摘要
设A～CW_p(Q,n),z～CN_p(θ,Q)且相互独立,设原假设为(1)(?)设A_j～CW_p(Q_j,m_j),z_j～CN_p(θ_J,Q_j)(j=1,2,…,k),且相互独立.设原假设为(2)(?)(3)(?)本文证明了相应于备择假设A_i≠H_i,i=1,2,3,检验假设H_i的似然比检验是无偏性。
Let A～CW_p(Q,n), z～CN_p(θ,Q) and let them be mutually inde-
pendent,Let the null hypothesis be
(1) H_1:Q=σ~2Q_0, θ=θ_0
Let A_j～CW_P(Q_j,m_j), z_j～CN_P(θ_j,Q_j)(j=1,2,…,k) and let them be
mutually independent.Let the null hypothesises be
(2)H_2:Q_j=σ~2Q_(0j),θ_j=θ_(0j),σ~2>0 (j=1,2,…,k)
(3) H_3:Q_j=σ_j^2 Q_(0j), θ_j=θ_(0j), σ_j>0(j=1,2…,k)
This article proves that the likelihood tests of the null hypothesises
H_i (i=1,2,3) against above alternative hypothesises A_i≠H_i are unbiased.
出处
《湘潭大学自然科学学报》
CAS
CSCD
1989年第3期21-30,共10页
Natural Science Journal of Xiangtan University
关键词
期望
协方差
似然比检验
无偏性
Likelihood ratio test statistics
Rejection region
un-biasedness
