On the asymptotic distribution of a class of aligned rank order test statistics in randomized block designs

In the present investigation, the unconditional asymptotic distribution of a class of aligned rank order test statistics for randomized block designs is derived under the null hypothesis and for nearby alternatives, as the number of blocks tends to infinity. The proofs of these results are based on the asymptotic equivalence in quadratic mean between aligned observations and their ranks and thus are quite similar to the Hájek and SKidák (1967) approach.     

Estimating the asymptotic relative efficiency of weighted rankings

Five tests for the hypothesis of no treatment effects in complete blocks designs are compared with respect to asymptotic relative efficiency: the ordinary two-way analysis of variance, the analysis of variance of ranks (Friedman, 1937), the method of ranking after alignment (Hodges and Lehmann, 1962), and a method of weighted rankings proposed by Quade (1972, 1979). This comparison required devising a procedure for estimating the asymptotic relative efficiencies of test statistics with asymp-totic chi-squared distributions.     

Asymptotic optimality of a class of rank tests for replicated latin-square designs

This paper is concerned with the class of conditionally distribution-free rank tests introduced by Monga and Tardif (1994) for replicated Latin-square designs. It is possible to proceed with an enlargement of this class by making use of the method of ranking after substitution. The unconditional asymptotic behaviour of any member of the enlarged class is derived under the null hypothesis of no treatment effects as well as under a sequence of contiguous alternatives. This enables the establishment of the asymptotic Pitman efficiency of any member relative to the asymptotically minimax test and to conclude that at least one member of the class is asymptotically as efficient as the latter.     

Asymptotic optimality of rank tests for randomized blocks

Both the method of ranking after alignment and the Tukey-Quade method of weighted rankings for the analysis of complete blocks are generalized so as to give rise to classes of tests containing a conditionally distribution-free test and strictly distribution-free tests that are asymptotically optimal in the sense that, when the number of blocks tends to infinity, their asymptotic local power reaches the one of the asymptotically minimax test based on block-location-free statistics.     

Comparison of unweighted and weighted rank based tests for an ordered alternative in randomized complete block designs

In randomized complete block designs, a monotonic relationship among treatment groups may already be established from prior information, e.g., a study with different dose levels of a drug. The test statistic developed by Page and another from Jonckheere and Terpstra are two unweighted rank based tests used to detect ordered alternatives when the assumptions in the traditional two-way analysis of variance are not satisfied. We consider a new weighted rank based test by utilizing a weight for each subject based on the sample variance in computing the new test statistic. The new weighted rank based test is compared with the two commonly used unweighted tests with regard to power under various conditions. The weighted test is generally more powerful than the two unweighted tests when the number of treatment groups is small to moderate.     

A modified Friedman test for randomized complete block designs

The Friedman test is often used for a randomized complete block design when the normality assumption is not satisfied or the data are ordinal. The Friedman test can be viewed as an extension of the sign test for multiple measurements within each subject or block. We propose a modified Friedman test based on the Wilcoxon sign rank approach. Coincidentally, Tukey proposed a test statistic similar to our proposed test, but blocks are ranked by the minimum difference within each block. In the proposed test, we use the variance of block to rank the blocks, with the least variance being ranked the smallest. In both Tukey test and the modified Friedman test, linear ranks are used for blocks and treatments. The Tukey test belongs to the family of weighted-ranking test from Quade (1979 Quade, D. (1979). Using weighted rankings in the analysis of complete blocks with additive block effects. Journal of the American Statistical Association 74(367):680–683. [Google Scholar]).The modified Friedman test, the Friedman test and the Tukey test are compared under various conditions and the results indicate that the proposed test is generally more powerful than the Friedman test and the Tukey test when the number of groups is small.     

A study of several useful tests for ordered alternatives in the randomized block design

This study investigates the small sample powers of several tests designed against ordered location alternatives in randomized block experiments. The results are intended to aid the researcher in the selection process. Toward this end the small sample powers of three classes of rank tests — tests based on ‘within-blocks’ rankings (W-tests), ‘among-b locks’ rankings (A-tests), and ‘ranking after alignment’ within blocks (RAA-tests)— are compared and contrasted with the asymptotic properties given by Pirie (1974) as well as with the empirical powers of competing parametric procedures.     

On the block structure of proper block designs

In this paper we consider proper block designs and derive an upper bound for the number of blocks which can have a fixed number of symbols common with a given block of the design. To arrive at the desired bound, a generalization of an integer programming theorem due to Bush (1976) is first obtained. The integer programming theorem is then used to derive the main result of this paper. The bound given here is then compared with a similar bound obtained by Kageyama and Tsuji (1977).     

A monte carlo study of the f test and three tests based on ranks of treatment effects in randomized block designs

The F test is compared with three procedures based on ranks for testing treatment effects in the randomized complete block, fixed effects, model with one observation per cell.     

Testing equality of conditionally jfclhwdqw exponential distributions

For the models given V = v (a common random stress), X and Y are independently exponentially distributed with failure rates λ₁and λ₂v, testing H₀λ₁λ₂using a random ‘paired’ sample is considered. It is shown that a uniformly most powerful invariant test does not exist even for one sided alternatives; locally most powerful invariant tests are derived and compared with existing procedures. The method is illustrated with reliability data. Finally, the robustness of the tests when the relationships of the failure rates to V is more complex are established.     

A Bayesian approach to analysis of covariance in balanced randomized block experiments

Analysis of covariance in designed experiments has a long history dating back to the middle of the twentieth century. Given the popularity of Bayesian approaches to statistical modelling and inference, it is somewhat surprising that there is so little literature on the application of Bayesian methods in this context. This paper proposes methods based on a recent formulation of the problem in terms of a multivariate variance components model which allows for a conjugate Bayesian analysis of balanced randomized block experiments with concomitant information. The analysis is complicated by a linear constraint involving two covariance matrices. Two solutions are proposed and implemented using Markov chain Monte Carlo methods.     

A class of nonparametric tests for location and scale parameters

A class of nonparametric two-sample tests for testing identity of distributions versus alternatives containing both location and scale parameters is proposed and some properties are derived. A recursion formula for the exact distribution under the hypothesis is presented and, the asymptotic distribution is given under both the hypothesis and a contiguous sequence of alternatives. Some asymptotic optimality properties are deduced for particular tests of the class and finally, the asymptotic efficiency is found.     

Weighted combinations of rank tests for location-scale alternatives

All existing location-scale rank tests use equal weights for the components. We advocate the use of weighted combinations of statistics. This approach can partly be substantiated by the theory of locally most powerful tests. We specifically investi= gate a Wilcoxon-Mood combination. We give exact critical values for a range of weights. The asymptotic normality of the test statistic is proved under a general hypothesis and Chernoff-Savage conditions. The asymptotic relative efficiency of this test with respect to unweighted combinations shows that a careful choice of weights results in a gain in efficiency.     

Approximate and exact distributions of rank tests for balanced incomplete block designs

Judges rank k out of t objects according to m replic ations of abasic balanced incomplete block design with bblocks. In Alvo and Cabilio(1991),it is shown that the Durbin test, which is the usual test in this situation, can be written in terms of Spearman correlations between the blocks, and using a Kendall correlation, they generated a new statistic for this situation.This Kendall tau based statistic has a richer support than the Durbin statistic, and is at least as efficient.In the present paper,exact and simulation based tables are generated for both statistics, and various approximations to these null distributions are considered and compared.     

A note on asymptotic expansions for the power of perturbed tests

For simplicity or tractability reasons one sometimes uses modified test statistics, which differ from the original ones up to O_p(a_n) terms with a_n→0. In this note, some technical conditions are provided under which a corresponding expansion for the powers of such perturbed tests holds. The necessity of some of these conditions is discussed and illustrated by examples. An application to invariant testing multivariate normality is presented.     

On the asymptotic efficiency of moment and maximum likelihood estimators in the three-parameter inverse gaussian distribution

The asymptotic distribution of estimators generated by the methods of moments and maximum likelihood are considered. Simple formulae are provided which enable comparisons of asymptotic relative efficiency to be effected.     

Measures of non orthogonality in block designs

Orthogonality is an important concept in block design. Necessary and sufficient condition for a connected block design to be orthogonal is well known. However, when a design is not orthogonal, it is not clear how much it deviates from orthogonality. In this paper, an attempt has been made to first define the measures of or indices to non orthogonality in block design and then to characterize designs possessing minimum non orthogonality indices. It is shown that a Balanced Incomplete Block Design (BIBD) and a Balanced Block Design (BBD), if exist, possess this property.     

Adaptively combining independent jonckheere statistics in a randomized block design with unequal scales

Jonckheere (1954) proposed a test statistic which is commonly used in testing for ordered alternatives in block designs.- We consider the application of Jonckheere's test statistic in block designs which have unequal scale parameters for the blocks. Estimates of the unknown scale parameters ar-fcrmed and are used to construct a modification of Jonckheere's test statistic using adaptive ideas. A Monte Carlo study shows that the modified Jonckheere is significantly more powerful than the original Jonckheere in many unequal scale situations.     

Some useful nonparametric tests for ordered alternatives in randomized block experiments

Testing for ordered alternatives in randomized block designs has been a problem of interest for almost three decades (Jonckheere (1954)). Three classes of rank tests have evolved—tests based on “within-blocks” rankings (W-tests), tests based on “ranking after alignment” within blocks (RAA-tests), and tests based on “among-blocks” rankings (A-Tests). This paper focuses on the latter. A simplified version of the Skillings-Wolfe generalized Purl test (1977) is suggested and two very useful A-tests—a generalized Johnson-Mehrotra “Optimal contrast” procedure and a generalized Tryon-Hettmansperger rank test—are developed. These procedures are compared and contrasted with other recent competitors presented by Skllllngs and Wolfe (1978) and by Salama and Quade (1981).     

On an asymptotic relative efficiency concept based on expected volumes of confidence regions

ABSTRACT

The paper deals with an asymptotic relative efficiency concept for confidence regions of multidimensional parameters that is based on the expected volumes of the confidence regions. Under standard conditions the asymptotic relative efficiencies of confidence regions are seen to be certain powers of the ratio of the limits of the expected volumes. These limits are explicitly derived for confidence regions associated with certain plugin estimators, likelihood ratio tests and Wald tests. Under regularity conditions, the asymptotic relative efficiency of each of these procedures with respect to each one of its competitors is equal to 1. The results are applied to multivariate normal distributions and multinomial distributions in a fairly general setting.