Penalized contrast estimator for adaptive density deconvolution

The authors consider the problem of estimating the density g of independent and identically distributed variables X_I, from a sample Z₁,… Z_n such that Z_I = X_I + σ? for i = 1,…, n, and E is noise independent of X, with σ? having a known distribution. They present a model selection procedure allowing one to construct an adaptive estimator of g and to find nonasymptotic risk bounds. The estimator achieves the minimax rate of convergence, in most cases where lower bounds are available. A simulation study gives an illustration of the good practical performance of the method.     

Approximating bayesian inference by weighted likelihood

The author proposes to use weighted likelihood to approximate Bayesian inference when no external or prior information is available. He proposes a weighted likelihood estimator that minimizes the empirical Bayes risk under relative entropy loss. He discusses connections among the weighted likelihood, empirical Bayes and James‐Stein estimators. Both simulated and real data sets are used for illustration purposes.     

A robust prediction error criterion for pareto modelling of upper tails

Estimation of the Pareto tail index from extreme order statistics is an important problem in many settings. The upper tail of the distribution, where data are sparse, is typically fitted with a model, such as the Pareto model, from which quantities such as probabilities associated with extreme events are deduced. The success of this procedure relies heavily not only on the choice of the estimator for the Pareto tail index but also on the procedure used to determine the number k of extreme order statistics that are used for the estimation. The authors develop a robust prediction error criterion for choosing k and estimating the Pareto index. A Monte Carlo study shows the good performance of the new estimator and the analysis of real data sets illustrates that a robust procedure for selection, and not just for estimation, is needed.     

Corrected proof of the result of 'A prediction error property of the Lasso estimator and its generalization' by Huang (2003)

The Lasso achieves variance reduction and variable selection by solving an ?₁‐regularized least squares problem. Huang (2003) claims that ‘there always exists an interval of regularization parameter values such that the corresponding mean squared prediction error for the Lasso estimator is smaller than for the ordinary least square estimator’. This result is correct. However, its proof in Huang (2003) is not. This paper presents a corrected proof of the claim, which exposes and uses some interesting fundamental properties of the Lasso.     

A new Method of Estimating the Asymptotic Standard Error of the Hodges-Lehmann Estimator Based on Generalized Least Squares

A method of estimating the asymptotic standard error of the Hodges-Lehmann estimator based on generalized least squares is described. The results of a Monte Carlo study comparing the new method with existing ones are given.     

Criteria for the equality between ordinary least squares and best linear unbiased estimators under certain linear models

A new necessary and sufficient condition is derived for the equality between the ordinary least-squares estimator and the best linear unbiased estimator of the expectation vector in linear models with certain specific design matrices. This condition is then applied to special cases involving one-way and two-way classification models.     

On UMVU estimators and Bhattacharya bounds in exponential distributions

A subfamily of exponential distributions is considered and it is shown that the variance of the UMVU estimator of an estimable function g(θ) having power series expansion is the limit of Bhattacharya bounds.     

Confidence bands from censored samples

Several types of asymptotic confidence bands have been proposed in the literature when the data are randomly censored on the right. Introducing new classes of bands, we place the old bands and their relationship to one another within a comprehensive theory of bands. A thorough analysis yields narrower bands and two kinds of modifications which are asymptotically distribution- and censor-free. One of these is useful when the interval on which the bands are constructed is predetermined and the width of the bands is random; the other, when there is a predetermined bound on the width and the interval is random. We illustrate our bands on the Szeged pacemaker data. These methods also provide a general modification of the Kolmogorov band in the uncensored case.     

A TWO-STAGE UNRELATED RANDOMISED RESPONSE PROCEDURE

In a sample survey, questions requiring personal or controversial assertions often give rise to resistance. A randomised response procedure can be used to help the researcher gather accurate data in this case. This paper describes a new two-stage unrelated randomised response procedure that combines the use of two randomisation devices (Mangat & Singh, 1990) and an unrelated question (Horwitz et al. 1967). It examines the situation where the respondents are not completely truthful in their answers. The efficiency of this new method is compared with the original one-stage procedure proposed by Horwitz et al. (1967), and guidelines for choosing the values of different parameters for the procedures are provided. Results from an empirical study which examines the efficiency and feasibility of the proposed method are given.     

Nonparametric estimation of the limiting availability

The point availability of a repairable system is the probability that the system is operating at a specified time. As time increases, the point availability converges to a positive constant called the limiting availability. Baxter and Li (1994a) developed a technique for constructing nonparametric confidence intervals for the point availability. However, nonparametric estimators of the limiting availability have not previously been studied in the literature. In this paper, we consider two separate cases: (1) the data are complete and (2) the data are subject to right censorship. For each case, a nonparametric confidence interval for the limiting availability is derived. Applications and simulation studies are presented.deceased after the paper was accepted