A new class of tests for convex-ordered families based on expected order statistics
Year: 2025
Type: article
Abstract: Consider a pair of cumulative distribution functions F and G, where F is unknown and G is a known reference distribution. Given a sample from F, we propose tests to detect the convexity or the concavity of G−1∘F versus equality in distribution (up to location and scale transformations). This framework encompasses well-known cases, including increasing hazard rate distributions, as well as some other relevant families that have garnered attention more recently, for which no tests are currently available. We introduce test statistics based on the estimated probability that the random variable of interest does not exceed a given expected order statistic, which, in turn, is estimated via L-estimation. The tests are unbiased, consistent, and exhibit monotone power with respect to the convex transform order. To ensure consistency, we show that our L-estimators satisfy a strong law of large numbers, even when the mean is not finite, thereby making the tests suitable for heavy-tailed distributions. Unlike other approaches, these tests are broadly applicable, regardless of the choice of G and without support restrictions. The performance of the method under various conditions is demonstrated via simulations, and its applicability is illustrated through a concrete example.
Source: Electronic Journal of Statistics
DOI: 10.1214/25-ejs2398
Authors: Tommaso Lando, Mohammed Es-Salih Benjrada
Institution: University of Bergamo
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $675
OpenAlex ID: W4411710061