A strong approximation of the shortt process
Year: 1998
Type: preprint
Abstract: A shortt of a one dimensional probability distribution is defined to be an interval which has at least probability t and minimal length. The length of a shortt, U(t), and its obvious estimator, U_n(t), are significant measures of scale of a probability distribution and the corresponding random sample, respectively. The shortt process is defined to be $ \\sqrt{n}(U_n(t)-U(t)) / U'(t) $, similarly to the definition of the quantile process. It is known that this process converges weakly, under natural regularity conditions, to a Brownian bridge. In this note a strong approximation of the shortt process by a Kiefer process is established, which yields the weak convergence as a corollary. Applications of the result to the global and local strong limiting behaviour of the shortt process are also presented.
Authors: Jhj John Einmahl, M Mario Geilen
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2048126922