The aim of this contribution is to provide an adaptive estimation of the long-memory parameter in the classical semi-parametric framework for Gaussian stationary processes using a wavelet method. In particular, the choice of a data-driven optimal band of scales is introduced and developed. Moreover, a central limit theorem for the estimator of the long-memory parameter reaching the minimax rate...

We examine the recently introduced NSB estimator of entropies of severely undersampled discrete variables and devise a procedure for calculating the involved integrals. We discover that the output of the estimator has a well defined limit for large cardinalities of the variables being studied. Thus one can estimate entropies with no a priori assumptions about these cardinalities, and a closed f...

let be a random sample from a normal distribution with unknown mean and known variance the usual estimator of the mean, i.e., sample mean is the maximum likelihood estimator which under squared error loss function is minimax and admissible estimator. in many practical situations, is known in advance to lie in an interval, say for some in this case, the maximum likelihood estimator changes and d...

In this paper we propose a generalised iterative algorithm for calculating variational Bayesian estimates for a normal mixture model and we investigate its convergence properties. It is shown theoretically that the variational Bayes estimator converges locally to the maximum likelihood estimator at the rate of O(1/n) in the large sample limit. We also demonstrate by numerical experiments that t...

Mosig et al. (2001) propose an intuitively appealing method for estimating the number of null hypotheses that are false in a multiple test situation. They present an iterative algorithm that relies on the distribution of observed -values to obtain their estimator. We characterize the limit of their iterative algorithm and show that their estimator can be computed directly without iteration from...

This work is intended as a contribution to a wavelet-based adaptive estimator of the memory parameter in the classical semi-parametric framework for Gaussian stationary processes. In particular we introduce and develop the choice of a data-driven optimal bandwidth. Moreover, we establish a central limit theorem for the estimator of the memory parameter with the minimax rate of convergence (up t...

This paper focuses on the problem of the estimation of the cumulative hazard function of a distribution on a general complete separable metric space when the data points are subject to censoring by an arbitrary adapted random set. A problem involving observability of the estimator proposed in [8] and [9] is resolved and a functional central limit theorem is proven for the revised estimator. Sev...

The central limit theorem says that, provided an estimator fulfills certain weak conditions, then, for reasonable sample sizes, the sampling distribution of the estimator converges to normality. We propose a procedure to find out what a “reasonably large sample size” is. The procedure is based on the properties of Gini’s mean difference decomposition. We show the results of implementations of t...

The paper uses empirical process techniques to study the asymptotics of the least-squares estimator for the fitting of a nonlinear regression function. By combining and extending ideas of Wu and Van de Geer, it establishes new consistency and central limit theorems that hold under only second moment assumptions on the errors. An application to a delicate example of Wu’s illustrates the use of t...

Methods A retrospective chart review was conducted of all JIA patients who received IACI from 6/05 to 3/10, and had at least six months of follow-up. Data collected included demographic information, JIA subtype, date of injection and arthritis flare, type of joint injected and concomitant medications. Any joint that did not flare by the study end date in 9/10 was censored. Time to flare of arth...