Asymptotic Efficiencies of Spacings Tests for Goodness of Fit.
Asymptotic efficiency and robustness of -estimators
Asymptotic Efficiency of the Maximum Probability Estimate in the i.i.d. Case
Asymptotic expansion and a local limit theorem for the signed Wilcoxon statistic
Asymptotic Expansion of the Minimax Value in Survey Sampling .
Asymptotic Expansion of the Power Function of the Two-Sample Binomial Test with and without Randomization.
Asymptotic expansions of functions of statistics
Asymptotic law of the intergrated quadratic errors of kernel density and regression estimators under the conditions of dependence. (Loi asymptotique des erreurs quadratiques intégrées des estimateurs à noyau de la densité et de la régression sous des conditions de dépendance.)
Asymptotic Normality
Asymptotic normality and convergence rates of linear rank statistics under alternatives
Asymptotic normality and efficiency of two Sobol index estimators
Many mathematical models involve input parameters, which are not precisely known. Global sensitivity analysis aims to identify the parameters whose uncertainty has the largest impact on the variability of a quantity of interest (output of the model). One of the statistical tools used to quantify the influence of each input variable on the output is the Sobol sensitivity index. We consider the statistical estimation of this index from a finite sample of model outputs: we present two estimators and...
Asymptotic normality and efficiency of variance components estimators with high breakdown points
For estimating the variance components of a one-way random effect model recently Uhlig (1995, 1997) and Lischer (1996) proposed non-iterative estimators with high breakdown points. These estimators base on the high breakdown point scale estimators of Rousseeuw and Croux (1992, 1993), which they called Q-estimators. In this paper the asymptotic normal distribution of the new variance components estimators is derived so that the asymptotic efficiency of these estimators can be compared with that of...
Asymptotic normality in density support estimation.
Asymptotic normality in mixture models
Asymptotic normality in mixture models
We study the estimation of a linear integral functional of a distribution F, using i.i.d. observations which density is a mixture of a family of densities k(.,y) under F. We examine the asymptotic distribution of the estimator obtained by plugging the non parametric maximum likelihood estimator (NPMLE) of F in the functional. A problem here is that usually, the NPMLE does not dominate F. Our main aim here is to show that this can be overcome by considering a convex combination of F and the...
Asymptotic Normality of Linear Functions of Concomitants of Order Statistics
Asymptotic normality of multivariate linear rank statistics under general alternatives
Let , be independent random -vectors with respective continuous cumulative distribution functions . Define the -vectors by setting equal to the rank of among . Let denote a multivariate score function in , and put , the being arbitrary regression constants. In this paper the asymptotic distribution of is investigated under various sets of conditions on the constants, the score functions, and the underlying distribution functions. In particular, asymptotic normality of is established...
Asymptotic normality of randomly truncated stochastic algorithms
We study the convergence rate of randomly truncated stochastic algorithms, which consist in the truncation of the standard Robbins–Monro procedure on an increasing sequence of compact sets. Such a truncation is often required in practice to ensure convergence when standard algorithms fail because the expected-value function grows too fast. In this work, we give a self contained proof of a central limit theorem for this algorithm under local assumptions on the expected-value function, which are fairly...
Asymptotic normality of the integrated square error of a density estimator in the convolution model.
In this paper we consider a kernel estimator of a density in a convolution model and give a central limit theorem for its integrated square error (ISE). The kernel estimator is rather classical in minimax theory when the underlying density is recovered from noisy observations. The kernel is fixed and depends heavily on the distribution of the noise, supposed entirely known. The bandwidth is not fixed, the results hold for any sequence of bandwidths decreasing to 0. In particular the central limit...
Asymptotic normality of the kernel estimate for the Markovian transition operator
We build a kernel estimator of the Markovian transition operator as an endomorphism on L¹ for some discrete time continuous states Markov processes which satisfy certain additional regularity conditions. The main result deals with the asymptotic normality of the kernel estimator constructed.