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In this paper a method is developed for estimating the parameters in the multivariate normal distribution in which the missing observations are not restricted to follow certain patterns as in most previous papers. The large sample properties of the estimators are discussed. Equivalence with maximum likelihood estimators has been established for a subclass of problems. The results of some simulation studies are provided to support the theoretical development. [ABSTRACT FROM AUTHOR]

When two correlation coefficients are calculated from a single sample, rather than from two samples, they are not statistically independent, and the usual methods for testing equality of the population correlation coefficients no longer apply. This paper considers the situation when the sample is from a multivariate normal distribution. Several possible large sample testing procedures are given, all based on Fisher's z-transformation. Power curves are given for each procedure and for seven values of the asymptotic correlation between the two sample correlation coefficients. [ABSTRACT FROM AUTHOR]

This paper deals with proportional stratified sampling in the situation where the estimation variable X is difficult and expensive to observe, while the possibly erroneous stratification variable Y is easy and inexpensive to get at. The usually biased estimate [Multiple line equation(s) cannot be represented in ASCII text] is compared with the unbiased estimate [Multiple line equation(s) cannot be represented in ASCII text] where the P[sub I] are stratum weights and y[sub I] and x[sub I] are means of the units sampled from the I:th stratum. The two estimates are similar in that they utilize information from only those population units that make up the sample. While mu[sub a] is the more inexpensive estimate, mu[sub b] is usually preferable if one judges by the size of the mean square error, which, among other things, depends on the number of strata and the location of the stratum boundaries. In particular, the properties of mu[sub a] and mu[sub b] are discussed in connection with an example involving the bivariate normal distribution. [ABSTRACT FROM AUTHOR]

Let X[sub i1], X[sub i2],..., X[sub iota n], I=1, 2, be a pair of random samples from populations which are normally distributed with means theta[sub iota], and common known variance tau[sup 2]. The problem is to estimate the function psi(theta[sub 1], theta[sub 2]) = maximum (theta[sub 1], theta[sub 2]). In this paper we consider five different estimators (or sets of estimators) for psi(theta[sub 1], theta[sub 2]) and evaluate their biases and mean square errors. The estimators are (I) psi(X[sub 1], X[sub 2]), where X[sub I] is the sample mean of the ith sample; (ii) the analogue of the Pitman estimator, i.e. the a posteriori expected value of psi(theta[sub 1], theta[sub 2]) when the generalized prior distribution is the uniform distribution on two dimensional space; (iii) a class of estimators which are generalized Bayes with respect to generalized priors which are products of uniform and normal priors; (iv) hybrid estimators, i.e. those which estimate by (X[sub 1] + X[sub 2])/2 when |X[sub 1] -X[sub 2]| is small, and estimate by psi(X[sub 1], X[sub 2]) when |X[sub 1] - X[sub 2]| is large; (v) maximum likelihood estimator. The bias and mean square errors for these estimators are tabled, graphed, and compared. Also the invariance properties of these estimators are discussed with a rationale for restricting to invariant estimators. [ABSTRACT FROM AUTHOR]

In this paper we examine how well the asymptotic null distribution of a two sample test due to Lehmann approximates the small sample distribution of the test, compare the validity of this Lehman test with the validity of the two sample t test under the null hypothesis of equal means, and compare the power of this Lehmannn test with the power of the t test. Our general conclusion is that experimenters will prefer to use the t test when the underlying distribution is the scale contaminated compound normal distribution and the sample sizes are less than thirty. [ABSTRACT FROM AUTHOR]