Communications in Statistics: Theory and Methods

Yeh, Ching-Ming; Bradley, Ralph A.

doi: 10.1080/03610928308828438pmid: N/A

Designs for which treatment and block contrasts are orthogonal to specified common trend components within blocks have been called trend-free block designs. A necessary and sufficient condition for the existence of such designs was given in a reference. A matrix sum was required to have certain properties. It is shown now that the existence of a matrix with the required properties assures the existence of the necessary component matrices] The existence of trend-free block designs for specified trends in one or more dimensions is examined in a number of theorems and corollaries. Initial results are general and then trends in one dimension are considered. An alternative formulation of the necessary and sufficient condition for a trendfin one dimension are sufficient condition for a trendfree block design is given when each treatment has the same number of replications. Some special results are obtained for complete and balanced incomplete block designs. Some design construction methods are developed to establish the existence of certain trend-free block designs. But apart from the matter treatment labelling, trend-free block designs may not be uique. The construction methods used may lead to designs particularly vulnerable to incorrect modelling of trend components.

Gokhale, D.V.; Beaver, R.J.; Sirotnik, B.W.

doi: 10.1080/03610928308828439pmid: N/A

This paper provides a model-robust approach to the analysis of paired comparison experiments using the constrained likelihood ratio or the minimum discrimination information approach. In addition to tests of hypotheses regarding treatment worths and other effects, the present approach makes it possible to examine the assumption of linearity of intrinsic treatment worths on which many models are based.

Hua, Tsushung A.; Gunst, Richard F.

doi: 10.1080/03610928308828440pmid: N/A

Generalized ridge regression is extended to include negative values of the ridge parameter. In doing so, classes of biased estimators and estimators obtained by variable selection proce¬dures can be formulated as ridge estimators having stochastic, possibly negative, ridge parameter values.

Ponnapalli, R.

doi: 10.1080/03610928308828441pmid: N/A

When the multinomial probabilities are functions of a vector 8 it is shown that when bias correction is applied, the maximum likelihood estimator of 0 is least deficient in a class of estimators which includes the minimum chi-square and the minimum modified chi-square estimators. For the Hardy-Weinberg model Monte Carlo simulation is made for sample sizes ranging from ten to hundred which indicates the superiority of the maximum likeli¬hood estimator even for moderate sample sizes.

Kaiser, Lee D.; Bowden, David C.

doi: 10.1080/03610928308828442pmid: N/A

Four multiple comparisons procedures for all linear con¬trasts are applied in the one-way analysis of variance setting with possibly unequal variances and sample sizes. The achieved confidence level of each procedure is estimated in a simulation study. These methods include the method of Brown and Forsythe (1974b), the method derivable from the approximate degrees of freedom test of Welch (1951), and the standard method of Scheffe (1959). The method of Brown and Forsythe is found to perform poorly and an adjustment to their method is suggested and in¬cluded in the study. This adjusted method and the method from Welch's test have achieved confidence levels quite close to nominal levels.

Dey, Dipak K.

doi: 10.1080/03610928308828443pmid: N/A

Let X1,…Xpbe independent random variables, where each of the p distributions of the random variables belongs to the family of one parameter discrete exponential distributions. The problem is to estimate the unknown parameters simultaneously in the pres¬ence of extreme observations. Hudson (1978) and Tsui (1979) show that the minimum variance unbiased estimator (MVUE) of the param¬eters is inadmissible if p⩾3 under squared error loss, and esti¬mators better than MVUE are proposed. In this paper, a truncated version of the shrinkage estimator is proposed, in the case of discrete exponential family. This estimator is based on ordered observations which improves the MVUE.

Bera, A.; John, S.

doi: 10.1080/03610928308828444pmid: N/A

We consider a multivariate Pearson family of distributions. Certain parametric restrictions lead to the multivariate normal distribution. Using this fact we propose a number of asymptotically efficient tests. Through Monte Carlo experiments these tests are compared with some of the existing test procedures. A table is provided from which finite-sample critical points can be obtained.

Kulp, R.W.; Nagarsenker, B.N.

doi: 10.1080/03610928308828445pmid: N/A

In this paper new asymptotic expansions of the distributions of the sphericity test criterion are obtained in the null and the non-null case when the alternatives are close to the hypothesis. These expansions are obtained for the first time in terms of beta distributions. These appear to be better than the ones available in the literature.