caa a22 4500 475826477 CHVBK 20180406123830.0 cr unu---uuuuu 170329e20000301xx s 000 0 eng 10.1023/A:1004176730214 doi (NATIONALLICENCE)springer-10.1023/A:1004176730214 Huimei Liu Department of Statistics, National Chung Hsing University, 67 Ming Sheng East Rd., Sec. 3, 10433, Taipei, Taiwan, R.O.C aut Uniformly More Powerful, Two-Sided Tests for Hypotheses about Linear Inequalities [Elektronische Daten] [Liu Huimei] Let Xhave a multivariate, p-dimensional normal distribution (p ≥ 2) with unknown mean μ and known, nonsingular covariance Σ. Consider testing H 0 : b iμ ≤ 0, for some i = 1,..., k, and b iμ ≥ 0, for some i = 1,..., k, versus H 1 : b i μ < 0, for all i = 1,..., k, or b i μ < 0, for all i = 1,..., k, where b 1,..., b k , k ≥ 2, are known vectors that define the hypotheses and suppose that for each i = 1,..., k there is an j ∈ {1,..., k} (j will depend on i) such that b i∑ b j≤ 0. For any 0 < α < 1/2. We construct a test that has the same size as the likelihood ratio test (LRT) and is uniformly more powerful than the LRT. The proposed test is an intersection-union test. We apply the result to compare linear regression functions. The Institute of Statistical Mathematics, 2000 Intersection-union test nationallicence likelihood ratio test nationallicence linear inequalities hypotheses nationallicence uniformly more powerful test nationallicence Annals of the Institute of Statistical Mathematics Kluwer Academic Publishers 52/1(2000-03-01), 15-27 0020-3157 52:1<15 2000 52 10463 https://doi.org/10.1023/A:1004176730214 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1023/A:1004176730214 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Huimei Liu Department of Statistics, National Chung Hsing University, 67 Ming Sheng East Rd., Sec. 3, 10433, Taipei, Taiwan, R.O.C aut NATIONALLICENCE 773 0- Annals of the Institute of Statistical Mathematics Kluwer Academic Publishers 52/1(2000-03-01), 15-27 0020-3157 52:1<15 2000 52 10463 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer