Small area estimation is becoming important in survey sampling due to a growing demand for reliable small statistics from both public and private sectors. It now widely recognized that direct estimates areas are likely yield unacceptably large standard errors the smallness of sample sizes areas. This makes it necessary "borrow strength" related find more accurate given or, simultaneously, several has led development alternative methods such as synthetic, size dependent, empirical best linear...

Penalized regression methods for simultaneous variable selection and coefficient estimation, especially those based on the lasso of Tibshirani (1996), have received a great deal attention in recent years, mostly through frequentist models. Properties such as consistency been studied, are achieved by different variations. Here we look at fully Bayesian formulation problem, which is flexible enough to encompass most versions that previously considered. The advantages hierarchical formulations...

The paper revisits the Bayesian group lasso and uses spike slab priors for variable selection. In process, connection of our model with penalized regression is demonstrated, role posterior median thresholding pointed out. We show that estimator has oracle property selection estimation under orthogonal designs, while suboptimal asymptotic rate when consistency achieved. Next we consider bi-level problem propose sparse again to select variables both at level also within a group. demonstrate...

Efron (1979, 1982), in his treatment of the bootstrap, discusses its use for estimation asymptotic variance sample median, sampling situation independent and identically distributed random variables with common distribution function $F$ having a positive derivative continuous neighborhood true median $\mu$. The natural conjecture that bootstrap estimator converges almost surely to is shown by an example be false unless tail condition imposed on $F$. We prove such strong convergence does hold...

Two problems have been discussed in this paper. First, for independent and identically distributed random variables with unknown mean variance, a sequential procedure is proposed point estimation of themean when the distribution unspecified. Second, estimating difference means two populations variances are (and not necessarily equal). The loss structure both cost observations plus squared error due to theunknown or means. Without any assumption on nature functions other than finiteness...

Abstract Bayesian techniques are widely used in these days for simultaneous estimation of several parameters compound decision problems. Often, however, the main objective is to produce an ensemble parameter estimates whose histogram some sense close population parameters. This example situation subgroup analysis, where problem not only estimate different components a vector, but also identify that above, and others below certain specified cutoff point. We have proposed this paper Bayes very...

Abstract Empirical Bayes methods are becoming increasingly popular in statistics. Robbins (1955) introduced the method context of nonparametric estimation a completely unspecified prior distribution. Subsequently, has been explored very successfully series articles by Efron and Morris (1973, 1975, 1977) parametric framework. In Efron—Morris setup, family distributions is used as possible priors, but only when one or more parameters estimated from data. (1983) listed number areas where...

Bayesian methods are increasingly applied in these days the theory and practice of statistics. Any inference depends on a likelihood prior. Ideally one would like to elicit prior from related sources information or past data. However, its absence, need rely some "objective" "default" priors, resulting posterior can still be quite valuable. Not surprisingly, over years, catalog objective priors also has become prohibitively large, set specific criteria for selection such priors. Our aim is...

The problem of obtaining sequential confidence intervals for the median an unknown symmetric distributon based on a general class one-sample rank-order statistics is considered. It shown that usual statistic possesses martingale or sub-martingale property according as parent distribution about origin not. Certain asymptotic almost sure convergence results (with specified order convergence) processes and empirical are derived, these then utilized study properties proposed procedures.

Covariance estimation and selection for high-dimensional multivariate datasets is a fundamental problem in modern statistics. Gaussian directed acyclic graph (DAG) models are popular class of used this purpose. DAG introduce sparsity the Cholesky factor inverse covariance matrix, pattern turn corresponds to specific conditional independence assumptions on underlying variables. A variety priors have been developed recent years Bayesian inference models, yet crucial convergence properties...

This paper extends and unifies the theory of simultaneous estimation for discrete exponential family. We discuss construction estimators which theoretically dominate uniformly minimum variance unbiased estimator (UMVUE) under a weighted squared error loss function, show by means computer simulation results that new Poisson perform more favorably than those previously proposed. Our improved shift UMVUE towards possibly nonzero point or data-based point.

Summary In surveys of natural populations animals, a sampling protocol is often spatially replicated to collect representative sample the population. these surveys, differences in abundance animals among locations may induce spatial heterogeneity counts associated with particular protocol. For some species, sources be unknown or unmeasurable, leading one specify variation stochastically. However, choosing parametric model for distribution unmeasured potentially subject error and can have...

Summary We suggest a technique, related to the concept of ‘detection boundary’ that was developed by Ingster and Donoho Jin, for comparing theoretical performance classifiers constructed from small training samples very large vectors. The resulting ‘classification boundaries’ are obtained variety distance-based methods, including support vector machine, distance-weighted discrimination kth-nearest-neighbour classifiers, thresholded forms those techniques based on Jin's higher criticism...

Abstract Inference procedures based on some simple rank statistics are proposed and studied for the statistical analysis of longitudinal data. These robust asymptotically efficient do not require basic assumption multivariate normality underlying distributions. The theory is illustrated with two examples.

The need for small area estimates is increasingly felt in both the public and private sectors order to formulate their strategic plans. It now widely recognized that direct survey are highly unreliable owing large standard errors coefficients of variation. reason behind this a usually designed achieve specified level accuracy at higher geography than areas. Lack additional resources makes it almost imperative use same data produce estimates. For example, if estimate per capita income state,...

Consider the problem of simultaneous testing for means independent normal observations. In this paper, we study some asymptotic optimality properties certain multiple rules induced by a general class one-group shrinkage priors in Bayesian decision theoretic framework, where overall loss is taken as number misclassified hypotheses. We assume two-groups mixture model data and consider framework adopted Bogdan et al. (2011) who introduced notion Bayes under sparsity context testing. The rich...

This paper considers benchmarking issues in the context of small area estimation.We find optimal estimators within class benchmarked linear under constraints.This extends existing results for external and internal benchmarking, also links two.Necessary sufficient conditions self-benchmarking are found an augmented model.Most this using ideas orthogonal projection.

Abstract. This paper considers simultaneous estimation of means from several strata. A model‐based approach is taken, where the covariates in superpopulation model are subject to measurement errors. Empirical Bayes (EB) and Hierarchical estimators strata developed asymptotic optimality EB proved. Their performances examined compared with that sample mean a simulation study as well data analysis.