A quest for certain linear spaces on thirty points

We investigate the structure of linear spaces on 30 points which have no lines of sizes 2, 3, 6, 30.     

Rank-order tests for the parallelism of several regression surfaces

For testing the hypothesis that several (s?2) linear regression surfaces X_ki=α_k+β_kc_ki+Z_ki (k=1,…,s) are parallel to one another, i.e., β₁=?=β_s, a class of rank-order tests are considered. The tests are shown to be asymptotically distribution-free, and their asymptotic efficiency relative to the general likelihood ratio test is derived. Asymptotic optimality in the sense of Wald is also discussed.     

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).     

Estimating the distribution of one-dimensional discrete scan statistics viewed as extremes of 1-dependent stationary sequences

Discrete one-dimensional scan statistics can be viewed as extremes of 1-dependent stationary sequences. A result of Haiman [1999. First passage time for some stationary processes. Stochastic Process. Appl. 80, 231–248] provides approximations of the distributions of extremes of 1-dependent stationary sequences together with sharp bounds for the corresponding errors. We apply this result to scan statistics generated by Bernoulli r.v.'s and to the charge problem.     

Note on the Cramér-Rao inequality in the nonregular case: the family of uniform distributions

We consider the family of uniform distributions with range of unit length. The main result of this note asserts that the average variance of any unbiased estimator of the midpoint of the range is not less than (2(n+1))(n+2))^-1 and this lower bound is sharp. The proof is based upon a nonregular version of the Cramér-Rao inequality.     

Conditional inference for subject-specific and marginal agreement: Two families of agreement measures

A two-stage procedure is described for assessing subject-specific and marginal agreement for data from a test-retest reliability study of a binary classification procedure. Subject-specific agreement is parametrized through the log odds ratio, while marginal agreement is reflected by the log ratio of the off-diagonal Poisson means. A family of agreement measures in the interval [-1, 1] is presented for both types of agreement. The conditioning argument described facilitates exact inference. The proposed methodology is demonstrated by way of an example involving hypothetical data chosen for illustrative purposes, and data from a National Health Survey Study (Rogot and Goldberg 1966).     

A note on the asymptotic optimality of a two population sequential probability ratio test

It is shown that a two population sequential probability ratio test studied by a number of recent authors in the context of sequential medical trials is asymptotically optimal.     

Complete designs with blocks of maximal multiplicity

The set of distinct blocks of a block design is known as its support. We construct complete designs with parameters v(?7), k=3, λ=v ? 2 which contain a block of maximal multiplicity and with support size $\text{b}{}^1\text{= (}{}^{\mathrm{v}}{}_3\text{) ? 4(v ? 2)}$. Any complete design which contains such a block, and has parameters v, k, λ as above, must be supported on at most (^v₃) ? 4(v ? 2) blocks. Attention is given to complete designs because of their direct relationship to simple random sampling.     

Robustness of the linear discriminant function to nonnormality: Johnson's system

The asymptotic distribution of the Errors of Misclassification in using the Linear Discriminant Function is investigated here. The purpose is to study the effects of nonnormality on these errors. The class of distributions considered is the Johnson's system. Each of the three random variables can be transformed to normality. In one particular case numerical evaluations are made, based on which it is possible to recommend whether or not it is necessary to make the transformation prior to classification. In a parallel study, we present similar results for the Edgeworth Series distribution, where the random variables cannot be transformed to normality.     

A note on the universal optimality criterion for full rank models

The aim of this note is to suggest a revised formulation of the universal optimality criterion for full rank models as stated in Kiefer (1975). We have presented the relevant results with indications of some possible applications.