Functional single-index composite quantile regression

Jiang, Zhiqiang; Huang, Zhensheng; Zhang, Jing

doi:10.1007/s00184-022-00887-w

Cited by 7 publications

(1 citation statement)

References 25 publications

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“…For example, new estimation and variable selection procedures for the semiparametric partially linear varying coefficient model were proposed by Kai et al [6], showing that compared with the least-squares-based method, the CQR method is much more efficient for many non-normal errors. Jiang et al [7] proposed a functional single-index composite quantile regression method and estimated the unknown slope function and link function using B-spline basis functions. Song et al [8] proposed a penalized composite quantile regression estimator based on SCAD and the Laplacian error penalty (LEP), which can realize variable selection and estimation at the same time.…”

Section: Introductionmentioning

confidence: 99%

Two-Stage Estimation of Partially Linear Varying Coefficient Quantile Regression Model with Missing Data

Luo,

Yan,

Zhang

2024

Mathematics

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In this paper, the statistical inference of the partially linear varying coefficient quantile regression model is studied under random missing responses. A two-stage estimation procedure is developed to estimate the parametric and nonparametric components involved in the model. Furthermore, the asymptotic properties of the estimators obtained are established under some mild regularity conditions. In addition, the empirical log-likelihood ratio statistic based on imputation is proposed, and it is proven that this statistic obeys the standard Chi-square distribution; thus, the empirical likelihood confidence interval of the parameter component of the model is constructed. Finally, simulation results show that the proposed estimation method is feasible and effective.

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Section: Introductionmentioning

confidence: 99%

Two-Stage Estimation of Partially Linear Varying Coefficient Quantile Regression Model with Missing Data

Luo,

Yan,

Zhang

2024

Mathematics

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A Nonparametric Model Checking Test for Functional Linear Composite Quantile Regression Models

Xia,

Du,

Zhang

2024

J Syst Sci Complex

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Limit Theorems in the Nonparametric Conditional Single-Index U-Processes for Locally Stationary Functional Random Fields under Stochastic Sampling Design

Bouzebda

2024

Mathematics

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In his work published in (Ann. Probab. 19, No. 2 (1991), 812–825), W. Stute introduced the notion of conditional U-statistics, expanding upon the Nadaraya–Watson estimates used for regression functions. Stute illustrated the pointwise consistency and asymptotic normality of these statistics. Our research extends these concepts to a broader scope, establishing, for the first time, an asymptotic framework for single-index conditional U-statistics applicable to locally stationary random fields {Xs,An:sinRn} observed at irregularly spaced locations in Rn, a subset of Rd. We introduce an estimator for the single-index conditional U-statistics operator that accommodates the nonstationary nature of the data-generating process. Our method employs a stochastic sampling approach that allows for the flexible creation of irregularly spaced sampling sites, covering both pure and mixed increasing domain frameworks. We establish the uniform convergence rate and weak convergence of the single conditional U-processes. Specifically, we examine weak convergence under bounded or unbounded function classes that satisfy specific moment conditions. These findings are established under general structural conditions on the function classes and underlying models. The theoretical advancements outlined in this paper form essential foundations for potential breakthroughs in functional data analysis, laying the groundwork for future research in this field. Moreover, in the same context, we show the uniform consistency for the nonparametric inverse probability of censoring weighted (I.P.C.W.) estimators of the regression function under random censorship, which is of its own interest. Potential applications of our findings encompass, among many others, the set-indexed conditional U-statistics, the Kendall rank correlation coefficient, and the discrimination problems.

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Functional single-index composite quantile regression

Cited by 7 publications

References 25 publications

Two-Stage Estimation of Partially Linear Varying Coefficient Quantile Regression Model with Missing Data

Two-Stage Estimation of Partially Linear Varying Coefficient Quantile Regression Model with Missing Data

A Nonparametric Model Checking Test for Functional Linear Composite Quantile Regression Models

Limit Theorems in the Nonparametric Conditional Single-Index U-Processes for Locally Stationary Functional Random Fields under Stochastic Sampling Design

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