| 摘要: | 考慮三個三維常態分布 N(u1, E1), N(u2, E2) 及 N(u3, E3),令 (X1,...,Xn) 表一樣本, 其中 Xk = (??1k , ??2k , ??3k ), k = 1,...,n. 並且 N(u2, E2) 為 N(u1, E1) 之特例, N(u3, E3) 為N(u2, E2) 之特例. 本文討論下列三個問題之最大概似比檢定.
問題A
H0 ? (X1, ... , Xn ) ~ N(u2, E2) vs H1 : (X1, ... , Xn ) ~ N(u1, E1)
問題B
H0 ? (X1, ... , Xn ) ~ N(u3, E3) vs H1 : (X1, ... , Xn ) ~ N(u1, E1)
問題C
H0 ? (X1, ... , Xn ) ~ N(u3, E3) vs H1 : (X1, ... , Xn ) ~ N(u2, E2);
Consider three trinormal distributions N(u1, E1), N(u2, E2) and N(u3, E3). Let (X1,...,Xn ) be a sample, where Xk = (??1k , ??2k , ??3k ), k = 1,...,n. Since
N(u3, E3), N(u2, E2) and N(u1, E1) are nested, it is interesting to discuss the following three generalized likelihood ratio tests.
Problem A
H0 ? (X1, ... , Xn ) ~ N(u2, E2) vs H1 : (X1, ... , Xn ) ~ N(u1, E1)
Problem B
H0 ? (X1, ... , Xn ) ~ N(u3, E3) vs H1 : (X1, ... , Xn ) ~ N(u1, E1)
Problem C
H0 ? (X1, ... , Xn ) ~ N(u3, E3) vs H1 : (X1, ... , Xn ) ~ N(u2, E2) |
