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In this article we propose two minimum chi-square estimators for a bivariate probit model. We call one estimator the Full Information and the other Limited Information Minimum Chi-Square because the first takes account of all the a priori information while the second does not. Both estimators are shown to be consistent. Moreover, the first is shown to be asymptotically as efficient as the maximum likelihood estimator and yet is computationally much simpler. For illustration, estimates are computed for the data used by Ashford and Sowden [1970.] [ABSTRACT FROM AUTHOR]

A method is given for obtaining sequential tests of composite hypotheses for a certain class of distributions. Approximate properties of the tests are derived and the method illustrated. [ABSTRACT FROM AUTHOR]

A test for the hypothesis of zero second-order interaction is proposed. The test is obtained by making use of conditional reference sets which are derived in Zelen [17]. This permits the derivation of an exact conditional test of significance for testing the hypothesis of zero second order interaction. The techniques used, in approximating the large sample distribution of this test, are extensions of those due to Gart [5] and Zelen [17]. The test is applied to a numerical example. [ABSTRACT FROM AUTHOR]

Suppose a population containing items classified either as defectives or as non-defectives. This article presents a new group testing method to detect all defectives in the population. The proposed method applies either when the actual number of defectives {or an upper bound) is known or when its probability distribution is known. The method is surprisingly simple yet compares favorably with other existing methods by the number of tests required to detect all defectives. [ABSTRACT FROM AUTHOR]

The probabilities of the Type I errors of the Welch approximate-t test and the Aspin-Welch test for the Behrens-Fisher problem have been calculated for selected sets of degrees of freedom and nominal significance levels. The results show satisfactory agreement to the desired level. Thus, in practice, one can just use the usual t-table to carry out the Welch approximate t-test without much loss of accuracy. [ABSTRACT FROM AUTHOR]

Let t[sub I]= x[sub I]/s, I = 1, 2 be noncentral Student t-variates with noncentrality parameters delta[sub I], where x[sub 1], x[sub 2] and s are independent. The simultaneous distribution of t[sub 1] and t[sub 2] is studied and the power function of the studentized maximum and minimum modulus tests are tabulated for significance level 0.05, degrees of freedom 1, 2, 5, 10, 20, 50, infinity and delta[sub 1], delta[sub 2] = 0(1)5. Asymptotically exact approximations to these power functions are discussed. The marginal power of the maximum modulus test is also tabulated. [ABSTRACT FROM AUTHOR]

An investigation of stratification is reported for a universe with strong positive skewness. The choice of stratification variable, the method of constructing strata, the sample allocation, and the number of strata are considered. Comparisons are made among four types of allocation in combination with the corresponding optimum stratifications. For four simpler methods of stratification, equal allocation and allocation proportional to stratum aggregates are contrasted. Gain from stratification are examined for several estimation variables. Illustrations utilize data for the 1961 universe of United States nonfederal general medical hospitals for short-term care. However, the finding apply to the stratification of other populations having similar distribution functions. [ABSTRACT FROM AUTHOR]

After a brief motivating discussion of approaches to significance tests in Section 1, the concept of expected significance level (ESL) is defined and its basic properties are presented in Section 2. Section 3 discusses the relationship between ESL and the familiar criterion of power. While a complete description of power for each size alpha is more informative than ESL, it is argued that ESL is often a reasonable compromise between high ideals and practicability. Section 4 gives two estimation methods for Monte Carlo simulation of ESL and shows how to estimate variances and covariances for the second of these methods. The first method leads to the familiar Wilcoxon two-sample statistic which is clearly a sample analogue of ESL. The second and more apposite method leads to a modification of the Wilcoxon statistic. [ABSTRACT FROM AUTHOR]

Two exact tests are presented for testing the hypothesis that the residuals from a least squares regression are homoscedastic. The results can be used to test the hypothesis that a linear [ratio] model explains the relationship between variables as opposed to the alternative that the ratio [linear ] specification is correct. The first test is parametric and uses the F-statistic. The second test is nonparametric and uses the number of peaks in the ordered sequence of unsigned residuals. In conclusion, the results of some experimental calculations of the powers of the tests are discussed. [ABSTRACT FROM AUTHOR]

This paper deals with the asymptotic relative efficiency (A.R.E.) and the asymptotic power of certain tests. These tests are distribution-free goodness-of-fit tests based on the empirical distribution function. They are the one and two sided Kolmogorov-Smirnov tests and a new one based on the absolute values of the order statistics. The method of obtaining the A.R.E. is due to Quade [5] and is outlined in Section 1. In this paper we are concerned with the case of scalar alternatives. The asymptotic power for the Kolmogorov-Smirnov tests is obtained in Section 2. Section 3 deals with a new test which allows a more facile use of a one-sided statistic while utilizing the same information normally included in a two-sided statistic. In Section 4, three examples are considered to illustrate the superiority of this new test. [ABSTRACT FROM AUTHOR]

This paper presents derivations of expressions for the probability of killing a randomly located point target and for the expected coverage of an area target, of variable density. Particular emphasis is placed upon a general situation in which the phase distribution is not necessarily uniform. General distributions are employed to describe the phase, radial, and component behavior of the target and from these functions the distribution of a quadratic form is derived that provides the expected coverage or kill probability. The targeting conditions include a fixed lethal radius (kill-no-kill) when the center of gravity of the weapon impact points coincides with the center of the target density and a variable lethal radius when a weapon bias is present. [ABSTRACT FROM AUTHOR]

A method is presented of obtaining the minimum chi[sup 2, sub 1] estimates for the problem of "no interaction" defined in the model of logit additivity, with some examples, and these are compared with the ML estimates. The chi[sup 2, sub L] of Nagnur is compared with the Pearson chi[sup 2] for the two sets of estimates, and a striking difference in the comparison of the two chi[sup 2]'s for the ML and minimum chi[sup 2, sub 1] estimates is noted. [ABSTRACT FROM AUTHOR]

The planned replacement problem assumes a known failure distribution F(t) and that replacement occurs at the earlier of a planned replacement interval (at cost ci) and the time of failure (at cost c2). We show that it cannot be optimal to select a planned replacement interval at a point for which the failure rate f(t)f[I-F(t)1 is decreasing. [ABSTRACT FROM AUTHOR]