Nengxiang Ling

On Complete Convergence of Moving Average Process for AANA Sequence

We investigate the moving average process such that , , where and is a sequence of asymptotically almost negatively associated (AANA) random variables. The complete convergence, complete moment convergence, and the existence of the moment of supermum of normed partial sums are presented for this moving average process.

Conditional mode estimation for functional stationary ergodic data with responses missing at random

In this paper, we investigate the asymptotic properties of a non-parametric conditional mode estimation given a functional explanatory variable, when functional stationary ergodic data and missing at random responses are observed. First of all, we establish asymptotic properties for a conditional density estimator from which we derive almost sure convergence (with rate) and asymptotic normality of a conditional mode estimator. This new estimate take into account missing data, and a simulation study is performed to illustrate how this fact allows to get higher predictive performances than those obtained with standard estimates.

On asymptotic properties of functional conditional mode estimation with both stationary ergodic and responses MAR

This contribution deals with functional conditional mode estimation given a functional explanatory variable with both stationary ergodic and responses missing at random (MAR). More precisely, we propose the estimators for functional conditional density and conditional mode respectively in this case. The main results of the work are the establishment of the asymptotic properties of such estimators.

Nonparametric modelling for functional data: selected survey and tracks for future

ABSTRACT Nonparametric functional data analysis is a field whose development started some 15 years ago and there is a very extensive literature on the topic (hundreds of papers published now). The first aim of this survey is to discuss the state of art in the field through a necessarily selected, bibliographical survey. The second aim is to present a wide scope of open questions in order to promote further discussions. Our main purpose is restricted to methodological contributions and also to emphasize on kernel functional regression analysis before extending discussions in two directions: alternative techniques to kernel methods for functional regression and other statistical problems besides regression.