Displaying similar documents to “Local linear estimation of conditional cumulative distribution function in the functional data: Uniform consistency with convergence rates”

Local linear estimation of the conditional mode under left truncation for functional regressors

Halima Boudada, Sarra Leulmi (2023)

Kybernetika

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In this work, we introduce a local linear estimator of the conditional mode for a random real response variable which is subject to left-truncation by another random variable where the covariate takes values in an infinite dimensional space. We first establish both of pointwise and uniform almost sure convergences, with rates, of the conditional density estimator. Then, we deduce the strong consistency of the obtained conditional mode estimator. We finally illustrate the outperformance...

Strong uniform consistency rates of some characteristics of the conditional distribution estimator in the functional single-index model

Amina Angelika Bouchentouf, Tayeb Djebbouri, Abbes Rabhi, Khadidja Sabri (2014)

Applicationes Mathematicae

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The aim of this paper is to establish a nonparametric estimate of some characteristics of the conditional distribution. Kernel type estimators for the conditional cumulative distribution function and for the successive derivatives of the conditional density of a scalar response variable Y given a Hilbertian random variable X are introduced when the observations are linked with a single-index structure. We establish the pointwise almost complete convergence and the uniform almost complete...

Smoothing and preservation of irregularities using local linear fitting

Irène Gijbels (2008)

Applications of Mathematics

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For nonparametric estimation of a smooth regression function, local linear fitting is a widely-used method. The goal of this paper is to briefly review how to use this method when the unknown curve possibly has some irregularities, such as jumps or peaks, at unknown locations. It is then explained how the same basic method can be used when estimating unsmooth probability densities and conditional variance functions.

Mean square error of the estimator of the conditional hazard function

Abbes Rabhi, Samir Benaissa, El Hadj Hamel, Boubaker Mechab (2013)

Applicationes Mathematicae

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This paper deals with a scalar response conditioned by a functional random variable. The main goal is to estimate the conditional hazard function. An asymptotic formula for the mean square error of this estimator is calculated considering as usual the bias and variance.

Uniform strong consistency of a frontier estimator using kernel regression on high order moments

Stéphane Girard, Armelle Guillou, Gilles Stupfler (2014)

ESAIM: Probability and Statistics

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We consider the high order moments estimator of the frontier of a random pair, introduced by [S. Girard, A. Guillou and G. Stupfler, 116 (2013) 172–189]. In the present paper, we show that this estimator is strongly uniformly consistent on compact sets and its rate of convergence is given when the conditional cumulative distribution function belongs to the Hall class of distribution functions.

Some applications of probability generating function based methods to statistical estimation

Manuel L. Esquível (2009)

Discussiones Mathematicae Probability and Statistics

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After recalling previous work on probability generating functions for real valued random variables we extend to these random variables uniform laws of large numbers and functional limit theorem for the empirical probability generating function. We present an application to the study of continuous laws, namely, estimation of parameters of Gaussian, gamma and uniform laws by means of a minimum contrast estimator that uses the empirical probability generating function of the sample. We...

The LASSO estimator: Distributional properties

Rakshith Jagannath, Neelesh S. Upadhye (2018)

Kybernetika

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The least absolute shrinkage and selection operator (LASSO) is a popular technique for simultaneous estimation and model selection. There have been a lot of studies on the large sample asymptotic distributional properties of the LASSO estimator, but it is also well-known that the asymptotic results can give a wrong picture of the LASSO estimator's actual finite-sample behaviour. The finite sample distribution of the LASSO estimator has been previously studied for the special case of...

Nonparametric bivariate estimation for successive survival times.

Carles Serrat, Guadalupe Gómez (2007)

SORT

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Several aspects of the analysis of two successive survival times are considered. All the analyses take into account the dependent censoring on the second time induced by the first. Three nonparametric methods are described, implemented and applied to the data coming from a multicentre clinical trial for HIV-infected patients. Visser's and Wang and Wells methods propose an estimator for the bivariate survival function while Gómez and Serrat's method presents a conditional approach for...