Abstract
We present sharp bounds on expected values of concomitants based on a sample of identically distributed random pairs. The dependence between pair components is described by regression functions or modelled by copulas, or generated by sampling without replacement from finite populations.
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References
Balakrishnan N, Charalambides C, Papadatos N (2003) Bounds on expectation of order statistics from a finite population. J Statist Plann Inference 113:569–588
Bhattacharya PK (1974) Convergence of sample paths of normalized sums of induced order statistics. Ann Statist 2:1034–1039
Danielak K, Rychlik T (2004) Sharp bounds for expectations of spacings from decreasing density and failure rate families. Appl Math 31:369–395
David HA, Nagaraja HN (1998) Concomitants of order statistics. In: Balakrishnan N, Rao CR (eds) Handbook of statistics, vol 16. pp 105–145
David HA, Nagaraja HN (2003) Order statistics. Wiley, New York
de la Cal J, Cárcamo J (2005) Inequalities for expected extreme order statistics. Statist Probab Lett 73:219–231
Do K-A, Hall P (1992) Distribution estimation using concomitants of order statistics, with applications to Monte Carlo simulation for the bootstrap. J Roy Statist Soc Ser B 54:595–607
Embrechts P, Hoenning A, Juri A (2003) Using copulae to bound value-at-risk for functions of dependent risks. Finance Stoch 7:145–167
Goel PK, Hall P (1994) On the average difference between concomitants and order statistics. Ann Probab 22:126–144
Gumbel EJ (1954) The maxima of the mean largest value and of the range. Ann Math Statist 25:76–84
Hartley HO, David HA (1954) Universal bounds for mean range and extreme observation. Ann Math Statist 25:85–99
Kaluszka M, Okolewski A (2003) Sharp exponential and entropy bounds on expectations of generalized order statistics. Metrika 58:159–171
Kaluszka M, Okolewski A. (2005) Sharp bounds for generalized order statistics via logarithmic moments. Commun Statist Theory Meth 34:1–13
Ludwig O (1960) Über erwartungsworte und varianzen von ranggrössen in kleinen stichproben. Metrika 38:218–233
Müller A, Stoyan D (2002) Comparison methods for stochastic models and risks. Wiley, Chichester
Moriguti S (1953) A modification of Schwarz’s inequality with applications to distributions. Ann Math Statist 24:107–113
Nagaraja HN, David HA (1994) Distribution of the maximum of concomitants of selected order statistics. Ann Statist 22:478–494
Nelsen RB (1999) An introduction to copulas. Springer, Berlin Heidelberg New York
Nelsen RB, Quesada-Molina JJ, Rodriguez-Lallena JA, Ubeda-Flores M (2001) Bounds on bivariate distribution functions with given margins and measures of association. Commun Statist Theory Meth 30:1155–1168
Papadatos N (1997) Exact bounds for the expectations of order statistics from non-negative populations. Ann Inst Statist Math 49:727–736
Rychlik T (1993) Bounds for expectation of L-estimates for dependent samples. Statistics 24:1–7
Rychlik T (1998) Bounds for expectations of L-estimates. In: Balakrishnan N, Rao CR (eds) Handbook of Statistics, vol. 16, 105–145
Rychlik T (2001) Projecting statistical functionals. Springer, Berlin Heidelberg New York
Yang SS (1977) General distribution theory of the concomitants of order statistics. Ann Statist 5:996–1002
Yang SS (1981) Linear functions of concomitants of order statistics with application to nonparametric estimation of a regression function. J Amer Statist Assoc 76:658–662
Yeo WB, David HA (1984) Selection through an associated characteristic with applications to the random effect model. J Amer Statist Assoc 79:399–405
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Okolewski, A., Kaluszka, M. Bounds for expectations of concomitants. Stat Papers 49, 603–618 (2008). https://doi.org/10.1007/s00362-006-0041-4
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DOI: https://doi.org/10.1007/s00362-006-0041-4