On spatial conditional mode estimation for a functional regressor

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

show abstract

“…Hence, by Slutsky's Theorem (see Theorem 11.1.5 in [25]), (8) is straightforward consequence of the following two claims:…”

Section: Proof Of Lemma 34mentioning

confidence: 96%

Local linear conditional cumulative distribution function with mixing data

Bouanani

Rahmani

Ait-Hennani³

2019

Arab. J. Math.

View full text Add to dashboard Cite

show abstract

“…Under the assumptions on conditional density, the covariate is more responsible for the smoothing effect than the response. Various studies have reported the convergence of unimodal regression with dependent covariates (Attaoui, 2014;Collomb et al, 1986;Dabo-Niang & Laksaci, 2010;Khardani et al, 2010Khardani et al, , 2011Ould-Saïd, 1993, 1997Ould-Saïd & Cai, 2005). Strong consistency was investigated in Collomb et al (1986)) and Ould-Saïd (1993, 1997).…”

Section: Unimodal Regressionmentioning

confidence: 99%

“…Strong consistency was investigated in Collomb et al (1986)) and Ould-Saïd (1993, 1997). The convergence rate has also been derived in unimodal regression with functional dependent covariates (Attaoui, 2014;Dabo-Niang & Laksaci, 2010), and with censored response (Khardani et al, 2010(Khardani et al, , 2011Ould-Saïd & Cai, 2005).…”

Section: Unimodal Versus Multimodal Regressionmentioning

confidence: 99%

“…Various studies have reported the convergence of uni-modal regression with dependent covariates (Attaoui, 2014;Collomb et al, 1986;Dabo-Niang and Laksaci, 2010;Khardani et al, 2010Khardani et al, , 2011Ould-Saïd, 1993, 1997Ould-Saïd and Cai, 2005). Strong consistency was investigated in (Collomb et al, 1986;Ould-Saïd, 1993, 1997.…”

Section: Uni-modal Regressionmentioning

confidence: 99%

See 1 more Smart Citation

Modal regression using kernel density estimation: A review

Chen

2018

WIREs Computational Stats

View full text Add to dashboard Cite

We review recent advances in modal regression studies using kernel density estimation. Modal regression is an alternative approach for investigating the relationship between a response variable and its covariates. Specifically, modal regression summarizes the interactions between the response variable and covariates using the conditional mode or local modes. We first describe the underlying model of modal regression and its estimators based on kernel density estimation. We then review the asymptotic properties of the estimators and strategies for choosing the smoothing bandwidth. We also discuss useful algorithms and similar alternative approaches for modal regression, and propose future direction in this field. This article is categorized under: Statistical and Graphical Methods of Data Analysis > Bayesian Methods and Theory Statistical and Graphical Methods of Data Analysis > Nonparametric Methods Statistical and Graphical Methods of Data Analysis > Density Estimation

show abstract

“…The modelling of the spatial data was also considered in nonparametric estimation for functional data. On this subject, Dabo-Niang et al (2012) studied the almost convergence of an estimator with kernel for the function of regression. Laksaci et al (2009) treated the almost complete convergence of the estimator with a kernel of the function of conditional distribution and the conditional quantiles.…”

Section: Introductionmentioning

confidence: 99%

On the nonparametric estimation of the conditional hazard estimator in a single functional index

Gagui

Chouaf

2022

Statistics in Transition New Series

View full text Add to dashboard Cite

This paper deals with the conditional hazard estimator of a real response where the variable is given a functional random variable (i.e it takes values in an infinite-dimensional space). Specifically, we focus on the functional index model. This approach offers a good compromise between nonparametric and parametric models. The principle aim is to prove the asymptotic normality of the proposed estimator under general conditions and in cases where the variables satisfy the strong mixing dependency. This was achieved by means of the kernel estimator method, based on a single-index structure. Finally, a simulation of our methodology shows that it is efficient for large sample sizes.

show abstract

On spatial conditional mode estimation for a functional regressor

Cited by 14 publications

References 13 publications

Local linear conditional cumulative distribution function with mixing data

Local linear conditional cumulative distribution function with mixing data

Modal regression using kernel density estimation: A review

On the nonparametric estimation of the conditional hazard estimator in a single functional index

Contact Info

Product

Resources

About