An upper bound for the correlation ratio of records. (English) Zbl 1093.62536

Summary: We obtain an upper bound for a measure of the performance of the least squares predictor of the \(j\)th record of a sequence of continuous i.i.d. random variables as a function of the \(i\)th record. We show also that such bound is attainable, except for location and scale parameters, by exponential distributions.


62G32 Statistics of extreme values; tail inference
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[1] Arnold BC, Balakrishnan N, Nagaraja HN (1992) A first course in order statistics. Wiley, New York · Zbl 0850.62008
[2] Chihara TS (1978) An introduction to orthogonal polynomials. Gordon and Breach Science Publishers. · Zbl 0389.33008
[3] Lopez-Blazquez F (1990) Caracterización de distribuciones mediante el valor esperado de estadisticos de orden y records. Unpublished Ph.D. Thesis, Universidad de Sevilla
[4] Nagaraja HN (1978) On the expected values of record values. J. Statis 20: 176–182 · Zbl 0407.62025
[5] Nagaraja HN, Nevzorov VB (1996) Correlations between functions of records can be negative. Stat. Prob. Letters 29: 95–100 · Zbl 0865.62034
[6] Nevzorov VB (1992) A characterization of exponential distributions by correlations between records. Math. Methods Statist. 1:49–54 · Zbl 0791.62015
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