应用概率统计
應用概率統計
응용개솔통계
CHINESE JOURNAL OF APPLIED PROBABILITY AND STATISTICS
2006年
3期
288-294
,共7页
多维广义线性模型%拟极大似然估计%弱相合性%收敛速度
多維廣義線性模型%擬極大似然估計%弱相閤性%收斂速度
다유엄의선성모형%의겁대사연고계%약상합성%수렴속도
Multivariate generalized linear models%quasi-maximum likelihood estimates%weak consistency%convergence rate
本文考虑多维广义线性模型的拟似然方程n∑i=1Xi(yi-μ(X'iβ))=0,在一定条件下证明了此方程的解(β)n渐近存在,并得到了其收敛速度,即(β)n-β0=Op((λ)n-1/2),其中β0为参数β的真值,(λ)n是方阵Sn=n∑i=1XiX'i的最小特征值.
本文攷慮多維廣義線性模型的擬似然方程n∑i=1Xi(yi-μ(X'iβ))=0,在一定條件下證明瞭此方程的解(β)n漸近存在,併得到瞭其收斂速度,即(β)n-β0=Op((λ)n-1/2),其中β0為參數β的真值,(λ)n是方陣Sn=n∑i=1XiX'i的最小特徵值.
본문고필다유엄의선성모형적의사연방정n∑i=1Xi(yi-μ(X'iβ))=0,재일정조건하증명료차방정적해(β)n점근존재,병득도료기수렴속도,즉(β)n-β0=Op((λ)n-1/2),기중β0위삼수β적진치,(λ)n시방진Sn=n∑i=1XiX'i적최소특정치.
In this paper, we study quasi-likelihood equation n∑i=1 Xi(yi -μ(X'iβ)) = 0 for multivariategeneralized linear models (GLMs). Under mild conditions, we prove the asymptotic existence of the solution (β)n to the above equation and present its convergence rate, that is (β)n - β0 =Op((λ)n-1/2), where β0 is the true value of parameter β and (λ)n denotes the smallest eigenvalue of the matrix Sn = n∑i=1 XiX'i.
