2019/03/19 by Fernando López-Blázquez, López-Blázquez, Fernando, Nan‐Cheng Su +3
Computer Science · Decision Sciences · Economics, Econometrics and Finance · Mathematics · #60E05 #62E10 #Bayesian Methods and Mixture Models #FOS: Mathematics #Financial Risk and Volatility Modeling #Probabilistic and Robust Engineering Design #Probability (math.PR) #Statistical Distribution Estimation and Applications
paper · pdf · doi:10.48550/arxiv.1903.08047
openalex publication_date 2019/03/19 · openalex created_date 2022/07/29 · openalex updated_date 2026/07/28
In this paper we are interested in the joint distribution of two order\nstatistics from overlapping samples. We give an explicit formula for the\ndistribution of such a pair of random variables under the assumption that the\nparent distribution is absolutely continuous (with respect to the Lebesgue\nmeasure on the real line). The distribution is identified through the form of\nthe density with respect to a measure which is a sum of the bivariate Lebesgue\nmeasure on R2 and the univariate Lebesgue measure on the diagonal\n (x,x): ,x\∈ R .\n We are also interested in the question to what extent conditional expectation\nof one of such order statistic given another determines the parent\ndistribution. In particular, we provide a new characterization by linearity of\nregression of an order statistic from the extended sample given the one from\nthe original sample, special case of which solves a problem explicitly stated\nin the literature. It appears that to describe the correct parent distribution\nit is convenient to use quantile density functions. In several other cases of\nregressions of order statistics we provide new results regarding uniqueness of\nthe distribution in the sample. Nevertheless the general question of\nidentifiability of the parent distribution by regression of order statistics\nfrom overlapping samples remains open.\n