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Journal articles on the topic 'Estimation of probability density function'

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Published: 30 May 2022
Last updated: 31 May 2022

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1

Kay, S. "Model-based probability density function estimation." IEEE Signal Processing Letters 5, no. 12 (December 1998): 318–20. http://dx.doi.org/10.1109/97.735424.

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2

BALÁZS, FERENC, and SÁNDOR IMRE. "QUANTUM COMPUTATION BASED PROBABILITY DENSITY FUNCTION ESTIMATION." International Journal of Quantum Information 03, no. 01 (March 2005): 93–98. http://dx.doi.org/10.1142/s0219749905000578.

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Signal processing techniques will lean on blind methods in the near future, where no redundant, resource allocating information will be transmitted through the channel. To achieve a proper decision, however, it is essential to know at least the probability density function (PDF), which to estimate is classically a time consumpting and/or less accurate hard task that may make decisions to fail. This paper describes the design of a quantum assisted PDF estimation method also by way of an example, which promises to achieve the exact PDF by proper setting of parameters in a very rapid way.
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3

Chen, Song Xi. "Probability Density Function Estimation Using Gamma Kernels." Annals of the Institute of Statistical Mathematics 52, no. 3 (September 2000): 471–80. http://dx.doi.org/10.1023/a:1004165218295.

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4

López-Rubio, Ezequiel, and Juan Miguel Ortiz-de-Lazcano-Lobato. "Soft clustering for nonparametric probability density function estimation." Pattern Recognition Letters 29, no. 16 (December 2008): 2085–91. http://dx.doi.org/10.1016/j.patrec.2008.07.010.

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5

Alencar, M. S. "Estimation of probability density function using spectral analysis." Electronics Letters 34, no. 2 (1998): 150. http://dx.doi.org/10.1049/el:19980170.

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6

Srikanth, M., H. K. Kesavan, and P. H. Roe. "Probability density function estimation using the MinMax measure." IEEE Transactions on Systems, Man and Cybernetics, Part C (Applications and Reviews) 30, no. 1 (2000): 77–83. http://dx.doi.org/10.1109/5326.827456.

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7

Kwasniok, Frank. "Semiparametric maximum likelihood probability density estimation." PLOS ONE 16, no. 11 (November 9, 2021): e0259111. http://dx.doi.org/10.1371/journal.pone.0259111.

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A comprehensive methodology for semiparametric probability density estimation is introduced and explored. The probability density is modelled by sequences of mostly regular or steep exponential families generated by flexible sets of basis functions, possibly including boundary terms. Parameters are estimated by global maximum likelihood without any roughness penalty. A statistically orthogonal formulation of the inference problem and a numerically stable and fast convex optimization algorithm for its solution are presented. Automatic model selection over the type and number of basis functions is performed with the Bayesian information criterion. The methodology can naturally be applied to densities supported on bounded, infinite or semi-infinite domains without boundary bias. Relationships to the truncated moment problem and the moment-constrained maximum entropy principle are discussed and a new theorem on the existence of solutions is contributed. The new technique compares very favourably to kernel density estimation, the diffusion estimator, finite mixture models and local likelihood density estimation across a diverse range of simulation and observation data sets. The semiparametric estimator combines a very small mean integrated squared error with a high degree of smoothness which allows for a robust and reliable detection of the modality of the probability density in terms of the number of modes and bumps.
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8

Xiang, Xiaojing. "Estimation of conditional quantile density function." Journal of Nonparametric Statistics 4, no. 3 (January 1995): 309–16. http://dx.doi.org/10.1080/10485259508832621.

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9

Kraft, C. H., Y. Lepage, and C. Van Eeden. "Estimation of a symmetric density function." Communications in Statistics - Theory and Methods 14, no. 2 (January 1985): 273–88. http://dx.doi.org/10.1080/03610928508828911.

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10

Oryshchenko, Vitaliy, and Richard J. Smith. "Improved density and distribution function estimation." Electronic Journal of Statistics 13, no. 2 (2019): 3943–84. http://dx.doi.org/10.1214/19-ejs1619.

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11

LÓPEZ-RUBIO, EZEQUIEL. "ROBUST LOCATION AND SPREAD MEASURES FOR NONPARAMETRIC PROBABILITY DENSITY FUNCTION ESTIMATION." International Journal of Neural Systems 19, no. 05 (October 2009): 345–57. http://dx.doi.org/10.1142/s0129065709002075.

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Robustness against outliers is a desirable property of any unsupervised learning scheme. In particular, probability density estimators benefit from incorporating this feature. A possible strategy to achieve this goal is to substitute the sample mean and the sample covariance matrix by more robust location and spread estimators. Here we use the L 1-median to develop a nonparametric probability density function (PDF) estimator. We prove its most relevant properties, and we show its performance in density estimation and classification applications.
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12

Fahmy, Suhaib A., and A. R. Mohan. "Architecture for Real-Time Nonparametric Probability Density Function Estimation." IEEE Transactions on Very Large Scale Integration (VLSI) Systems 21, no. 5 (May 2013): 910–20. http://dx.doi.org/10.1109/tvlsi.2012.2201187.

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13

Sarajedini, A., R. Hecht-Nielsen, and P. M. Chau. "Conditional probability density function estimation with sigmoidal neural networks." IEEE Transactions on Neural Networks 10, no. 2 (March 1999): 231–38. http://dx.doi.org/10.1109/72.750544.

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14

Dobronets, Boris S., and Olga A. Popova. "Improving the Accuracy of the Probability Density Function Estimation." Journal of Siberian Federal University. Mathematics & Physics 10, no. 1 (March 2017): 16–21. http://dx.doi.org/10.17516/1997-1397-2017-10-1-16-21.

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15

Ghaniee Zarch, Majid, Yousef Alipouri, and Javad Poshtan. "Fault Detection Based On Online Probability Density Function Estimation." Asian Journal of Control 18, no. 6 (May 11, 2016): 2193–202. http://dx.doi.org/10.1002/asjc.1314.

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16

López-Rubio, Ezequiel, and José Muñoz-Pérez. "Probability density function estimation with the frequency polygon transform." Information Sciences 298 (March 2015): 136–58. http://dx.doi.org/10.1016/j.ins.2014.12.014.

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17

Laster, J. D., J. H. Reed, and W. H. Tranter. "Bit error rate estimation using probability density function estimators." IEEE Transactions on Vehicular Technology 52, no. 1 (January 2003): 260–67. http://dx.doi.org/10.1109/tvt.2002.807229.

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18

Cox, Nicholas J. "Speaking Stata: Density Probability Plots." Stata Journal: Promoting communications on statistics and Stata 5, no. 2 (June 2005): 259–73. http://dx.doi.org/10.1177/1536867x0500500210.

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Density probability plots show two guesses at the density function of a continuous variable, given a data sample. The first guess is the density function of a specified distribution (e.g., normal, exponential, gamma, etc.) with appropriate parameter values plugged in. The second guess is the same density function evaluated at quantiles corresponding to plotting positions associated with the sample's order statistics. If the specified distribution fits well, the two guesses will be close. Such plots, suggested by Jones and Daly in 1995, are explained and discussed with examples from simulated and real data. Comparisons are made with histograms, kernel density estimation, and quantile–quantile plots.
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19

FIORI, SIMONE. "PROBABILITY DENSITY FUNCTION LEARNING BY UNSUPERVISED NEURONS." International Journal of Neural Systems 11, no. 05 (October 2001): 399–417. http://dx.doi.org/10.1142/s0129065701000898.

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In a recent work, we introduced the concept of pseudo-polynomial adaptive activation function neuron (FAN) and presented an unsupervised information-theoretic learning theory for such structure. The learning model is based on entropy optimization and provides a way of learning probability distributions from incomplete data. The aim of the present paper is to illustrate some theoretical features of the FAN neuron, to extend its learning theory to asymmetrical density function approximation, and to provide an analytical and numerical comparison with other known density function estimation methods, with special emphasis to the universal approximation ability. The paper also provides a survey of PDF learning from incomplete data, as well as results of several experiments performed on real-world problems and signals.
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20

Sasaki, Hiroaki, Yung-Kyun Noh, Gang Niu, and Masashi Sugiyama. "Direct Density Derivative Estimation." Neural Computation 28, no. 6 (June 2016): 1101–40. http://dx.doi.org/10.1162/neco_a_00835.

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Estimating the derivatives of probability density functions is an essential step in statistical data analysis. A naive approach to estimate the derivatives is to first perform density estimation and then compute its derivatives. However, this approach can be unreliable because a good density estimator does not necessarily mean a good density derivative estimator. To cope with this problem, in this letter, we propose a novel method that directly estimates density derivatives without going through density estimation. The proposed method provides computationally efficient estimation for the derivatives of any order on multidimensional data with a hyperparameter tuning method and achieves the optimal parametric convergence rate. We further discuss an extension of the proposed method by applying regularized multitask learning and a general framework for density derivative estimation based on Bregman divergences. Applications of the proposed method to nonparametric Kullback-Leibler divergence approximation and bandwidth matrix selection in kernel density estimation are also explored.
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21

Chen, Zhicheng, Yuequan Bao, Hui Li, and Billie F. Spencer. "A novel distribution regression approach for data loss compensation in structural health monitoring." Structural Health Monitoring 17, no. 6 (December 8, 2017): 1473–90. http://dx.doi.org/10.1177/1475921717745719.

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Structural health monitoring has arisen as an important tool for managing and maintaining civil infrastructure. A critical problem for all structural health monitoring systems is data loss or data corruption due to sensor failure or other malfunctions, which bring into question in subsequent structural health monitoring data analysis and decision-making. Probability density functions play a very important role in many applications for structural health monitoring. This article focuses on data loss compensation for probability density function estimation in structural health monitoring using imputation methods. Different from common data, continuous probability density functions belong to functional data; the conventional distribution-to-distribution regression technique has significant potential in missing probability density function imputation; however, extrapolation and directly borrowing shape information from the covariate probability density function are the main challenges. Inspired by the warping transformation of distributions in the field of functional data analysis, a new distribution regression approach for imputing missing correlated probability density functions is proposed in this article. The warping transformation for distributions is a mapping operation used to transform one probability density function to another by deforming the original probability density function with a warping function. The shape mapping between probability density functions can be characterized well by warping functions. Given a covariate probability density function, the warping function is first estimated by a kernel regression model; then, the estimated warping function is used to transform the covariate probability density function and obtain an imputation for the missing probability density function. To address issues with poor performance when the covariate probability density function is contaminated, a hybrid approach is proposed that fuses the imputations obtained by the warping transformation approach with the conventional distribution-to-distribution regression approach. Experiments based on field monitoring data are conducted to evaluate the performance of the proposed approach. The corresponding results indicate that the proposed approach can outperform the conventional method, especially in extrapolation. The proposed approach shows good potential to provide more reliable estimation of distributions of missing structural health monitoring data.
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22

Agostini, Alejandro, and Enric Celaya. "Online Reinforcement Learning Using a Probability Density Estimation." Neural Computation 29, no. 1 (January 2017): 220–46. http://dx.doi.org/10.1162/neco_a_00906.

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Function approximation in online, incremental, reinforcement learning needs to deal with two fundamental problems: biased sampling and nonstationarity. In this kind of task, biased sampling occurs because samples are obtained from specific trajectories dictated by the dynamics of the environment and are usually concentrated in particular convergence regions, which in the long term tend to dominate the approximation in the less sampled regions. The nonstationarity comes from the recursive nature of the estimations typical of temporal difference methods. This nonstationarity has a local profile, varying not only along the learning process but also along different regions of the state space. We propose to deal with these problems using an estimation of the probability density of samples represented with a gaussian mixture model. To deal with the nonstationarity problem, we use the common approach of introducing a forgetting factor in the updating formula. However, instead of using the same forgetting factor for the whole domain, we make it dependent on the local density of samples, which we use to estimate the nonstationarity of the function at any given input point. To address the biased sampling problem, the forgetting factor applied to each mixture component is modulated according to the new information provided in the updating, rather than forgetting depending only on time, thus avoiding undesired distortions of the approximation in less sampled regions.
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23

Andronova, Natalia G., and Michael E. Schlesinger. "Objective estimation of the probability density function for climate sensitivity." Journal of Geophysical Research: Atmospheres 106, no. D19 (October 1, 2001): 22605–11. http://dx.doi.org/10.1029/2000jd000259.

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24

Odongo, L. O., and M. Samanta. "On Estimation of a Functional of a Probability Density Function." Calcutta Statistical Association Bulletin 43, no. 1-2 (March 1993): 13–24. http://dx.doi.org/10.1177/0008068319930102.

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The problem of estimating the integral of the square of a probability density function is considered, It is shown that under some regularity conditions the kernel estimate of this functional is asymptotically normally distributed. An expression for the smoothing parameter that minimizes the mean square error of the estimate is derived. Results of simulation studies are included. AMS (1980) Subject Classification: Primary 62G07 Secondary 60FOS.
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25

Huang, Jianhua Z., Xueying Wang, Ximing Wu, and Lan Zhou. "Estimation of a probability density function using interval aggregated data." Journal of Statistical Computation and Simulation 86, no. 15 (February 18, 2016): 3093–105. http://dx.doi.org/10.1080/00949655.2016.1150481.

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26

Hong, X., S. Chen, and C. J. Harris. "Using zero-norm constraint for sparse probability density function estimation." International Journal of Systems Science 43, no. 11 (November 2012): 2107–13. http://dx.doi.org/10.1080/00207721.2011.564673.

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27

Bolbolian Ghalibaf, Mohammad. "Relationship Between Kendall's tau Correlation and Mutual Information." Revista Colombiana de Estadística 43, no. 1 (January 1, 2020): 3–20. http://dx.doi.org/10.15446/rce.v43n1.78054.

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Mutual information (MI) can be viewed as a measure of multivariate association in a random vector. However, the estimation of MI is difficult since the estimation of the joint probability density function (PDF) of non Gaussian distributed data is a hard problem. Copula function is an appropriate tool for estimating MI since the joint probability density function ofrandom variables can be expressed as the product of the associated copula density function and marginal PDF’s. With a little search, we find that the proposed copulas-based mutual information is much more accurate than conventional methods such as the joint histogram and Parzen window-based MI. In this paper, by using the copulas-based method, we compute MI forsome family of bivariate distribution functions and study the relationship between Kendall’s tau correlation and MI of bivariate distributions. Finally, using a real dataset, we illustrate the efficiency of this approach.
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28

Węglarczyk, Stanisław. "Kernel density estimation and its application." ITM Web of Conferences 23 (2018): 00037. http://dx.doi.org/10.1051/itmconf/20182300037.

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Kernel density estimation is a technique for estimation of probability density function that is a must-have enabling the user to better analyse the studied probability distribution than when using a traditional histogram. Unlike the histogram, the kernel technique produces smooth estimate of the pdf, uses all sample points' locations and more convincingly suggest multimodality. In its two-dimensional applications, kernel estimation is even better as the 2D histogram requires additionally to define the orientation of 2D bins. Two concepts play fundamental role in kernel estimation: kernel function shape and coefficient of smoothness, of which the latter is crucial to the method. Several real-life examples, both for univariate and bivariate applications, are shown.
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29

Hu, Hong Ying, and Chun Ming Kan. "Fully Nonparametric Probability Density Function Estimation Based on Empirical Mode Decomposition." Advanced Materials Research 460 (February 2012): 189–92. http://dx.doi.org/10.4028/www.scientific.net/amr.460.189.

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Empirical Mode Decomposition (EMD) is a non-stationary signal processing method developed recently. It has been applied in many engineering fields. EMD has many similarities with wavelet decomposition. But EMD Decomposition has its own characteristics, especially in accurate rend extracting. Therefore the paper firstly proposes an algorithm of extracting slow-varying trend based on EMD. Then, according to wavelet probability density function estimation method, a new density estimation method based on EMD is presented. The simulations of Gaussian single and mixture model density estimation prove the advantages of the approach with easy computation and more accurate result
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30

Miller, Gad, and David Horn. "Probability Density Estimation Using Entropy Maximization." Neural Computation 10, no. 7 (October 1, 1998): 1925–38. http://dx.doi.org/10.1162/089976698300017205.

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We propose a method for estimating probability density functions and conditional density functions by training on data produced by such distributions. The algorithm employs new stochastic variables that amount to coding of the input, using a principle of entropy maximization. It is shown to be closely related to the maximum likelihood approach. The encoding step of the algorithm provides an estimate of the probability distribution. The decoding step serves as a generative mode, producing an ensemble of data with the desired distribution. The algorithm is readily implemented by neural networks, using stochastic gradient ascent to achieve entropy maximization.
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31

Zhuang, Zhe Min, Fen Lan Li, and Chu Liang Wei. "A Probability Density Estimation for Fault Detection." Advanced Materials Research 562-564 (August 2012): 1113–16. http://dx.doi.org/10.4028/www.scientific.net/amr.562-564.1113.

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In this paper, a time-domain analysis method based on probability density estimation is presented for rotating machine fault detection. Generally, the vibration signals obtained from a rotating machine are time-variant since they are strongly related to the rotational speed that is not constant even in the macro steady state. Since the mostly used signal processing method, the Fourier analysis is only suitable for stationary signals, the development of the joint time-frequency analysis is demanded. Here, the probability density estimation method based on Parzen window is introduced. The probability density function of the vibration signal of the rotating machine is estimated by Parzen window, and a threshold value is predefined to decide the state of the rotating machine. By inspecting the change of the probability density of the vibration signal, the condition of the machine is monitored. Air gap eccentricity and ball cage broken bearing are considered in the experiment section, they are difficult to be detected in frequency domain while the rotating speed is not constant. The validity of the method is proved by the experiment.
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32

Falk, Michael. "On the estimation of the quantile density function." Statistics & Probability Letters 4, no. 2 (March 1986): 69–73. http://dx.doi.org/10.1016/0167-7152(86)90020-9.

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33

Johnston, Lloyd P. M., and Mark A. Kramer. "Probability density estimation using elliptical basis functions." AIChE Journal 40, no. 10 (October 1994): 1639–49. http://dx.doi.org/10.1002/aic.690401006.

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34

Ibragimov, I. A. "On adaptive estimation of probability density functions." Journal of Mathematical Sciences 167, no. 4 (May 25, 2010): 512–21. http://dx.doi.org/10.1007/s10958-010-9938-5.

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35

Zhang, X. F., Y. E. Zhao, Y. M. Zhang, X. Z. Huang, and H. Li. "A points estimation and series approximation method for uncertainty analysis." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 223, no. 9 (April 16, 2009): 1997–2007. http://dx.doi.org/10.1243/09544062jmes1229.

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The objective of this article is to present an algorithm for moment evaluation and probability density function approximation of performance function for structural reliability analysis. In doing so, a point estimation method for probability moment of performance function is discussed at first. Based on the coherent relationship between the orthogonal polynomial and probability density function, formulas for point estimation are derived. Vector operators are defined to alleviate computational burden for computer programming. Then, by utilizing C-type Gram—Charlier series expansion method, a procedure for probability density function approximation of the performance function is studied. At last, the accuracy of the proposed method is demonstrated using three numerical examples.
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36

Sadeh, Iftach. "ANNz2 - Photometric redshift and probability density function estimation using machine-learning." Proceedings of the International Astronomical Union 10, S306 (May 2014): 316–18. http://dx.doi.org/10.1017/s1743921314010849.

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AbstractLarge photometric galaxy surveys allow the study of questions at the forefront of science, such as the nature of dark energy. The success of such surveys depends on the ability to measure the photometric redshifts of objects (photo-zs), based on limited spectral data. A new major version of the public photo-z estimation software, ANNz, is presented here. The new code incorporates several machine-learning methods, such as artificial neural networks and boosted decision/regression trees, which are all used in concert. The objective of the algorithm is to dynamically optimize the performance of the photo-z estimation, and to properly derive the associated uncertainties. In addition to single-value solutions, the new code also generates full probability density functions in two independent ways.
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37

Farmer, Jenny, Zach Merino, Alexander Gray, and Donald Jacobs. "Universal Sample Size Invariant Measures for Uncertainty Quantification in Density Estimation." Entropy 21, no. 11 (November 15, 2019): 1120. http://dx.doi.org/10.3390/e21111120.

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Previously, we developed a high throughput non-parametric maximum entropy method (PLOS ONE, 13(5): e0196937, 2018) that employs a log-likelihood scoring function to characterize uncertainty in trial probability density estimates through a scaled quantile residual (SQR). The SQR for the true probability density has universal sample size invariant properties equivalent to sampled uniform random data (SURD). Alternative scoring functions are considered that include the Anderson-Darling test. Scoring function effectiveness is evaluated using receiver operator characteristics to quantify efficacy in discriminating SURD from decoy-SURD, and by comparing overall performance characteristics during density estimation across a diverse test set of known probability distributions.
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38

Xu, Huaping, Shuo Li, Yanan You, Aifang Liu, and Wei Liu. "Unwrapped Phase Estimation via Normalized Probability Density Function for Multibaseline InSAR." IEEE Access 7 (2019): 4979–88. http://dx.doi.org/10.1109/access.2018.2886702.

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39

Hong, Xia, Sheng Chen, Abdulrohman Qatawneh, Khaled Daqrouq, Muntasir Sheikh, and Ali Morfeq. "Sparse probability density function estimation using the minimum integrated square error." Neurocomputing 115 (September 2013): 122–29. http://dx.doi.org/10.1016/j.neucom.2013.02.003.

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40

Wang, Eric X., Svetlana Avramov-Zamurovic, Richard J. Watkins, Charles Nelson, and Reza Malek-Madani. "Probability density function estimation of laser light scintillation via Bayesian mixtures." Journal of the Optical Society of America A 31, no. 3 (February 14, 2014): 580. http://dx.doi.org/10.1364/josaa.31.000580.

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41

Datta, Debanshee. "Wavelet Analysis Based Estimation of Probability Density Function of Wind Data." International Journal of Energy, Information and Communications 5, no. 3 (June 30, 2014): 23–34. http://dx.doi.org/10.14257/ijeic.2014.5.3.03.

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42

Joshi, N., T. Kadir, and S. M. Brady. "Simplified Computation for Nonparametric Windows Method of Probability Density Function Estimation." IEEE Transactions on Pattern Analysis and Machine Intelligence 33, no. 8 (August 2011): 1673–80. http://dx.doi.org/10.1109/tpami.2011.51.

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43

Veraverbeke, Noël. "Studentized estimation of a certain functional of a probability density function." Scandinavian Actuarial Journal 1985, no. 3-4 (July 1985): 131–47. http://dx.doi.org/10.1080/03461238.1985.10413786.

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44

Bonnéry, Daniel, F. Jay Breidt, and François Coquet. "Kernel estimation for a superpopulation probability density function under informative selection." METRON 75, no. 3 (October 5, 2017): 301–18. http://dx.doi.org/10.1007/s40300-017-0127-x.

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45

Huh, Jib. "Kernel estimation of a probability density function with a discontinuity point." Journal of the Korean Data And Information Science Society 33, no. 1 (January 31, 2022): 1–10. http://dx.doi.org/10.7465/jkdi.2022.33.1.1.

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46

Saboor, Abdus, Hassan S. Bakouch, Fernando A. Moala, and Sheraz Hussain. "Properties and methods of estimation for a bivariate exponentiated Fréchet distribution." Mathematica Slovaca 70, no. 5 (October 27, 2020): 1211–30. http://dx.doi.org/10.1515/ms-2017-0426.

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AbstractIn this paper, a bivariate extension of exponentiated Fréchet distribution is introduced, namely a bivariate exponentiated Fréchet (BvEF) distribution whose marginals are univariate exponentiated Fréchet distribution. Several properties of the proposed distribution are discussed, such as the joint survival function, joint probability density function, marginal probability density function, conditional probability density function, moments, marginal and bivariate moment generating functions. Moreover, the proposed distribution is obtained by the Marshall-Olkin survival copula. Estimation of the parameters is investigated by the maximum likelihood with the observed information matrix. In addition to the maximum likelihood estimation method, we consider the Bayesian inference and least square estimation and compare these three methodologies for the BvEF. A simulation study is carried out to compare the performance of the estimators by the presented estimation methods. The proposed bivariate distribution with other related bivariate distributions are fitted to a real-life paired data set. It is shown that, the BvEF distribution has a superior performance among the compared distributions using several tests of goodness–of–fit.
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47

Helali, Salima, Afif Masmoudi, and Yousri Slaoui. "Semi-Parametric Estimation Using Bernstein Polynomial and a Finite Gaussian Mixture Model." Entropy 24, no. 3 (February 23, 2022): 315. http://dx.doi.org/10.3390/e24030315.

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The central focus of this paper is upon the alleviation of the boundary problem when the probability density function has a bounded support. Mixtures of beta densities have led to different methods of density estimation for data assumed to have compact support. Among these methods, we mention Bernstein polynomials which leads to an improvement of edge properties for the density function estimator. In this paper, we set forward a shrinkage method using the Bernstein polynomial and a finite Gaussian mixture model to construct a semi-parametric density estimator, which improves the approximation at the edges. Some asymptotic properties of the proposed approach are investigated, such as its probability convergence and its asymptotic normality. In order to evaluate the performance of the proposed estimator, a simulation study and some real data sets were carried out.
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48

Zamini, R., V. Fakoor, and M. Sarmad. "On estimation of a density function in multiplicative censoring." Statistical Papers 56, no. 3 (June 5, 2014): 661–76. http://dx.doi.org/10.1007/s00362-014-0602-x.

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49

Lakhdar, Yissam, and El Hassan Sbai. "Online Variable Kernel Estimator." International Journal of Operations Research and Information Systems 8, no. 1 (January 2017): 58–92. http://dx.doi.org/10.4018/ijoris.2017010104.

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In this work, the authors propose a novel method called online variable kernel estimation of the probability density function (pdf). This new online estimator combines the characteristics and properties of two estimators namely nearest neighbors estimator and the Parzen-Rosenblatt estimator. Their approach allows a compact online adaptation of the estimated probability density function from the new arrival data. The performance of the online variable kernel estimator (OVKE) depends on the choice of the bandwidth. The authors present in this article a new technique for determining the optimal smoothing parameter of OVKE based on the maximum entropy principle (MEP). The robustness and performance of the proposed approach are demonstrated by examples of online estimation of real and simulated data distributions.
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50

Chen, Lijuan, Zihao Zhang, Yapeng Zhang, Xiaoshuang Xiong, Fei Fan, and Shuangbao Ma. "Research on Projection Filtering Method Based on Projection Symmetric Interval and Its Application in Underwater Navigation." Symmetry 13, no. 9 (September 16, 2021): 1715. http://dx.doi.org/10.3390/sym13091715.

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For non-linear systems (NLSs), the state estimation problem is an essential and important problem. This paper deals with the nonlinear state estimation problems in nonlinear and non-Gaussian systems. Recently, the Bayesian filter designer based on the Bayesian principle has been widely applied to the state estimation problem in NLSs. However, we assume that the state estimation models are nonlinear and non-Gaussian, applying traditional, typical nonlinear filtering methods, and there is no precise result for the system state estimation problem. Therefore, the larger the estimation error, the lower the estimation accuracy. To perfect the imperfections, a projection filtering method (PFM) based on the Bayesian estimation approach is applied to estimate the state. First, this paper constructs its projection symmetric interval to select the basis function. Second, the prior probability density of NLSs can be projected into the basis function space, and the prior probability density solution can be solved by using the Fokker–Planck Equation (FPE). According to the Bayes formula, the proposed estimator utilizes the basis function in projected space to iteratively calculate the posterior probability density; thus, it avoids calculating the partial differential equation. By taking two illustrative examples, it is also compared with the traditional UKF and PF algorithm, and the numerical experiment results show the feasibility and effectiveness of the novel nonlinear state estimation filter algorithm.
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