Sankhya: The Indian Journal of Statistics

1998, Volume 60, Series B, Pt. 2, 221--227

LINEARITY OF BEST PREDICTORS FOR NON-ADJACENT RECORD VALUES

By

MOHAMMAD AHSANULLAH Rider University, Lawrenceville
and
JACEK WESOLOWSKI Warsaw University of Technology, Warsaw

SUMMARY. Let {Xn, n >= 1} be a sequence of independent and identically distributed random variables with absolutely continuous distribution function. Suppose X U( k ), k=1, 2,... be the upper record values of { Xn, n >= 1 }. A complete solution of the problem of determining the distribution by the linearity of the regression of X U( m+2 ) with respect to X U( m ) is given. It is shown that the class of possible distributions consists of exponential, power function and Pareto type. Equivalently, the best unbiased predictors of X U( m+2 ) given X U( m ) is linear only for this class.

AMS (1991) subject classification.62E10, 62G30.

Key words and phrases. Best unbiased predictor, linear prediction, characterizations, record values, linearity of regression, exponential distribution, power function distribution, pareto distribution, conditional expectation.

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