Linear Function of Concomitants of Order Statistics.
Abstract
Let (X(i), Y(i)) (i-1,2,...,n) be i.i.d. as (X, Y). Then the rth ordered X-variate is denoted by X(r:n) and the associated Y-variate, the concomitant of the rth order statistic, by Y(r:n). This paper considers statistics of the form 1/n sum over i from 1 to n J (i/(n+1)) Y(r:n) and more generally of the form 1/n sum over i from 1 to n J(i/(n+1)) H(X(i:n), Y(r:n)), where j is a bounded smooth function and may depend on n. Under certain regularity conditions, the asymptotic normality of these statistics are established. These statistics are used to construct consistent estimators of various conditional quantities, for example E(Y bar X=x), P(Y an element of A bar X=x) and Var(Y bar X=x). Based on one of these statistics, a large sample test is also proposed for testing a specified regression function. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Sep 09, 1977
- Accession Number
- ADA044723
Entities
People
- S. S. Yang
Organizations
- Massachusetts Institute of Technology