Exact Asymptotic Errors of the Hazard Conditional Rate Kernel for Functional Random Fields

We consider the problem of nonparametric estimation of the kernel type estimators for the conditional cumulative distribution function and the successive derivatives of the conditional density for spatial data. More precisely, given a strictly stationary random field Z = (X, Y), we investigate a kernel estimate of the conditional hazard function of univariate response variable Y given the functional variable X. The principal aim of this paper is to give the mean squared convergence rate of the proposed estimator. Finally, we apply these theoretical results to the estimation of the conditional hazard function where we give the mean squared convergence rate of the proposed estimator

Missing at random in nonparametric regression for functional stationary ergodic data in the functional index model

The main objective of this paper is to estimate non-parametrically the the estimator for the regression function operator when the observations are linked with a single-index. The functional stationary ergodic data with missing at random (MAR) are considered.In particular, we construct the kernel type estimator of the regression operator, some asymptotic properties such as the convergence rate in probability as well as the asymptotic normality of the estimator are established under some mild conditions respectively. As an application, the asymptotic $(1 -\zeta)$ confidence interval of the regression operator is also presented for $0 < \zeta < 1.

(R1463) On the Central Limit Theorem for Conditional Density Estimator In the Single Functional Index Model

The main objective of this paper is to investigate the nonparametric estimation of the conditional density of a scalar response variable Y, given the explanatory variable X taking value in a Hilbert space when the sample of observations is considered as an independent random variables with identical distribution (i.i.d.) and are linked with a single functional index structure. First of all, a kernel type estimator for the conditional density function (cond-df) is introduced. Afterwards, the asymptotic properties are stated for a conditional density estimator when the observations are linked with a single-index structure from which we derive an central limit theorem (CLT) of the conditional density estimator to show the asymptotic normality of the kernel estimate of this model. As an application the conditional mode in functional single-index model is presented. As an application the conditional mode in functional single-index model is presented as well as the asymptotic ( 1 - \xi) confidence interval of the conditional mode function is given for 0 \u3c \xi \u3c 1. Simulation study is also presented to illustrate the validity and finite sample performance of the considered estimator

Strong Uniform Consistency of Hazard Function with Functional Explicatory Variable in Single Functional Index Model under Censored Data

In this paper we deal with nonparametric estimate of the conditional hazard function, when the covariate is functional. Kernel type estimators for the conditional hazard function of a scalar response variable Y given a Hilbertian random variable X are introduced, where the observations are linked with a single-index structure. We establish the pointwise almost complete convergence and the uniform almost complete convergence (with the rate) of the kernel estimate of this model in various situations, including censored and non-censored data. The rates of convergence emphasize the crucial role played by the small ball probabilities with respect to the distribution of the explanatory functional variable

Some Asymptotic Properties of Conditional Density Function for Functional Data Under Random Censorship

In this work, we investigate the asymptotic properties of a nonparametric mode of a conditional density when the real response variable is censored and the explanatory variable is valued in a semi- metric space under ergodic data. First of all, we establish asymptotic properties for a conditional density estimator from which we derive an central limit theorem (CLT) of the conditional mode estimator. Simulation study is also presented to illustrate the validity and finite sample performance of the considered estimator

Stability Condition of a Retrial Queueing System with Abandoned and Feedback Customers

This paper deals with the stability of a retrial queueing system with two orbits, abandoned and feedback customers. Two independent Poisson streams of customers arrive to the system, and flow into a single-server service system. An arriving one of type i; i = 1; 2, is handled by the server if it is free; otherwise, it is blocked and routed to a separate type-i retrial (orbit) queue that attempts to re-dispatch its jobs at its specific Poisson rate. The customer in the orbit either attempts service again after a random time or gives up receiving service and leaves the system after a random time. After the customer is served completely, the customer will decide either to join the retrial group again for another service or leave the system forever with some probability

A Note on Asymptotic Normality of a Copula Function in Regression Model

Over the last decade, there has been significant and rapid development of the theory of copulas. Much of the work has been motivated by their applications to stochastic processes, economics, risk management, finance, insurance, the environment (hydrology, climate, etc.), survival analysis, and medical sciences. In many statistical models. The copula approach is a way to solve the difficult problem of finding the whole bivariate or multivariate distribution. In this paper, we give the asymptotic normality of the copulas function in a regression model