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Multimodal regression estimation methods are introduced for regression models involving circular response and/or covariate. The regression estimators are based on the maximization of the conditional densities of the response variable over…

Methodology · Statistics 2024-01-10 María Alonso-Pena , Rosa M. Crujeiras

This study considers regression analysis of a circular response with an error-prone linear covariate. Starting with an existing estimator of the circular regression function that assumes error-free covariate, three approaches are proposed…

Methodology · Statistics 2025-08-25 Nicholas Woolsey , Xianzheng Huang

This paper investigates the nonparametric estimation of a circular regression function in an errors-in-variables framework. Two settings are studied, depending on whether the covariates are circular or linear. Adaptive estimators are…

Statistics Theory · Mathematics 2025-08-27 Tien Dat Nguyen , Thanh Mai Pham Ngoc

We consider nonparametric regression with functional covariates, that is, they are elements of an infinite-dimensional Hilbert space. A locally polynomial estimator is constructed, where an orthonormal basis and various tuning parameters…

Statistics Theory · Mathematics 2025-04-09 Moritz Jirak , Alois Kneip , Alexander Meister , Mario Pahl

Nonparametric density and regression estimators commonly depend on a bandwidth. The asymptotic properties of these estimators have been widely studied when bandwidths are nonstochastic. In practice, however, in order to improve finite…

Statistics Theory · Mathematics 2014-09-02 Carlos Martins-Filho , Paulo Saraiva

In this work, we consider a multivariate regression model with one-sided errors. We assume for the regression function to lie in a general H\"{o}lder class and estimate it via a nonparametric local polynomial approach that consists of…

Statistics Theory · Mathematics 2021-02-11 Leonie Selk , Charles Tillier , Orlando Marigliano

In this paper, we consider a weighted local linear estimator based on the inverse selection probability for nonparametric regression with missing covariates at random. The asymptotic distribution of the maximal deviation between the…

Methodology · Statistics 2020-03-03 Li Cai , Lijie Gu , Qihua Wang , Suojin Wang

This paper presents a general framework for the estimation of regression models with circular covariates, where the conditional distribution of the response given the covariate can be specified through a parametric model. The estimation of…

Methodology · Statistics 2023-06-06 María Alonso-Pena , Irène Gijbels , Rosa M. Crujeiras

Nonparametric regression models offer a way to understand and quantify relationships between variables without having to identify an appropriate family of possible regression functions. Although many estimation methods for these models have…

Methodology · Statistics 2023-04-07 Matias Salibian-Barrera

Marginal structural models are a popular method for estimating causal effects in the presence of time-varying exposures. In spite of their popularity, no scalable non-parametric estimator exist for marginal structural models with…

Methodology · Statistics 2024-09-30 Axel Martin , Michele Santacatterina , Iván Díaz

In this paper, we deal with nonparametric regression for circular data, meaning that observations are represented by points lying on the unit circle. We propose a kernel estimation procedure with data-driven selection of the bandwidth…

Statistics Theory · Mathematics 2023-07-03 Tien Dat Nguyen , Thanh Mai Pham Ngoc , Vincent Rivoirard

We consider the problem of estimating a regression function when a covariate is measured with error. Using the local polynomial estimator of Delaigle, Fan, and Carroll (2009) as a benchmark, we propose an alternative way of solving the…

Methodology · Statistics 2017-01-24 Xianzheng Huang , Haiming Zhou

We propose local polynomial estimators for the conditional mean of a continuous response when only pooled response data are collected under different pooling designs. Asymptotic properties of these estimators are investigated and compared.…

Methodology · Statistics 2020-02-11 Dewei Wang , Xichen Mou , Xiang Li , Xianzheng Huang

The paper deals with the nonparametric estimation problem at a given fixed point for an autoregressive model with unknown distributed noise. Kernel estimate modifications are proposed. Asymptotic minimax and efficiency properties for…

Statistics Theory · Mathematics 2008-06-19 Ouerdia Arkoun , Serguei Pergamenchtchikov

A nonparametric procedure for robust regression estimation and for quantile regression is proposed which is completely data-driven and adapts locally to the regularity of the regression function. This is achieved by considering in each…

Statistics Theory · Mathematics 2009-04-06 Markus Reiss , Yves Rozenholc , Charles-Andre Cuenod

The main purpose is to estimate the regression function of a real random variable with functional explanatory variable by using a recursive nonparametric kernel approach. The mean square error and the almost sure convergence of a family of…

Statistics Theory · Mathematics 2013-08-07 Aboubacar Amiri , Christophe Crambes , Baba Thiam

We consider nonparametric estimation of a regression curve when the data are observed with multiplicative distortion which depends on an observed confounding variable. We suggest several estimators, ranging from a relatively simple one that…

Statistics Theory · Mathematics 2016-01-13 Aurore Delaigle , Peter Hall , Wen-Xin Zhou

New local linear estimators are proposed for a wide class of nonparametric regression models. The estimators are uniformly consistent regardless of satisfying traditional conditions of depen\-dence of design elements. The estimators are the…

Statistics Theory · Mathematics 2022-07-05 Yuliana Linke , Igor Borisov , Pavel Ruzankin , Vladimir Kutsenko , Elena Yarovaya , Svetlana Shalnova

Testing procedures for assessing a parametric regression model with circular response and $\mathbb{R}^d$-valued covariate are proposed and analyzed in this work both for independent and for spatially correlated data. The test statistics are…

Methodology · Statistics 2020-09-01 Andrea Meilán-Vila , Mario Francisco-Fernández , Rosa M. Crujeiras

A nonparametric and locally adaptive Bayesian estimator is proposed for estimating a binary regression. Flexibility is obtained by modeling the binary regression as a mixture of probit regressions with the argument of each probit regression…

Methodology · Statistics 2007-09-25 Sally Wood , Robert Kohn , Remy Cottet , Wenxin Jiang , Martin Tanner
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