Local linear conditional cumulative distribution function with mixing data

Abstract

This paper investigates a conditional cumulative distribution of a scalar response given by a functional random variable with an α-mixing stationary sample using a local polynomial technique. The main purpose of this study is to establish asymptotic normality results under selected mixing conditions satisfied by many time-series analysis models in addition to the other appropriate conditions to confirm the planned prospects.Mathematics Subject Classification 62G05 · 62G08 · 62G20 · 62G07 · 62G30 · 62H12 Introduction and motivationsWith the evolution of the measuring instruments and the growth of research studies mainly since the publication of the pioneer paper of Ferraty and Vieu [19], functional data analysis (FDA) has attracted the attention of many works as in the recent monograph of Horváth and Kokoszka [23]. On the other hand, alternative conditional predictions of the classical regression have also gained a considerable interest in basically all the fields of statistics, especially for estimating conditional models using the kernel approach (or local constant) as investigated in the papers of Ferraty et al. [18], , or Ezzahrioui and Ould-Saïd [15].In numerous nonparametric statistic problems, the estimation of a conditional distribution function (CDF) constitutes a key aspect of inference. Accordingly, the present study employs a specific CDF model for constructing prediction intervals that can be involved in many applications such as the survival analysis and reliability. Interestingly, it is well known that the CDF has the advantage to completely characterize the conditional law of the considered random variables. The determination of the CDF allows, in fact, to obtain the conditional density and conditional hazard functions. Moreover, several prediction tools can also be implemented for the nonparametric statistics modeling, taking the example of conditional mode, median, or quantile. In addition, an extensive literature including various nonparametric approaches has taken place in the conditional estimation of independent samples and dependent observations in finite-and infinite-dimensional spaces (see, for instance, Berlinet et al. [3], Honda [22], and Ferraty and Vieu [17]). In many situations, the

Statistical Inference for Multivariate Conditional Cumulative Distribution Function Estimation By Stochastic Approximation Method

“…Thereafter, [43] built up a new estimator of CCDF investing a method of pre-adjusting the original observations non-parametrically. Recently, [8] introduced a new method to settle CCDF estimation problem based on local polynomial technique.…”

A non-parametric estimation of the conditional quantile for truncated and functional data

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