Testing a Specification Form in Single Functional Index Model

AbstractThe main objective of this paper is to non-parametrically estimate the quantiles of a conditional distribution in the censorship model when the sample is considered as an -mixing sequence. First of all, a kernel type estimator for the conditional cumulative distribution function (cond-cdf) is introduced. Afterwards, we estimate the quantiles by inverting this estimated cond-cdf and state the asymptotic properties when the observations are linked with a single-index structure. The pointwise almost complete convergence and the uniform almost complete convergence (with rate) of the kernel estimate of this model are established. This approach can be applied in time series analysis.

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Cross-validated estimations in the single-functional index model

Statistics ◽

10.1080/02331880801980377 ◽

2008 ◽

Vol 42 (6) ◽

pp. 475-494 ◽

Cited By ~ 64

Author(s):

Ahmed Ait-Saïdi ◽

Frédéric Ferraty ◽

Rabah Kassa ◽

Philippe Vieu

Keyword(s):

Functional Index ◽

Index Model

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The conditional cumulative distribution function in single functional index model

Communication in Statistics- Theory and Methods ◽

10.1080/03610926.2014.932808 ◽

2015 ◽

Vol 45 (16) ◽

pp. 4896-4911 ◽

Cited By ~ 1

Author(s):

Ahmed Ait Saidi ◽

Mecheri Kheira

Keyword(s):

Distribution Function ◽

Cumulative Distribution Function ◽

Cumulative Distribution ◽

Functional Index ◽

Index Model

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CLT for single functional index quantile regression under dependence structure

Acta Universitatis Sapientiae Mathematica ◽

10.2478/ausm-2021-0003 ◽

2021 ◽

Vol 13 (1) ◽

pp. 45-77

Author(s):

Nadia Kadiri ◽

Abbes Rabhi ◽

Salah Khardani ◽

Fatima Akkal

Keyword(s):

Asymptotic Properties ◽

Likelihood Method ◽

Dependence Structure ◽

Finite Sample ◽

Functional Index ◽

Conditional Quantile ◽

Index Model ◽

Conditional Quantile Estimator ◽

Pseudo Maximum Likelihood ◽

Random Responses

Abstract In this paper, we investigate the asymptotic properties of a nonparametric conditional quantile estimation in the single functional index model for dependent functional data and censored at random responses are observed. First of all, we establish asymptotic properties for a conditional distribution estimator from which we derive an central limit theorem (CLT) of the conditional quantile estimator. Simulation study is also presented to illustrate the validity and finite sample performance of the considered estimator. Finally, the estimation of the functional index via the pseudo-maximum likelihood method is discussed, but not tackled.

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