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 {**X**_{n}, 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 {** X**_{n}, 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.