance of a given model specification. Finally, users can obtain the predicted probabilities from each model by using the randregretpred command.

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Vos, Daniël, and Sicco Verwer. "Robust Optimal Classification Trees against Adversarial Examples." Proceedings of the AAAI Conference on Artificial Intelligence 36, no. 8 (June 28, 2022): 8520–28. http://dx.doi.org/10.1609/aaai.v36i8.20829.

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Decision trees are a popular choice of explainable model, but just like neural networks, they suffer from adversarial examples. Existing algorithms for fitting decision trees robust against adversarial examples are greedy heuristics and lack approximation guarantees. In this paper we propose ROCT, a collection of methods to train decision trees that are optimally robust against user-specified attack models. We show that the min-max optimization problem that arises in adversarial learning can be solved using a single minimization formulation for decision trees with 0-1 loss. We propose such formulations in Mixed-Integer Linear Programming and Maximum Satisfiability, which widely available solvers can optimize. We also present a method that determines the upper bound on adversarial accuracy for any model using bipartite matching. Our experimental results demonstrate that the existing heuristics achieve close to optimal scores while ROCT achieves state-of-the-art scores.

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Zhao, Xi, Yun Zhang, Shoulie Xie, Qianqing Qin, Shiqian Wu, and Bin Luo. "Outlier Detection Based on Residual Histogram Preference for Geometric Multi-Model Fitting." Sensors 20, no. 11 (May 27, 2020): 3037. http://dx.doi.org/10.3390/s20113037.

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Geometric model fitting is a fundamental issue in computer vision, and the fitting accuracy is affected by outliers. In order to eliminate the impact of the outliers, the inlier threshold or scale estimator is usually adopted. However, a single inlier threshold cannot satisfy multiple models in the data, and scale estimators with a certain noise distribution model work poorly in geometric model fitting. It can be observed that the residuals of outliers are big for all true models in the data, which makes the consensus of the outliers. Based on this observation, we propose a preference analysis method based on residual histograms to study the outlier consensus for outlier detection in this paper. We have found that the outlier consensus makes the outliers gather away from the inliers on the designed residual histogram preference space, which is quite convenient to separate outliers from inliers through linkage clustering. After the outliers are detected and removed, a linkage clustering with permutation preference is introduced to segment the inliers. In addition, in order to make the linkage clustering process stable and robust, an alternative sampling and clustering framework is proposed in both the outlier detection and inlier segmentation processes. The experimental results also show that the outlier detection scheme based on residual histogram preference can detect most of the outliers in the data sets, and the fitting results are better than most of the state-of-the-art methods in geometric multi-model fitting.

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Journal articles on the topic 'Robust model fitting'

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