Minimax prediction in finite populations

In this paper, minimax predictors are considered for some population quantities of interest, under some specific superpopulation models. Minimax predictors are derived under a binomial superpopulation model. The well known ratio estimator is shown to be minimax under the usual simple regression normal model. Nonparametric minimax predictors are considered under some models. Some of the predictors considered also shown to be admis s ible.     

Alternative parameter estimators based upon grouped data

The problem of estimating population parameters based upon grouped data is considered and several alternative estimation schemes such as the method of scoring, least lines, least squares, minimum chi square, and a method of approximating method of moments and maximum likelihood estimators are considered. These estimators are compared with maximum likelihood and method of moments estimators based upon individual observations using a Monte Carlo study where the parent population is characterized by a gamma distribution. An application of these techniques to fitting a gamma distribution to 1970-74 census income data is considered.     

Sample-size requirements for confidence bounds of prescribed precision on multivariate normal quantiles

The problem of setting confidence bounds on a central multivariate normal quantile is considered. It is shown that for the setting of exact confidence bounds of specified closeness to the quantile,the required minimum size of a normal sample is large and rises rapidly with the number of variates considered.     

ON THE SIMPLE PROJECTION PREDICTOR IN FINITE POPULATIONS

In this paper, necessary and sufficient conditions for optimality of the simple projection predictor (SPP) are considered under a superpopula-tion model with a not necessarily diagonal covariance matrix. Conditions under which the SPP remains optimal, under possible covariance matrix misspecifications, are also considered.     

Non Asymptotic Minimax Estimation of Functionals with Noisy Observations

The minimax estimation of functionals by a finite number of noisy observations is considered. A new way to formalize the problem that enables one to calculate non asymptotic optimal estimates is proposed. The calculations can be turned into and executed as a computer algorithm or carried out analytically under week assumptions on random variables. Some examples are considered.     

Estimating the Population Coefficient of Variation by Confidence Intervals

Several researchers considered various interval estimators for estimating the population coefficient of variation (CV) of symmetric and skewed distributions. Since they considered at different times and under different simulation conditions, their performances are not comparable as a whole. In this article, an attempt has been made to review some existing estimators along with some proposed methods and compare them under the same simulation condition. In particular, we have considered Hendricks and Robey, Mckay, Miller, Sharma and Krishna, Curto and Pinto, and also some bootstrap proposed interval estimators for estimating the population CV. A simulation study has been conducted to compare the performance of the estimators. Both average widths and coverage probabilities are considered as a criterion of the good estimators. Two real life health related data sets are analyzed to illustrate the findings of the article. Based on the simulation study, some possible good interval estimators have been recommended for the practitioners.     

Information loss on the dependence parameter due to incomplete data from a one-parameter spatial gaussian process

The Fisher information loss on the dependence parameter is considered for three one-parameter Gaussian processes on a rectangular lattice when some values are not observed. Formulae are given for the general case, and simplified versions for two of the special cases. Approximations are considered, and cases with a small number of missing sites are compared.     

Bayesian D-optimal design for logistic regression model with exponential distribution for random intercept

ABSTRACT

Nowadays, generalized linear models have many applications. Some of these models which have more applications in the real world are the models with random effects; that is, some of the unknown parameters are considered random variables. In this article, this situation is considered in logistic regression models with a random intercept having exponential distribution. The aim is to obtain the Bayesian D-optimal design; thus, the method is to maximize the Bayesian D-optimal criterion. For the model was considered here, this criterion is a function of the quasi-information matrix that depends on the unknown parameters of the model. In the Bayesian D-optimal criterion, the expectation is acquired in respect of the prior distributions that are considered for the unknown parameters. Thus, it will only be a function of experimental settings (support points) and their weights. The prior distribution of the fixed parameters is considered uniform and normal. The Bayesian D-optimal design is finally calculated numerically by R3.1.1 software.     

Confidence intervals for finite difference solutions

Although applications of Bayesian analysis for numerical quadrature problems have been considered before, it is only very recently that statisticians have focused on the connections between statistics and numerical analysis of differential equations. In line with this very recent trend, we show how certain commonly used finite difference schemes for numerical solutions of ordinary and partial differential equations can be considered in a regression setting. Focusing on this regression framework, we apply a simple Bayesian strategy to obtain confidence intervals for the finite difference solutions. We apply this framework on several examples to show how the confidence intervals are related to truncation error and illustrate the utility of the confidence intervals for the examples considered.     

On conditional sampling strategies

Estimation of the population average by means of a conditional strategy has been considered e.g. in [2–6,9] and [10]. Let us assume that the sampling design depends on a function of an auxiliary variable called an auxiliary statistic like: the sample mean or the sample variance. Under the conditional versions of these designs several estimators of the population mean are considered: the Horvitz-Thompson statistic, ratio and regression type estimators. The unbiasedness and accuracy of the strategies are considered. The empirical example of the accuracy comparisons of strategies is developed. The conditional strategies could improve the accuracy of estimation and protect it against outliers observations.     

Sample size needed to get given ratio of endpoints for confidence interval of standard deviation in a normal distribution

Confidence interval (CI) for a standard deviation in a normal distribution, based on pivotal quantity with a Chi-square distribution, is considered. As a measure of CI quality, the ratio of its endpoints is taken. There are given formulas for sample sizes so that this ratio does not exceed a fixed value. Both equally tailed and minimum ratio of endpoint CIs are considered.     

Estimating parameters in autoregressive models in non-normal situations: symmetric innovations

The estimation of coefficients in a simple regression model with autocorrelated errors is considered. The underlying distribution is assumed to be symmetric, one of Student's t family for illustration. Closed form estimators are obtained and shown to be remarkably efficient and robust. Skew distributions will be considered in a future paper.     

A likelihood ratio test for interaction among variances

A likelihood ratio test for interaction in an analysis of variance model, when observations are variances is considered. Another statistic based on the logarithmic transformation is also considered and the null and non-null distributions of the test statistics are considered.     

Outliers in Multi-Response Experiments

Cook-statistic has been developed for detecting outliers in two likely situations of occurrence of outliers in multi-response experiments. In the first situation, more than one outlying observations vector has been considered. Each of these vectors is obtained on the assumption that a particular observation from each of the responses is an outlier. A general expression of Cook-statistic for detecting any such t outlying observations vectors has been obtained. Then some particular cases have been considered. In the second case a situation is considered where observations from all the responses may not be outliers. Here also a general expression of Cook-statistic is obtained for detecting any t observations from each of any k responses as outliers. In both the cases Cook-statistic is applied to real experimental data.     

Bayesian approach to change point problems

A Bayesian approach is considered to study the change point problems. A hypothesis for testing change versus no change is considered using the notion of predictive distributions. Bayes factors are developed for change versus no change in the exponential families of distributions with conjugate priors. Under vague prior information, both Bayes factors and pseudo Bayes factors are considered. A new result is developed which describes how the overall Bayes factor has a decomposition into Bayes factors at each point. Finally, an example is provided in which the computations are performed using the concept of imaginary observations.     

Bounds on deviations of estimates arising in finite population regression models

Bounds for the maximum deviation between parameters of a finite population and their corresponding sample estimates are found in the multiple regression model. The parameters considered are the vector of regression coefficients and the value ofthe regression function for given values of the independent variable (or variables). Applications are considered to several widely employed sampling methods.     

The geometric CUSUM chart with sampling inspection for monitoring fraction defective

The detection of an upward shift in the fraction defective of a repetitive process is considered using the geometric CUSUM. This CUSUM makes use of the information provided by the run-lengths of non-defective items between successive defective items, and was initially developed for the case of 100% inspection. This paper considers the geometric CUSUM under sampling inspection, and emphasizes that the pattern of sampling inspection can be quite haphazard without causing any difficulty for the operation of the CUSUM. Two separate mechanisms for the occurrence of a shift are considered. Methods for evaluating zero-state and steady-state ARL are presented for both 100% inspection and sampling inspection. Parameter choice is also considered, and recommendations made. Comparisons with some np -charts are provided.     

Anova and minque type of estimators for the one-way random effects model

The one-way random effects model with unequal variances and unequal sample sizes is considered. Estimation of the variances, variance of a single observation (total variance), and the standard error of the unweighted mean are considered. Precision of the Analysis of Variance and Unweighted Sums of Squares type of estimators and the Minimum Norm Quadratic Unbiased Estimators with a priori weights are examined.     

An economic rectification plan for a process subject to a random shift into a persistent defective state

A rectification strategy is considered for a process which is subject to a random shift into a persistent defective state. The expected costs associated with plans other than the basic retrospective unit by unit procedure are considered and a simple criterion is derived to identify that with approximate minimum expected cost. The validity of the application is discussed and an example is given to illustrate the inductive nature and simplicity of the technique.     

Influence measures in blocked designs of experiments with correlated errors

Diagnostics measures for detecting outliers in data from block designs of experiments with correlated errors are considered. Influence is often assessed by deleting suspected outlying observations. Autocorrelation of order one is considered to model correlation in each block. Cook-statistic is developed for detecting the effect of a single outlier, where results are illustrated with an example.