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Recursive nonparametric regression estimation for dependent strong mixing functional data

STATISTICAL INFERENCE FOR STOCHASTIC PROCESSES 2020年第3期23卷 665-697页

作者： Slaoui, Yousri Univ Poitiers Lab Math & Appl Futuroscope Chasseneuil Poitiers France

In the present paper, we extend the work of Slaoui (Stat Sin 30:417-437, 2020) in the case of strong mixing data. Since, we are interested in nonparametric regression estimation, we focus on well adapted dependence structures based on mixing type conditions. We study the properties of these regression estimators and compare them with the nonparametric non-recursive regression estimator. The bias, variance and mean squared error are computed explicitly. We showed that using a selected wild bootstrap bandwidth procedure and a special stepsize, our proposed recursive regression estimators allowed us to obtain quite similar results compared to the non-recursive regression estimator under alpha-mixing condition in terms of estimation error and much better in terms of computational costs.

关键词： Asymptotic normality Functional data nonparametric regression estimation Stochastic approximation algorithm alpha-Mixing

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Local linear regression estimator on the boundary correction in nonparametric regression estimation

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Journal of Statistical Theory and Applications 2020年第3期19卷 460-471页

作者： Cheruiyot, Langat Reuben Department of Mathematics and Computer Sciences School of Science and Technology University of Kabianga Kericho Kenya

The precision and accuracy of any estimation can inform one whether to use or not to use the estimated values. It is the crux of the matter to many if not all statisticians. For this to be realized biases of the estimates are normally checked and eliminated or at least minimized. Even with this in mind getting a model that fits the data well can be a challenge. There are many situations where parametric estimation is disadvantageous because of the possible misspecification of the model. Under such circumstance, many researchers normally allow the data to suggest a model for itself in the technique that has become so popular in recent years called the nonparametric regression estimation. In this technique the use of kernel estimators is common. This paper explores the famous Nadaraya-Watson estimator and local linear regression estimator on the boundary bias. A global measure of error criterion-asymptotic mean integrated square error (AMISE) has been computed from simulated data at the empirical stage to assess the performance of the two estimators in regression estimation. This study shows that local linear regression estimator has a sterling performance over the standard Nadaraya-Watson estimator. © 2020 The Authors.

关键词： Bias Kernel estimators Local linear regression nonparametric regression estimation Variance

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Wavelet estimation of a regression model with mixed noises

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RESEARCH IN THE MATHEMATICAL SCIENCES 2024年第4期11卷 1-16页

作者： Kou, Junke Huang, Qinmei Guilin Univ Elect Technol Sch Math & Computat Sci Guilin 541004 Guangxi Peoples R China

Chesneau et al. (Journal of Computational and Applied Mathematics, 2020) study nonparametric wavelet estimations over L-2 risk of a regression model with additive and multiplicative noises. This paper considers convergence rates over L-p(1 <= p < +infinity) risk of linear wavelet estimator and nonlinear wavelet estimator under some mild conditions. It turns out that our results reduce to the theorems of Chesneau et al., when p = 2.

关键词： nonparametric regression estimation Mixed noises L-p risk Wavelets

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Bernstein polynomial of recursive regression estimation with censored data

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STOCHASTIC MODELS 2022年第3期38卷 462-487页

作者： Slaoui, Yousri Univ Poitiers Lab Math & Appl Poitiers France

In this paper, we deal with the problem of the regression estimation near the edges under censoring. For this purpose, we consider a new recursive estimator based on the stochastic approximation algorithm and Bernstein polynomials of the regression function when the response random variable is subject to random right censoring. We give the central limit theorem and the strong pointwise convergence rate for our proposed nonparametric recursive estimators under some mild conditions. Finally, we provide pointwise moderate deviation principles (MDP) for the proposed estimators. We corroborate these theoretical results through simulations as well as the analysis of a real data set.

关键词： Asymptotic convergence Bernstein polynomial censored data nonparametric regression estimation stochastic approximation algorithm

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Fast estimation of Multidimensional regression Functions by the Parzen Kernel-Based Method 29th

Fast Estimation of Multidimensional Regression Functions by ...

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29th International Conference on Neural Information Processing

作者： Galkowski, Tomasz Krzyzak, Adam Czestochowa Tech Univ Inst Computat Intelligence Armii Krajowej 36 Czestochowa Poland Concordia Univ Dept Comp Sci & Software Engn Montreal PQ H3G 1M8 Canada Westpomeranian Univ Technol Dept Elect Engn Sikorskiego 37 PL-70313 Szczecin Poland

ISBN: (纸本)9789819916382;9789819916399

Various methods for estimation of unknown functions from the set of noisy measurements are applicable to a wide variety of problems. Among them the non-parametric algorithms based on the Parzen kernel are commonly used. Our method is basically developed for multidimensional case. The two-dimensional version of the method is thoroughly explained and analysed. The proposed algorithm is an effective and efficient solution significantly improving computational speed. Computational complexity and speed of convergence of the algorithm are also studied. Some applications for solving real problems with our algorithms are presented. Our approach is applicable to multidimensional regression function estimation as well as to estimation of derivatives of functions. It is worth noticing that the presented algorithms have already been used successfully in various image processing applications, achieving significant accelerations of calculations.

关键词： Parzen kernel algorithms nonparametric regression estimation multidimensional functions

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On uniform consistency of nonparametric estimators smoothed by the gamma kernel

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ANNALS OF THE INSTITUTE OF STATISTICAL MATHEMATICS 2025年第3期77卷 459-489页

作者： Funke, Benedikt Hirukawa, Masayuki TH Koln Univ Appl Sci Inst Insurance Studies Gustav Heinemann Ufer 54 D-50968 Cologne Germany Ryukoku Univ Fac Econ 67 Tsukamoto-choFukakusaFushimi Ku Kyoto 6128577 Japan

This paper documents a set of uniform consistency results with rates for nonparametric density and regression estimators smoothed by the gamma kernel having support on the nonnegative real line. It is known that this kernel can well calibrate the shapes of 'cost' distributions that are characterized by a sharp peak in the vicinity of the origin and a long right tail. In this paper, weak and strong uniform consistency and corresponding convergence rates of gamma kernel estimators are explored in a multivariate framework. Our analysis is built on compact sets expanding to the nonnegative orthant and general sequences of smoothing parameters. The results are useful for asymptotic analysis of two-step semiparametric estimation using a first-step kernel estimate as a plug-in.

关键词： Boundary bias Density derivative estimation Density estimation Gamma kernel nonparametric regression estimation Uniform convergence

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Estimating a Function and Its Derivatives Under a Smoothness Condition

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MATHEMATICS OF OPERATIONS RESEARCH 2025年第2期50卷 783-1583, C2页

作者： Lim, Eunji Adelphi Univ Decis Sci & Mkt Garden City NY 11530 USA

We consider the problem of estimating an unknown function f & lowast;: Rd d -> R and its partial derivatives from a noisy data set of n observations, where we make no assumptions about f & lowast;except that it is smooth in the sense that it has square integrable partial derivatives of order m . A natural candidate for the estimator of f & lowast;in such a case is the best fit to the data set that satisfies a certain smoothness condition. This estimator can be seen as a least squares estimator subject to an upper bound on some measure of smoothness. Another useful estimator is the one that minimizes the degree of smoothness subject to an upper bound on the average of squared errors. We prove that these two estimators are computable as solutions to quadratic programs, establish the consistency of these estimators and their partial derivatives, and study the convergence rate as n -> infinity . The effectiveness of the estimators is illustrated numerically in a setting where the value of a stock option and its second derivative are estimated as functions of the underlying stock price.

关键词： nonparametric regression estimation derivative estimation spline regression smoothing splines penalized least squares thin plate splines penalized smoothing splines

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Two-time-scale nonparametric recursive regression estimator for independent functional data

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COMMUNICATIONS IN STATISTICS-THEORY AND METHODS 2023年第15期52卷 5213-5245页

作者： Slaoui, Yousri Univ Poitiers Lab Math & Applicat Site Futuroscope F-86961 Poitiers France

In this paper, we propose and investigate a new kernel regression estimators based on the two-time-scale stochastic approximation algorithm in the case of independent functional data. We study the properties of the proposed recursive estimators and compare them with the recursive estimators based on single-time-scale stochastic algorithm proposed by Slaoui and to the non-recursive estimator proposed by Slaoui. It turns out that, with an adequate choice of the parameters, the proposed two-time-scale estimators perform better than the recursive estimators constructed using single-time-scale stochastic algorithm. We corroborate these theoretical results through some simulations and two real datasets.

关键词： Functional data nonparametric regression estimation stochastic approximation algorithm smoothing curve fitting two-time-Scale approximation algorithm

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On the rate of convergence of a deep recurrent neural network estimate in a regression problem with dependent data

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BERNOULLI 2023年第2期29卷 1663-1685页

作者： Kohler, Michael Krzyzak, Adam Tech Univ Darmstadt Fachbereich Math Schlossgartenstr 7 D-64289 Darmstadt Germany Concordia Univ Dept Comp Sci & Software Engn 1455 De Maisonneuve Blvd West Montreal PQ H3G 1M8 Canada

A regression problem with dependent data is considered. Regularity assumptions on the dependency of the data are introduced, and it is shown that under suitable structural assumptions on the regression function a deep... 详细信息

关键词： Curse of dimensionality recurrent neural networks nonparametric regression estimation rate of convergence

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Using Conditional Inference Trees to (Re)Explore Nonprofit Board Composition

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NONPROFIT AND VOLUNTARY SECTOR QUARTERLY 2023年第2期52卷 529-543页

作者： Simonoff, Jeffrey S. Abzug, Rikki NYU Leonard N Stern Sch Business Dept Technol Operat & Stat Stat New York NY USA Ramapo Coll Anisfield Sch Business Management 505 Ramapo Valley Rd Mahwah NJ 07430 USA

This Research Note introduces nonprofit scholars to the contemporary analytical tool of conditional inference trees as a means to shed more light on the institutional forces behind the changing composition of nonprofit boards of trustees. Revisiting the data of the Six-Cities Cultures of Trusteeship Project, this note illustrates the illuminating power of conditional inference trees for analyzing data (particularly categorical data), not well served by significance testing. Applying these popular models adds depth, nuance, and increased clarity to some of the original findings from the Six-Cities research project. This empirical case serves as a how-to for future researchers hoping to more flexibly model the relative impact of institutional (and other) variables on nonprofit organization structures, as well as expand their methodological toolkit when dealing with all sorts of regression problems.

关键词： conditional inference trees trusteeship methods interaction effects nonparametric regression estimation

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