Given a finite set of independent random variables, assume one can observe their sum, and denote with s its value. Efron in 1965, and Lehmann in 1966, described conditions on the involved variables such that each of them stochastically increases in the value s, i.e., such that the expected value of any non-decreasing function of the variable increases as s increases. In this paper, we investigate conditions such that this stochastic monotonicity property is satisfied when the assumption of independence is removed. Comparisons in the stronger likelihood ratio order are considered as well.

Stochastic monotonicity of dependent variables given their sum / Pellerey, Franco; Navarro, Jorge. - In: TEST. - ISSN 1133-0686. - STAMPA. - 31:(2022), pp. 543-561. [10.1007/s11749-021-00789-5]

Stochastic monotonicity of dependent variables given their sum

Franco Pellerey;
2022

Abstract

Given a finite set of independent random variables, assume one can observe their sum, and denote with s its value. Efron in 1965, and Lehmann in 1966, described conditions on the involved variables such that each of them stochastically increases in the value s, i.e., such that the expected value of any non-decreasing function of the variable increases as s increases. In this paper, we investigate conditions such that this stochastic monotonicity property is satisfied when the assumption of independence is removed. Comparisons in the stronger likelihood ratio order are considered as well.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11583/2930252