INFERENCE FOR THE CROSSING POINT OF 2 CONTINUOUS CDFS
成果类型：
Article
署名作者：
HAWKINS, DL; KOCHAR, SC
署名单位：
Indian Statistical Institute; Indian Statistical Institute Delhi
刊物名称：
ANNALS OF STATISTICS
ISSN/ISSBN：
0090-5364
DOI：
10.1214/aos/1176348266
发表日期：
1991
页码：
1626-1638
关键词：
摘要：
Let F denote the set of cdf's on R with density everywhere positive. Let C(A) = {(F, G) is-an-element-of F x F: there exists a unique x* is-an-element-of R such that F(x) > G(x) for x < x* and F(x) < G(x) for x > x*}, C(B) = {(F, G) is-an-element-of F x F: (G, F) is-an-element-of C(A)}. Based on independent random samples from F and G (assumed unknown), we give distribution-free tests of H0: F = G versus the alternatives that (F, G) is-an-element-of C(A), (F, G) is-an-element-of C(B) or (F, G) is-an-element-of C(A) union C(B). Next, assuming that (F, G) is-an-element-of C(A) (or in C(B)), a point estimate of the crossing point x* is obtained and is shown to be strongly consistent and asymptotically normal. Finally, an asymptotically distribution-free confidence interval for x* is obtained. All inferences are based on a special criterion functional of F and G, which yields x* when maximized (minimized) if (F, G) is-an-element-of C(A) [(F, G) is-an-element-of C(B)].