1. STATISTICAL DEPENDENCE BETWEEN RANDOM EFFECTS AND THE NUMBERS OF OBSERVATIONS ON THE EFFECTS FOR THE UNBALANCED ONE-WAY RANDOM CLASSIFICATION.
- Author
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Harville, David A.
- Subjects
- *
RANDOM variables , *PROBABILITY theory , *STATISTICAL correlation , *ANALYSIS of variance , *EXPERIMENTAL design , *DISTRIBUTION (Probability theory) , *MATHEMATICAL statistics , *REGRESSION analysis - Abstract
This paper deals with certain aspects of variance component estimation for the unbalanced one-way random classification where the number (N[sub I]) of observations in the ith class is treated as a random variable not necessarily independent of the class effect (A[sub iota]). It is assumed that in general P(N[sub I] = 0) > 0. The conditional expectations (given the number of observations in each class) of all estimators of the between variance component (sigma[sup 2, sub alpha]) belonging to a certain class of estimators are derived. A general expression is found for the expected value of that estimator of sigma[sup 2, sub alpha] yielded by analysis of variance of class means. The limit of this expression (as the number of classes arrow right Infinity) is given; and it is shown that, if the bivariate distribution function of A[sub I], N[sub I] belongs to a certain class of distribution functions, then this limit is less than sigma[sup 2, sub a]. Numerical approximations to the expected values of two estimators of sigma[sup 2, sub a] are presented for one subclass of such distribution functions. [ABSTRACT FROM AUTHOR]
- Published
- 1967
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