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nonparametric regression estimation using multivariable truncated splines for binary response data

METHODSX 2025年 14卷 103084页

作者： Suriaslan, Afiqah Saffa Budiantara, I. Nyoman Ratnasari, Vita Inst Teknol Sepuluh Nopember Fac Sci & Data Analyt Dept Stat Kampus ITS Sukolilo Surabaya 60111 Indonesia

In recent years, Truncated Spline estimators in nonparametric regression for quantitative data have gained significant attention. However, in practical applications, it is common to encounter situations where the response variable is qualitative (binary). As a result, Truncated Spline non- parametric regression models designed for quantitative data cannot be directly applied to binary response cases. Therefore, a method is needed that able to handle the relationship between variables whose patterns change at certain sub-intervals, where the response is binary. This article aims to develop a multivariable Truncated Spline nonparametric regression estimator specifically for binary response data. The proposed method is applied to analyze unmet need achievement status in East Java Province, Indonesia, and the percentage of the poor population in Indonesia. The findings indicate that the Truncated Spline nonparametric regression method provides more accurate estimates compared to binary logistic regression. Some of the highlights of the proposed method are: center dot This research develops a nonparametric truncated spline regression model tailored for binary response data analysis. center dot Using the Akaike Information Criterion (AIC) to select optimal knot points. center dot Evaluating the performance of the proposed model in comparing performance of nonparametric Truncated Spline model for binary response and binary logistic regression with the data real application.

关键词： Binary response data Truncated spline nonparametric regression

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Right-censored nonparametric regression with measurement error

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METRIKA 2025年第2期88卷 183-214页

作者： Aydin, Dursun Yilmaz, Ersin Chamidah, Nur Lestari, Budi Budiantara, I. Nyoman Mugla Sitki Kocman Univ Fac Sci Dept Stat Mugla Turkiye Airlangga Univ Dept Math Surabaya Indonesia Univ Jember Dept Math Jember Indonesia Sepuluh Nopember Inst Technol Dept Stat Surabaya Indonesia

This study focuses on estimating a nonparametric regression model with right-censored data when the covariate is subject to measurement error. To achieve this goal, it is necessary to solve the problems of censorship and measurement error ignored by many researchers. Note that the presence of measurement errors causes biased and inconsistent parameter estimates. Moreover, non-parametric regression techniques cannot be applied directly to right-censored observations. In this context, we consider an updated response variable using the Buckley-James method (BJM), which is essentially based on the Kaplan-Meier estimator, to solve the censorship problem. Then the measurement error problem is handled using the kernel deconvolution method, which is a specialized tool to solve this problem. Accordingly, three denconvoluted estimators based on BJM are introduced using kernel smoothing, local polynomial smoothing, and B-spline techniques that incorporate both the updated response variable and kernel *** performances of these estimators are compared in a detailed simulation study. In addition, a real-world data example is presented using the Covid-19 dataset.

关键词： Deconvolution Measurement error Right-censored data nonparametric regression Smoothing Buckley-James estimator

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Distributed penalizing function criterion for local polynomial estimation in nonparametric regression with massive data

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STATISTICAL PAPERS 2025年第3期66卷 1-26页

作者： Sun, Tianqi Li, Weiyu Lin, Lu Shandong Univ Zhongtai Secur Inst Financial Studies 27 Shanda Nanlu Jinan 250100 Shandong Peoples R China Shandong Univ Shandong Natl Ctr Appl Math 126 Shanda lu Jinan 250100 Shandong Peoples R China

The selection of bandwidth is one of the most important issues in local polynomial estimation. However, the related researches about data-driven bandwidth selection methodology in combination with divide-and-conquer (DC) strategy have still been rare in the existing literature, which is not feasible to support the application of local polynomial estimation for massive data sets. In this paper, as a development of traditional penalizing function criterion, we propose a distributed penalizing function (DPF) to achieve the selection of optimal bandwidth. The proposed DPF is computationally efficient for massive data sets and is shown to be "globally optimal" in the sense that the minimization of the DPF is asymptotically equivalent to the minimization of the true empirical loss of the averaged function estimator, i.e., the DC estimator. Besides, a novel algorithm is proposed to resolve the selection of bandwidth parameter with imbalance DC strategy. The performance of this DPF is presented in the simulation studies and the real data analysis.

关键词： nonparametric regression Local polynomial estimator Bandwidth selection Massive data Divide-and-conquer

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A difference-based method for testing no effect in nonparametric regression

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COMPUTATIONAL STATISTICS 2025年第1期40卷 153-176页

作者： Li, Zhijian Tong, Tiejun Wang, Yuedong BNU HKBU United Int Coll Guangdong Prov Key Lab Interdisciplinary Res & App Zhuhai Peoples R China Hong Kong Baptist Univ Dept Math Hong Kong Peoples R China Univ Calif Santa Barbara Dept Stat & Appl Probabil Santa Barbara CA USA

The paper proposes a novel difference-based method for testing the hypothesis of no relationship between the dependent and independent variables. We construct three test statistics for nonparametric regression with Gaussian and non-Gaussian random errors. These test statistics have the standard normal as the asymptotic null distribution. Furthermore, we show that these tests can detect local alternatives that converge to the null hypothesis at a rate close to n-1/2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n<^>{-1/2}$$\end{document} previously achieved only by the residual-based tests. We also propose a permutation test as a flexible alternative. Our difference-based method does not require estimating the mean function or its first derivative, making it easy to implement and computationally efficient. Simulation results demonstrate that our new tests are more powerful than existing methods, especially when the sample size is small. The usefulness of the proposed tests is also illustrated using two real data examples.

关键词： Difference-based test Asymptotic normality Locally most powerful test nonparametric regression Permutation Residual-based test

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A data-driven approach for estimating functions in a multivariate nonparametric regression model based on B-splines with an application to geoscience

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APPLIED MATHEMATICAL MODELLING 2025年 138卷

作者： Savino, Mary Edith Levy-Leduc, Celine Univ Paris Saclay French Natl Radioact Waste Management Agcy Andra Paris Saclay France Univ Paris Saclay AgroParisTech INRAE UMR MIA Paris Saclay France Univ Paris Cite F-75013 Paris France Sorbonne Univ CNRS Lab Probabil Stat & Modelisat F-75013 Paris France

In this paper, we will outline a novel data-driven method for estimating functions in a multivariate nonparametric regression model based on an adaptive knot selection for B-splines. The underlying idea of our approach for selecting knots is to apply the generalized lasso, since the knots of the B-spline basis can be seen as locations of the changes in the derivatives of the function to be estimated. This method was then extended to functions depending on several variables by processing each dimension independently, thus reducing the problem to a univariate setting. The regularization parameters were chosen by means of a criterion based on the Extended Bayesian Information Criterion. The nonparametric estimator was obtained using a multivariate B-spline regression with the corresponding selected knots. Our procedure was validated through numerical experiments by varying the number of observations, the level of noise and the observation sampling to investigate its behavior under such conditions. Our method was applied to two distinct classical geochemical cases. For each different example considered in this paper, our approach performed better than state-of-the-art methods. Our completely data-driven method is implemented in the glober R package which is available on the Comprehensive R Archive Network.

关键词： nonparametric regression B-splines Generalized lasso Geochemical applications Radioactive waste management

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Statistical inferences and applications of nonparametric regression models based on fourier series

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METHODSX 2025年 14卷

作者： Suliyanto Saifudin, Toha Rifada, Marisa Amelia, Dita Univ Airlangga Dept Math Surabaya Indonesia

This study develops statistical inference methods, including estimation and hypothesis testing procedures, which consist of partial and simultaneous tests for nonparametric regression models based on Fourier series approximations. The Fourier series is effective for data with periodic characteristics, offering flexible nonparametric regression solutions. While previous work primarily focused on estimation techniques, this research introduces a structured hypothesis testing framework using F-test and T-test statistics to evaluate the significance of model parameters. Utilizing real-world expenditure data from 29 districts in Papua, Indonesia, we examine the Gross Regional Domestic Product per capita, poverty rates, and labor force participation rates as predictors of per capita expenditure. The best oscillation parameter is determined through Generalized Cross Validation (GCV), improving the accuracy of the model. The findings demonstrate significant effects of the predictor variables on the model, supported by both simultaneous tests using the F-test and partial tests using T-tests. The highlights of this research are: center dot Introduces hypothesis testing using F-test and T-test for nonparametric regression with Fourier series. center dot Applies model to regional expenditure data with optimal parameter selection. center dot Validates model using real data, showing significant predictor influence.

关键词： Fourier series Hypothesis testing nonparametric regression Partial Simultaneous

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nonparametric regression ESTIMATION BASED ON SPATIALLY INHOMOGENEOUS DATA: MINIMAX GLOBAL CONVERGENCE RATES AND ADAPTIVITY

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ESAIM-PROBABILITY AND STATISTICS 2014年第1期18卷 1-41页

作者： Antoniadis, Anestis Pensky, Marianna Sapatinas, Theofanis Univ Grenoble 1 Lab Jean Kuntzmann F-38041 Grenoble 9 France Univ Cent Florida Dept Math Orlando FL 32816 USA Univ Cyprus Dept Math & Stat CY-1678 Nicosia Cyprus

We consider the nonparametric regression estimation problem of recovering an unknown response function f on the basis of spatially inhomogeneous data when the design points follow a known density g with a finite number of well-separated zeros. In particular, we consider two different cases: when g has zeros of a polynomial order and when g has zeros of an exponential order. These two cases correspond to moderate and severe data losses, respectively. We obtain asymptotic (as the sample size increases) minimax lower bounds for the L-2-risk when f is assumed to belong to a Besov ball, and construct adaptive wavelet thresholding estimators of f that are asymptotically optimal (in the minimax sense) or near-optimal within a logarithmic factor (in the case of a zero of a polynomial order), over a wide range of Besov balls. The spatially inhomogeneous ill-posed problem that we investigate is inherently more difficult than spatially homogeneous ill-posed problems like, e.g., deconvolution. In particular, due to spatial irregularity, assessment of asymptotic minimax global convergence rates is a much harder task than the derivation of asymptotic minimax local convergence rates studied recently in the literature. Furthermore, the resulting estimators exhibit very different behavior and asymptotic minimax global convergence rates in comparison with the solution of spatially homogeneous ill-posed problems. For example, unlike in the deconvolution problem, the asymptotic minimax global convergence rates are greatly influenced not only by the extent of data loss but also by the degree of spatial homogeneity of f. Specifically, even if 1/g is non-integrable, one can recover f as well as in the case of an equispaced design (in terms of asymptotic minimax global convergence rates) when it is homogeneous enough since the estimator is "borrowing strength" in the areas where f is adequately sampled.

关键词： Adaptivity Besov spaces inhomogeneous data minimax estimation nonparametric regression thresholding wavelet estimation

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nonparametric regression with warped wavelets and strong mixing processes

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ANNALS OF THE INSTITUTE OF STATISTICAL MATHEMATICS 2021年第6期73卷 1203-1228页

作者： Gomez, Luz M. Porto, Rogerio F. Morettin, Pedro A. Univ Sao Paulo Inst Math & Stat Rua Matao 1010 BR-05508090 Sao Paulo SP Brazil Bank Brazil SAUN Quadra 5Lote BGreen Towers BR-70742010 Brasilia DF Brazil

We consider the situation of a univariate nonparametric regression where either the Gaussian error or the predictor follows a stationary strong mixing stochastic process and the other term follows an independent and identically distributed sequence. Also, we estimate the regression function by expanding it in a wavelet basis and applying a hard threshold to the coefficients. Since the observations of the predictor are unequally distant from each other, we work with wavelets warped by the density of the predictor variable. This choice enables us to retain some theoretical and computational properties of wavelets. We propose a unique estimator and show that some of its properties are the same for both model specifications. Specifically, in both cases the coefficients are unbiased and their variances decay at the same rate. Also the risk of the estimator, measured by the mean integrated square error is almost minimax and its maxiset remains unaltered. Simulations and an application illustrate the similarities and differences of the proposed estimator in both situations.

关键词： nonparametric regression Wavelet Stationary process alpha-mixing, Warped wavelets

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nonparametric regression Method Based on Orthogonalization and Thresholding

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IEICE TRANSACTIONS ON INFORMATION AND SYSTEMS 2011年第8期E94D卷 1610-1619页

作者： Hagiwara, Katsuyuki Mie Univ Fac Educ Tsu Mie 5148507 Japan

In this paper. we consider a nonparametric regression problem using a learning machine defined by a weighted sum of fixed basis functions, where the number of basis functions, or equivalently, the number of weights, is equal to the number of training data. For the learning machine, we propose a training scheme that is based on orthogonalization and thresholding. On the basis of the scheme, vectors of basis function outputs are orthogonalized and coefficients of the orthogonalized vectors are estimated instead of weights. The coefficient is set to zero if it is less than a predetermined threshold level assigned component-wise to each coefficient. We then obtain the resulting weight vector by transforming the thresholded coefficients. In this training scheme, we propose asymptotically reasonable threshold levels to distinguish contributed components from unnecessary ones. To see how this works in a simple case, we derive an upper bound for the generalization error of the training scheme with the given threshold levels. It tells us that an increase in the generalization error is of O(log n/n) when there is a. sparse representation of a target function in an orthogonal domain. In implementing the training scheme, eigen-decomposition or the Gram-chmidt procedure is employed for orthogonalization, and the corresponding training methods are referred to as OHTED and OHTGS. Furthermore, modified versions of OHTED and OHTGS, called OHTED2 and OHTGS2 respectively, are proposed for reduced estimation bias. On real benchmark datasets, OHTED2 and OHTGS2 are found to exhibit relatively good generalization performance. In addition, OHTGS2 is found to be obtain a sparse representation of a target function in terms of the basis functions.

关键词： nonparametric regression orthogonalization hard thresholding model selection

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nonparametric regression with current status data

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ANNALS OF THE INSTITUTE OF STATISTICAL MATHEMATICS 2004年第1期56卷 49-72页

作者： Honda, T Univ Tsukuba Inst Social Sci Tsukuba Ibaraki 3058571 Japan

We apply nonparametric regression to current status data, which often arises in survival analysis and reliability analysis. While no parametric assumption on the distributions has been imposed, most authors have employed parametric models like linear models to measure the covariate effects on failure times in regression analysis with current status data. We construct a nonparametric estimator of the regression function by modifying the maximum rank correlation (MRC) estimator. Our estimator can deal with the cases where the other estimators do not work. We present the asymptotic bias and the asymptotic distribution of the estimator by adapting a result on equicontinuity of degenerate U-processes to the setup of this paper.

关键词： current status data case 1 interval censoring survival analysis nonparametric regression maximum rank correlation estimator local linear regression asymptotic properties degenerate U-processes VC-subgragh class equicontinuity

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