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Journal articles on the topic 'Boundary estimation'

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Author: Grafiati
Published: 4 June 2021
Last updated: 29 January 2023

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1

Carlstein, E., and C. Krishnamoorthy. "Boundary Estimation." Journal of the American Statistical Association 87, no. 418 (June 1992): 430–38. http://dx.doi.org/10.1080/01621459.1992.10475223.

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2

Cuevas, Antonio, and Alberto Rodríguez-Casal. "On boundary estimation." Advances in Applied Probability 36, no. 2 (June 2004): 340–54. http://dx.doi.org/10.1239/aap/1086957575.

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We consider the problem of estimating the boundary of a compact set S ⊂ ℝd from a random sample of points taken from S. We use the Devroye-Wise estimator which is a union of balls centred at the sample points with a common radius (the smoothing parameter in this problem). A universal consistency result, with respect to the Hausdorff metric, is proved and convergence rates are also obtained under broad intuitive conditions of a geometrical character. In particular, a shape condition on S, which we call expandability, plays an important role in our results. The simple structure of the considered estimator presents some practical advantages (for example, the computational identification of the boundary is very easy) and makes this problem quite close to some basic issues in stochastic geometry.
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3

Cuevas, Antonio, and Alberto Rodríguez-Casal. "On boundary estimation." Advances in Applied Probability 36, no. 02 (June 2004): 340–54. http://dx.doi.org/10.1017/s0001867800013501.

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We consider the problem of estimating the boundary of a compact set S ⊂ ℝ d from a random sample of points taken from S. We use the Devroye-Wise estimator which is a union of balls centred at the sample points with a common radius (the smoothing parameter in this problem). A universal consistency result, with respect to the Hausdorff metric, is proved and convergence rates are also obtained under broad intuitive conditions of a geometrical character. In particular, a shape condition on S, which we call expandability, plays an important role in our results. The simple structure of the considered estimator presents some practical advantages (for example, the computational identification of the boundary is very easy) and makes this problem quite close to some basic issues in stochastic geometry.
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4

Zhang, Shunpu, Zhong Li, and Zhiying Zhang. "Estimating a Distribution Function at the Boundary." Austrian Journal of Statistics 49, no. 1 (February 20, 2020): 1–23. http://dx.doi.org/10.17713/ajs.v49i1.801.

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Estimation of distribution functions has many real-world applications. We study kernel estimation of a distribution function when the density function has compact support. We show that, for densities taking value zero at the endpoints of the support, the kernel distribution estimator does not need boundary correction. Otherwise, boundary correction is necessary. In this paper, we propose a boundary distribution kernel estimator which is free of boundary problem and provides non-negative and non-decreasing distribution estimates between zero and one. Extensive simulation results show that boundary distribution kernel estimator provides better distribution estimates than the existing boundary correction methods. For practical application of the proposed methods, a data-dependent method for choosing the bandwidth is also proposed.
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5

Bii, Nelson Kiprono, Christopher Ouma Onyango, and John Odhiambo. "Boundary Bias Correction Using Weighting Method in Presence of Nonresponse in Two-Stage Cluster Sampling." Journal of Probability and Statistics 2019 (June 2, 2019): 1–8. http://dx.doi.org/10.1155/2019/6812795.

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Kernel density estimators due to boundary effects are often not consistent when estimating a density near a finite endpoint of the support of the density to be estimated. To address this, researchers have proposed the application of an optimal bandwidth to balance the bias-variance trade-off in estimation of a finite population mean. This, however, does not eliminate the boundary bias. In this paper weighting method of compensating for nonresponse is proposed. Asymptotic properties of the proposed estimator of the population mean are derived. Under mild assumptions, the estimator is shown to be asymptotically consistent.
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6

Moon, Kevin, Kumar Sricharan, Kristjan Greenewald, and Alfred Hero. "Ensemble Estimation of Information Divergence †." Entropy 20, no. 8 (July 27, 2018): 560. http://dx.doi.org/10.3390/e20080560.

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Recent work has focused on the problem of nonparametric estimation of information divergence functionals between two continuous random variables. Many existing approaches require either restrictive assumptions about the density support set or difficult calculations at the support set boundary which must be known a priori. The mean squared error (MSE) convergence rate of a leave-one-out kernel density plug-in divergence functional estimator for general bounded density support sets is derived where knowledge of the support boundary, and therefore, the boundary correction is not required. The theory of optimally weighted ensemble estimation is generalized to derive a divergence estimator that achieves the parametric rate when the densities are sufficiently smooth. Guidelines for the tuning parameter selection and the asymptotic distribution of this estimator are provided. Based on the theory, an empirical estimator of Rényi-α divergence is proposed that greatly outperforms the standard kernel density plug-in estimator in terms of mean squared error, especially in high dimensions. The estimator is shown to be robust to the choice of tuning parameters. We show extensive simulation results that verify the theoretical results of our paper. Finally, we apply the proposed estimator to estimate the bounds on the Bayes error rate of a cell classification problem.
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7

Chaji, K., M. El Bagdouri, and R. Channa. "A 2D domain boundary estimation." Journal of Physics: Conference Series 135 (November 1, 2008): 012029. http://dx.doi.org/10.1088/1742-6596/135/1/012029.

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8

Ben-Haim, Yakov, and H. G. Natke. "Sequential Adaptation in Estimating Elastic Boundary-Condition Influence Matrices." Journal of Dynamic Systems, Measurement, and Control 115, no. 3 (September 1, 1993): 370–78. http://dx.doi.org/10.1115/1.2899112.

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A method is discussed for adaptive estimation of the boundary-condition influence matrix of a linear elastic system, based on modal measurements (eigenvalues and eigenvectors) and on knowledge of the influence matrix of the system with respect to reference boundary conditions. The estimation is terminated adaptively by an algorithm motivated by the concept of sequential analysis. The boundary-condition influence matrix is re-estimated with measurement of each additional mode, until a termination criterion indicates that adequate accuracy has been attained. The advantage of adaptive termination of the estimation is the enhanced computational (and possibly instrumental) efficiency of estimating with minimal modal data. An analytical technique for comparing the adaptive termination with a reasonable non-adaptive method has been developed and demonstrated by application to a uniform beam. When uncertainty in the boundary conditions is represented by convex models, it is shown that the adaptive estimation can terminate much earlier than the non-adaptive procedure.
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9

Bin, Michelangelo, and Florent Di Meglio. "Boundary Estimation of Boundary Parameters for Linear Hyperbolic PDEs." IEEE Transactions on Automatic Control 62, no. 8 (August 2017): 3890–904. http://dx.doi.org/10.1109/tac.2016.2643442.

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10

Bouredji, H., and A. Sayah. "BIAS CORRECTION AT END POINTS IN KERNEL DENSITY ESTIMATION." Advances in Mathematics: Scientific Journal 10, no. 12 (December 1, 2021): 3515–31. http://dx.doi.org/10.37418/amsj.10.12.1.

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In this paper, we propose a new approach of boundary correction for kernel density estimation with the support $[0,1]$, in particular at the right endpoints and we derive the theoretical properties of this new estimator and show that it asymptotically reduce the order of bias at the boundary region, whereas the order of variance remains unchanged. Our Monte Carlo simulations demonstrate the good finite sample performance of our proposed estimator. Two examples with real data are provided.
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11

Kunisch, Karl, and Xiaosu Pan. "Estimation of Interfaces from Boundary Measurements." SIAM Journal on Control and Optimization 32, no. 6 (November 1994): 1643–74. http://dx.doi.org/10.1137/s0363012992226338.

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12

Jou, Jang, and Jinn-Liang Liu. "A posteriori boundary element error estimation." Journal of Computational and Applied Mathematics 106, no. 1 (June 1999): 1–19. http://dx.doi.org/10.1016/s0377-0427(99)00049-7.

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13

Rencis, Joseph J., and Kwo‐Yih Jong. "Error Estimation for Boundary Element Analysis." Journal of Engineering Mechanics 115, no. 9 (September 1989): 1993–2010. http://dx.doi.org/10.1061/(asce)0733-9399(1989)115:9(1993).

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14

Berry, Tyrus, and Timothy Sauer. "Density estimation on manifolds with boundary." Computational Statistics & Data Analysis 107 (March 2017): 1–17. http://dx.doi.org/10.1016/j.csda.2016.09.011.

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15

Murphy, K. A. "Parameter estimation in moving boundary problems." Applied Mathematics Letters 1, no. 3 (1988): 303–6. http://dx.doi.org/10.1016/0893-9659(88)90098-5.

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16

Ityokumbul, M. T., N. Kosaric, and W. Bulani. "Parameter estimation with simplified boundary conditions." Chemical Engineering Science 43, no. 9 (1988): 2457–62. http://dx.doi.org/10.1016/0009-2509(88)85180-7.

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17

Bagchi, Arunabha. "Boundary value processes: Estimation and identification." Computers & Mathematics with Applications 19, no. 1 (1990): 9–19. http://dx.doi.org/10.1016/0898-1221(90)90077-w.

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18

Catchpole, E. A., and B. J. T. Morgan. "Boundary Estimation in Ring Recovery Models." Journal of the Royal Statistical Society: Series B (Methodological) 56, no. 2 (July 1994): 385–91. http://dx.doi.org/10.1111/j.2517-6161.1994.tb01987.x.

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19

Liang, M. T., J. T. Chen, and S. S. Yang. "Error estimation for boundary element method." Engineering Analysis with Boundary Elements 23, no. 3 (March 1999): 257–65. http://dx.doi.org/10.1016/s0955-7997(98)00086-1.

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20

Nikoukhah, Ramine, Milton B. Adams, Alan S. Willsky, and Bernard C. Levy. "Estimation for boundary-value descriptor systems." Circuits, Systems, and Signal Processing 8, no. 1 (March 1989): 25–48. http://dx.doi.org/10.1007/bf01598744.

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21

Vazquez, Rafael, Eugenio Schuster, and Miroslav Krstic. "Magnetohydrodynamic state estimation with boundary sensors." Automatica 44, no. 10 (October 2008): 2517–27. http://dx.doi.org/10.1016/j.automatica.2008.02.022.

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22

Yang, Xin, Qingling Chang, Shiting Xu, Xinlin Liu, and Yan Cui. "Monocular Depth Estimation with Sharp Boundary." Computer Modeling in Engineering & Sciences 136, no. 1 (2023): 573–92. http://dx.doi.org/10.32604/cmes.2023.023424.

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23

TANAKA, Ken-ichi, Jun UENO, and Masafumi ADACHI. "ICONE23-1070 THE IMPROVEMENT OF NON-RADIOACTIVE WASTE (NR) BOUNDARY ESTIMATION PROCEDURE." Proceedings of the International Conference on Nuclear Engineering (ICONE) 2015.23 (2015): _ICONE23–1—_ICONE23–1. http://dx.doi.org/10.1299/jsmeicone.2015.23._icone23-1_38.

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24

Pateiro-López, Beatriz, and Alberto Rodríguez-Casal. "Length and surface area estimation under smoothness restrictions." Advances in Applied Probability 40, no. 2 (June 2008): 348–58. http://dx.doi.org/10.1239/aap/1214950207.

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The problem of estimating the Minkowski content L0(G) of a body G ⊂ ℝd is considered. For d = 2, the Minkowski content represents the boundary length of G. It is assumed that a ball of radius r can roll inside and outside the boundary of G. We use this shape restriction to propose a new estimator for L0(G). This estimator is based on the information provided by a random sample, taken on a square containing G, in which we know whether a sample point is in G or not. We obtain the almost sure convergence rate for the proposed estimator.
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25

Baszczyńska, Aleksandra Katarzyna. "Redukcja efektu brzegowego w estymacji jądrowej wybranych charakterystyk funkcyjnych zmiennej losowej." Central European Review of Economics and Management 16, no. 3 (October 15, 2016): 111. http://dx.doi.org/10.29015/cerem.216.

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For a random variable with bounded support, the kernel estimation of functional characteristics may lead to the occurrence of the so-called boundary effect. In the case of the kernel density estimation it can mean an increase of the estimator bias in the areas near the ends of the support, and can lead to a situation where the estimator is not a density function in the support of a random variable. In the paper the procedures for reducing boundary effect for kernel estimators of density function, distribution function and regression function are analyzed. Modifications of the classical kernel estimators and examples of applications of these procedures in the analysis of the functional characteristics relating to gross national product per capita are presented. The advantages of procedures are indicated taking into account the reduction of the bias in the boundary region of the support of the random variable considered.
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26

Ha, David, Shigeru Katagiri, Hideyuki Watanabe, and Miho Ohsaki. "An Improved Boundary Uncertainty-Based Estimation for Classifier Evaluation." Journal of Signal Processing Systems 93, no. 9 (June 10, 2021): 1057–84. http://dx.doi.org/10.1007/s11265-021-01671-1.

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AbstractThis paper proposes a new boundary uncertainty-based estimation method that has significantly higher accuracy, scalability, and applicability than our previously proposed boundary uncertainty estimation method. In our previous work, we introduced a new classifier evaluation metric that we termed “boundary uncertainty.” The name “boundary uncertainty” comes from evaluating the classifier based solely on measuring the equality between class posterior probabilities along the classifier boundary; satisfaction of such equality can be described as “uncertainty” along the classifier boundary. We also introduced a method to estimate this new evaluation metric. By focusing solely on the classifier boundary to evaluate its uncertainty, boundary uncertainty defines an easier estimation target that can be accurately estimated based directly on a finite training set without using a validation set. Regardless of the dataset, boundary uncertainty is defined between 0 and 1, where 1 indicates whether probability estimation for the Bayes error is achieved. We call our previous boundary uncertainty estimation method “Proposal 1” in order to contrast it with the new method introduced in this paper, which we call “Proposal 2.” Using Proposal 1, we performed successful classifier evaluation on real-world data and supported it with theoretical analysis. However, Proposal 1 suffered from accuracy, scalability, and applicability limitations owing to the difficulty of finding the location of a classifier boundary in a multidimensional sample space. The novelty of Proposal 2 is that it locally reformalizes boundary uncertainty in a single dimension that focuses on the classifier boundary. This convenient reduction with a focus toward the classifier boundary provides the new method’s significant improvements. In classifier evaluation experiments on Support Vector Machines (SVM) and MultiLayer Perceptron (MLP), we demonstrate that Proposal 2 offers a competitive classifier evaluation accuracy compared to a benchmark Cross Validation (CV) method as well as much higher scalability than both CV and Proposal 1.
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27

Pateiro-López, Beatriz, and Alberto Rodríguez-Casal. "Length and surface area estimation under smoothness restrictions." Advances in Applied Probability 40, no. 02 (June 2008): 348–58. http://dx.doi.org/10.1017/s000186780000255x.

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The problem of estimating the Minkowski content L 0(G) of a body G ⊂ ℝ d is considered. For d = 2, the Minkowski content represents the boundary length of G. It is assumed that a ball of radius r can roll inside and outside the boundary of G. We use this shape restriction to propose a new estimator for L 0(G). This estimator is based on the information provided by a random sample, taken on a square containing G, in which we know whether a sample point is in G or not. We obtain the almost sure convergence rate for the proposed estimator.
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28

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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29

Allman, Elizabeth, Hector Banos Cervantes, Serkan Hosten, Kaie Kubjas, Daniel Lemke, John Rhodes, and Piotr Zwiernik. "Maximum likelihood estimation of the Latent Class Model through model boundary decomposition." Journal of Algebraic Statistics 10, no. 1 (April 10, 2019): 51–84. http://dx.doi.org/10.18409/jas.v10i1.75.

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The Expectation-Maximization (EM) algorithm is routinely used for the maximum likelihood estimation in the latent class analysis. However, the EM algorithm comes with no guarantees of reaching the global optimum. We study the geometry of the latent class model in order to understand the behavior of the maximum likelihood estimator. In particular, we characterize the boundary stratification of the binary latent class model with a binary hidden variable. For small models, such as for three binary observed variables, we show that this stratification allows exact computation of the maximum likelihood estimator. In this case we use simulations to study the maximum likelihood estimation attraction basins of the various strata. Our theoretical study is complemented with a careful analysis of the EM fixed point ideal which provides an alternative method of studying the boundary stratification and maximizing the likelihood function. In particular, we compute the minimal primes of this ideal in the case of a binary latent class model with a binary or ternary hidden random variable.
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30

Kawanabe, Motoaki, and Shun-ichi Amari. "Estimation of Network Parameters in Semiparametric Stochastic Perceptron." Neural Computation 6, no. 6 (November 1994): 1244–61. http://dx.doi.org/10.1162/neco.1994.6.6.1244.

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It was reported (Kabashima and Shinomoto 1992) that estimators of a binary decision boundary show asymptotically strange behaviors when the probability model is ill-posed or semiparametric. We give a rigorous analysis of this phenomenon in a stochastic perceptron by using the estimating function method. A stochastic perceptron consists of a neuron that is excited depending on the weighted sum of inputs but its probability distribution form is unknown here. It is shown that there exists no √n-consistent estimator of the threshold value h, that is, no estimator h that converges to h in the order of 1/ √n as the number n of observations increases. Therefore, the accuracy of estimation is much worse in this semiparametric case with an unspecified probability function than in the ordinary case. On the other hand, it is shown that there is a √n-consistent estimator ŵ of the synaptic weight vector. These results elucidate strange behaviors of learning curves in a semiparametric statistical model.
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31

Ramachandrappa, Suraj. "Image Denoising and Estimation of its Boundary." International Journal of Innovative Research in Science, Engineering and Technology 4, no. 9 (September 15, 2015): 8819–23. http://dx.doi.org/10.15680/ijirset.2015.0409003.

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32

Djojosugito, Rianto A., and Paul L. Speckman. "Boundary bias correction in nonparametric density estimation." Communications in Statistics - Theory and Methods 21, no. 1 (January 1992): 69–88. http://dx.doi.org/10.1080/03610929208830765.

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33

Kartiko, Suryo Guritno, Dedi Rosadi, and Abdurakhman. "Simulation study for boundary effect density estimation." Applied Mathematical Sciences 7 (2013): 7053–63. http://dx.doi.org/10.12988/ams.2013.311625.

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34

Colbrook, Matthew J., Zdravko I. Botev, Karsten Kuritz, and Shev MacNamara. "Kernel density estimation with linked boundary conditions." Studies in Applied Mathematics 145, no. 3 (June 18, 2020): 357–96. http://dx.doi.org/10.1111/sapm.12322.

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35

Zhang, Shunpu, and Rohana J. Karunamuni. "On nonparametric density estimation at the boundary*." Journal of Nonparametric Statistics 12, no. 2 (January 2000): 197–221. http://dx.doi.org/10.1080/10485250008832805.

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36

Neilsen, Jens Perch. "Multivariate Boundary Kernels from Local Linear Estimation." Scandinavian Actuarial Journal 1999, no. 1 (January 1999): 93–95. http://dx.doi.org/10.1080/03461230050131902.

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37

Karunamuni, R. J., and T. Alberts. "On boundary correction in kernel density estimation." Statistical Methodology 2, no. 3 (September 2005): 191–212. http://dx.doi.org/10.1016/j.stamet.2005.04.001.

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38

Hermansen, Michael Blom, and Jon Juel Thomsen. "Vibration-based estimation of beam boundary parameters." Journal of Sound and Vibration 429 (September 2018): 287–304. http://dx.doi.org/10.1016/j.jsv.2018.05.016.

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39

Aaron, C., and O. Bodart. "Local convex hull support and boundary estimation." Journal of Multivariate Analysis 147 (May 2016): 82–101. http://dx.doi.org/10.1016/j.jmva.2016.01.003.

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40

Gao, Wayne Yuan. "Minimax linear estimation at a boundary point." Journal of Multivariate Analysis 165 (May 2018): 262–69. http://dx.doi.org/10.1016/j.jmva.2018.01.001.

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41

Hazelton, Martin L., and Jonathan C. Marshall. "Linear boundary kernels for bivariate density estimation." Statistics & Probability Letters 79, no. 8 (April 2009): 999–1003. http://dx.doi.org/10.1016/j.spl.2008.12.003.

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42

Retamoso, Mário R., Marco Túlio Vilhena, Haroldo F. de Campos Velho, and Fernando M. Ramos. "Estimation of boundary condition in hydrologic optics." Applied Numerical Mathematics 40, no. 1-2 (January 2002): 87–100. http://dx.doi.org/10.1016/s0168-9274(01)00059-9.

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43

Yang, Ching-yu. "Boundary estimation of hyperbolic bio-heat conduction." International Journal of Heat and Mass Transfer 54, no. 11-12 (May 2011): 2506–13. http://dx.doi.org/10.1016/j.ijheatmasstransfer.2011.02.011.

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44

Malec, Peter, and Melanie Schienle. "Nonparametric kernel density estimation near the boundary." Computational Statistics & Data Analysis 72 (April 2014): 57–76. http://dx.doi.org/10.1016/j.csda.2013.10.023.

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45

Banks, H. T., F. Kojima, and W. P. Winfree. "Boundary estimation problems arising in thermal tomography." Inverse Problems 6, no. 6 (December 1, 1990): 897–921. http://dx.doi.org/10.1088/0266-5611/6/6/003.

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46

Zhao, Zhiye, and Xin Wang. "Error estimation and h adaptive boundary elements." Engineering Analysis with Boundary Elements 23, no. 10 (December 1999): 793–803. http://dx.doi.org/10.1016/s0955-7997(99)00047-8.

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47

Delaigle, A., and I. Gijbels. "Data-driven boundary estimation in deconvolution problems." Computational Statistics & Data Analysis 50, no. 8 (April 2006): 1965–94. http://dx.doi.org/10.1016/j.csda.2005.02.012.

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48

Daouia, Abdelaati, Stéphane Girard, and Armelle Guillou. "A -moment approach to monotonic boundary estimation." Journal of Econometrics 178, no. 2 (February 2014): 727–40. http://dx.doi.org/10.1016/j.jeconom.2013.10.013.

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49

Zhu, J., and L. Huang. "Estimation of boundary parameters of plate structures." Journal of Sound and Vibration 179, no. 3 (January 1995): 455–61. http://dx.doi.org/10.1006/jsvi.1995.0029.

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50

Jones, M. C. "Simple boundary correction for kernel density estimation." Statistics and Computing 3, no. 3 (September 1993): 135–46. http://dx.doi.org/10.1007/bf00147776.

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