Asymptotic properties of a generalized regression-type predictor of a finite population variance in probability sampling

A system of predictors for estimating a finite population variance is defined and shown to be asymptotically design-unbiased (ADU) and asymptotically design-consistent (ADC) under probability sampling. An asymptotic mean squared error (MSE) of a generalized regression-type predictor, generated from the system, is obtained. The suggested predictor attains the minimum expected variance of any design-unbiased estimator when the superpopulation model is correct. The generalized regression-type predictor and the predictor suggested by Mukhopadhyay (1990) are compared.     

Relationships of optimality for individual factors of a design

The optimality of two-factor experimental designs is studied in the dual senses of estimating contrasts in the parameters for each of the factors. The outline of comparison employed allows one to judge the performance of different designs for estimating contrasts of one set of parameters directly with the performance of the complementary set without going through a common intermediary step of considering all the parameters. The results hold for a wide class of optimality criteria (not merely D-, A- and E-optimality), which must satisfy a functional equation obtained in connection with our method. Also we investigate the optimality of row–column designs which satisfy an ‘adjusted orthogonality’ condition. Our point of departure is the paper by Shah, Raghavarao and Khatri (1976) and that of Mitchell and John (1977).     

An infinite class of PBIB designs

In this paper, an infinite class of partially balanced incomplete block (PBIB) designs of m+1 associate classes is constructed through the use of a series of row-orthogonal matrices known as partially balanced orthogonal designs (PBOD) of m-associate classes. For the purpose, a series of PBOD is obtained through a method described herein. An infinite class of regular GD designs is also reported.     

Designing two factor experiments for selecting interactions

This paper considers the problem of devising a single stage procedure for selecting the treatment combination associated with the largest interaction in a two-factor rfx× c experiment having independent normally distributed observations with common known variance. The intuitive procedure based on the best linear unbiased estimators of the population interactions is employed. Initially an indifference zone formulation is used; the problem of determining the least favorable configuration is reduced to a nonlinear programming problem with log concave objective function and a convex polytope as feasible region. A solution technique is introduced in the context of an illustrative example. The problem is also considered using a preferred population formulation; this approach requires a strengthened version of the indifference zone probability requirement. It is shown that the same sample size guarantees this requirement as does the earlier one.     

Generalized Youden designs: construction and tables

Generalized Youden Designs are generalizations of the class of two-way balanced block designs which include Latin squares and Youden squares. They are used for the same purposes and in the same way that these classical designs are used, and satisfy most of the common criteria of design optimality.We explicitly display or give detailed instructions for constructing all these designs within a practical range: when υ, the number of treatments, is ?25; and b₁ and b₂, the dimensions of the design array, are each ?50.     

20世纪“帝王谷”重大发现简介

20世纪帝王谷考古发掘工作取得了重大突破,其中有三个重要坟墓的发现值得介绍和研究.KV62以其丰富的陪葬品被称为"埃及宝库",是20世纪最伟大的考古发现之一,KV5的规模之庞大令人赞叹,KV55所具有的争议性将长期受到国内外学者的关注.     

Inferences concerning interpersonal choices given anonymously

It may be difficult or impossible to make a reliable empirical investigation of an unknown network of interpersonal choices or contacts if these are in some respect sensitive for the individuals involved. We consider how choice data given anonymously can be used to reveal various features of the network. Using tools from statistical decision theory and information theory we can determine risks and capacities of disclosing choice data, the graph structure of choice data and its numbers of loops and mutuals. We give some general results, illustrate the combinatorial complexity of the problem and comment upon the computational difficulties.     

Optimal estimation of a finite population mean under generalized random permutation models

Employing certain generalized random permutation models and a general class of linear estimators of a finite population mean, it is shown that many of the conventional estimators are “optimal” in the sense of minimum average mean square error. Simple proofs are provided by using a well-known theorem on UMV estimation. The results also cover certain simple response error situations.     

Projective (2n,n,λ,1)-designs

A projective (2n,n,λ,1)-design is a set $\text{D}$ of n element subsets (called blocks) of a 2n-element set V having the properties that each element of V is a member of λ blocks and every two blocks have a non-empty intersection. This paper establishes existence and non-existence results for various projective (2n,n,λ,1)-designs and their subdesigns.     

Procedures for improving the mle for ordered binomial parameters

The problem is that of estimating the probabilities of m independent binomial random variables when their probabilities are known to be nondecreasing and the loss function is squared error. In the cases where the m.l.e. is inadmissible (essentially when the total number of trials is 7 or more) we present a method for modifying the m.l.e. to get a better estimator. The method requires a series of changes. At each step we alter the action taken by the m.l.e. on each of three, appropriately chosen, points in the sample space.