Abstract
Overlapping samples appear in several fields of statistical applications. In a model of successive pairwise overlap we consider two parameter estimators for the expectation of underlying random variables. The estimators are based on sample means having a tridiagonal covariance matrix. We are interested in the behavior of the relative efficiency as a function of certain problem parameters. Representations in terms of Chebyshev polynomials and some helpful relations lead to a monotonicity result which is then generalized to weighted sample means.
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