On the Asymmetric Marcinkiewicz-Zygmund Strong Law of Large Numbers for Linear Random Fields

In this article, the asymmetric Marcinkiewicz-Zygmund strong law of large numbers for linear random field under negative association is obtained. Our result generalizes a result in Gut and Studtmüller (2009 Gut , A. , Studtmüller , U. ( 2009 ) An asymmetric Marcinkiewicz-Zygmund LLN for random fields . Statist. Probab. Lett. 79 : 1016 – 1020 .[Crossref], [Web of Science ®] , [Google Scholar]). An asymmetric Marcinkiewicz-Zygmund LLN for random fields to the linear random field by using the Beverige-Nelson decomposition.     

Admissibility of a variance estimator in finite population sampling under Warner's randomized response plan with multiple responses

ABSTRACT

Let P be the proportion of individuals in a finite population possessing a sensitive attribute. We consider the problem of unbiased estimation of (i) the variance of a linear unbiased estimator of P and (ii) the population variance P (1—P) for a given probability sampling design under Warner's (1965 Warner, S.L. (1965). Randomized response - A survey technique for eliminating evasive answer bias. J. Amer. Statist. Assoc. 60:63–69.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) randomized response (RR) plan when independent responses are obtained from each sampled individual as many times as he/she is selected in the sample and prove the admissibility of a quadratic unbiased estimator for each.     

Construction of uniform designs for mixture experiments with complex constraints

Abstract

Mixture experiments have attracted increasingly attention due to their great practical value in production and living, while uniform designs over irregular experimental regions have become a hot topic in the area of experimental designs in the past two decades. Noting that the experimental region of a mixture experiment with q components under some constraints is in fact a (q ? 1)-dimensional geometry, this article proposes a new method for searching nearly uniform designs for mixture experiments with any complex constraints. Two examples with some tables and figures are given to illustrate this method.     

Testing for abrupt breaks in variance structures with smooth changes

Abstract

We investigate the problem of testing for variance breaks in the case where the variance structure is assumed to be smoothly time-varying under the null. Since the classical tests are aimed to detect any change in the variance, they are not able to distinguish between smooth non constant variance and abrupt breaks. In this paper a new procedure for detecting variance breaks taking into account for smooth changes in the variance under the null is proposed. The finite sample properties of the test we introduce are investigated by Monte Carlo experiments. The theoretical outputs are illustrated using U.S. macroeconomic data.     

A note on the estimation of pr{y<x} for truncation parameter distributions

In this note a relationship in the treatment of the lower and upper truncations considered in Beg (1980) is pointed out and the minimum variance unbiased estimator of P = Pr{Y<X) for the (upper) truncated exponential distribution is obtained.     

Estimation of pr{y<x) for truncation parameter distributions

Blackwell-Rao-Lehmann-Scheffe theory is used to derive the minimum variance ur biased estimator of P=Pr{Y<X} when the independent random variables X and Y follow thf truncation parameter distributions The two-parameter exponential, Pareto, power function and uniform distributions are considered in examples.     

On estimation of the mean parameter of a truncated normal disiribution with known coefficient of variation

This paper eals with the proplem on estimating the mean paramerer of a truncated normal distribution with known coefficient of variation. In the previous treatment of this problem most authors have used the sample standared deviation for estimating this parameter. In the present paper we use Gini’s coefficient of mean difference g and obtain the minimum variance unbiased estimate of the mean based on a linear function of the sample mean and g, It is shown that this new estimate has desirable properties for small samples as well as for large samples. We also give a numerical example.     

On the optimality of the sample variance

The present paper explores the structure of linear exponential families for which the sample variance is a uniformly minimum variance unbiased estimator.     

Decision and choice in transforming data

Statistics are developed for predicting the effect of data transformations on the F statistic when the assumptions of homoscedasticity and normality underlying the AN OVA are not necessarily satisfied. These statistics are useful for determining whether and how to transform, They are developed by partitioning the change in the observed value of the jF-statistic under the transformation, into two expressions, one of which depends on the "truth" of HQ while the other does not. Using this partition, desirable properties are derived for transformations. Criteria are developed defining transformations which tend to preserve the type 1 error while increasing power when needed. Using these criteria, the notion of model robustness is introduced. It is shown that the Box-Cox methodology for selecting a power transform may, under certain conditions, produce a transformation which does not permit inferences to be made about the parent population from the transformed population. An alternative approach suggested here does permit such inferences.