Generalized estimator of population mean by using conventional and non-conventional measures in the presence of measurement errors

In survey research, it is assumed that reported response by the individual is correct. However, given the issues of prestige bias, self-respect, respondent's reported data often produces estimated values which are highly deviated from the true values. This causes measurement error (ME) to be present in the sample estimates. In this article, the estimation of population mean in the presence of measurement error using information on a single auxiliary variable is studied. A generalized estimator of population mean is proposed. The class of estimators is obtained by using some conventional and non-conventional measures. Simulation and numerical study is also conducted to assess the performance of estimators in the presence and absence of measurement error.     

Estimation of the smallest scale parameter of two-parameter exponential distributions

Improved point and interval estimation of the smallest scale parameter of n independent populations following two-parameter exponential distributions are studied. The model is formulated in such a way that allows for treating the estimation of the smallest scale parameter as a problem of estimating an unrestricted scale parameter in the presence of a nuisance parameter. The classes of improved point and interval estimators are enriched with Stein-type, Brewster and Zidek-type, Maruyama-type and Strawderman-type improved estimators under both quadratic and entropy losses, whereas using as a criterion the coverage probability, with Stein-type, Brewster and Zidek-type, and Maruyama-type improved intervals. The sampling framework considered incorporates important life-testing schemes such as i.i.d. sampling, type-II censoring, progressive type-II censoring, adaptive progressive type-II censoring, and record values.     

On approximations via convolution-defined mixture models

An often-cited fact regarding mixing or mixture distributions is that their density functions are able to approximate the density function of any unknown distribution to arbitrary degrees of accuracy, provided that the mixing or mixture distribution is sufficiently complex. This fact is often not made concrete. We investigate and review theorems that provide approximation bounds for mixing distributions. Connections between the approximation bounds of mixing distributions and estimation bounds for the maximum likelihood estimator of finite mixtures of location-scale distributions are reviewed.     

Cytometry inference through adaptive atomic deconvolution

In this paper, we consider a statistical estimation problem known as atomic deconvolution. Introduced in reliability, this model has a direct application when considering biological data produced by flow cytometers. From a statistical point of view, we aim at inferring the percentage of cells expressing the selected molecule and the probability distribution function associated with its fluorescence emission. We propose here an adaptive estimation procedure based on a previous deconvolution procedure introduced by Es, Gugushvili, and Spreij [(2008), ‘Deconvolution for an atomic distribution’, Electronic Journal of Statistics, 2, 265–297] and Gugushvili, Es, and Spreij [(2011), ‘Deconvolution for an atomic distribution: rates of convergence’, Journal of Nonparametric Statistics, 23, 1003–1029]. For both estimating the mixing parameter and the mixing density automatically, we use the Lepskii method based on the optimal choice of a bandwidth using a bias-variance decomposition. We then derive some convergence rates that are shown to be minimax optimal (up to some log terms) in Sobolev classes. Finally, we apply our algorithm on the simulated and real biological data.     

On the asymptotic normality of the R-estimators of the slope parameters of simple linear regression models with associated errors

ABSTRACT

The purpose of this paper is to prove, under mild conditions, the asymptotic normality of the rank estimator of the slope parameter of a simple linear regression model with stationary associated errors. This result follows from a uniform linearity property for linear rank statistics that we establish under general conditions on the dependence of the errors. We prove also a tightness criterion for weighted empirical process constructed from associated triangular arrays. This criterion is needed for the proofs which are based on that of Koul [Behavior of robust estimators in the regression model with dependent errors. Ann Stat. 1977;5(4):681–699] and of Louhichi [Louhichi S. Weak convergence for empirical processes of associated sequences. Ann Inst Henri Poincaré Probabilités Statist. 2000;36(5):547–567].     

Difference-based matrix perturbation method for semi-parametric regression with multicollinearity

This paper addresses the collinearity problems in semi-parametric linear models. Under the difference-based settings, we introduce a new diagnostic, the difference-based variance inflation factor (DVIF), for detecting the presence of multicollinearity in semi-parametric models. The DVIF is then used to device a difference-based matrix perturbation method for solving the problem. The electricities distribution data set is analyzed, and numerical evidences validate the effectiveness of the proposed method.     

Shrinkage estimation of proportion via logit penalty

By releasing the unbiasedness condition, we often obtain more accurate estimators due to the bias–variance trade-off. In this paper, we propose a class of shrinkage proportion estimators which show improved performance over the sample proportion. We provide the “optimal” amount of shrinkage. The advantage of the proposed estimators is given theoretically as well as explored empirically by simulation studies and real data analyses.     

Estimation of parameters of inverse Weibull distribution and application to multi-component stress-strength model

The problem of estimation of the parameters of two-parameter inverse Weibull distributions has been considered. We establish existence and uniqueness of the maximum likelihood estimators of the scale and shape parameters. We derive Bayes estimators of the parameters under the entropy loss function. Hierarchical Bayes estimator, equivariant estimator and a class of minimax estimators are derived when shape parameter is known. Ordered Bayes estimators using information about second population are also derived. We investigate the reliability of multi-component stress-strength model using classical and Bayesian approaches. Risk comparison of the classical and Bayes estimators is done using Monte Carlo simulations. Applications of the proposed estimators are shown using real data sets.     

Swapping the Nested Fixed Point Algorithm: A Class of Estimators for Discrete Markov Decision Models

This paper proposes a new nested algorithm (NPL) for the estimation of a class of discrete Markov decision models and studies its statistical and computational properties. Our method is based on a representation of the solution of the dynamic programming problem in the space of conditional choice probabilities. When the NPL algorithm is initialized with consistent nonparametric estimates of conditional choice probabilities, successive iterations return a sequence of estimators of the structural parameters which we call K–stage policy iteration estimators. We show that the sequence includes as extreme cases a Hotz–Miller estimator (for K=1) and Rust's nested fixed point estimator (in the limit when K→∞). Furthermore, the asymptotic distribution of all the estimators in the sequence is the same and equal to that of the maximum likelihood estimator. We illustrate the performance of our method with several examples based on Rust's bus replacement model. Monte Carlo experiments reveal a trade–off between finite sample precision and computational cost in the sequence of policy iteration estimators.     

Small area estimation for longitudinal surveys

Over the last few years many studies have been carried out in Italy to identify reliable small area labour force indicators. Considering the rotated sample design of the Italian Labour Force Survey, the aim of this work is to derive a small area estimator which borrows strength from individual temporal correlation, as well as from related areas. Two small area estimators are derived as extensions of an estimation strategies proposed by Fuller (1990) for partial overlap samples. A simulation study is carried out to evaluate the gain in efficiency provided by our solutions. Results obtained for different levels of autocorrelation between repeated measurements on the same outcome and different population settings show that these estimators are always more reliable than the traditional composite one, and in some circumstances they are extremely advantageous.The present paper is financially supported by Murst-Cofin (2001) Lutilizzo di informazioni di tipo amministrativo nella stima per piccole aree e per sottoinsiemi della popolazione (National Coordinator Prof. Carlo Filippucci).