能力有限,给出翻译
Recall that if x then the moment generating function of x is 2,consider a single subject in a longitudinal study whose observed responses from a multivariate normal distribution with mean vetor zero and covariance matrix 2,where the 3 element of 4is 5,conditional on 6 assume that the count responses 7 at times 8 are independent poisson random variables with mean and variance equal to 8 ,where 9 .also suppose that
Where x is a vector of regression variables ovserved at the time 11is an intercept term and .apart from the intercept term 12,the regression 13 have the same marginal and conditional interpretations .derive expression for the variance varX and covariance cov
假设x是N(μ,Σ)的一个多元正态分布,其特征函数为:
E(....)=e....
。设εj为一个多元正态分布的随机误差向量,其均值为零,协方差矩阵为Σ,其中Σ(i,j)元为δij,考虑基于列向量ε=(εi..εj)T的满足如下假设的一个计数分布Y:在tj时基于εj的是相互独立的泊松分布,均值和方差均为μjαj,αj满足log(αj)=εj.假设μi可以表成:
式子log(μj)=β0+xjβT
xj是一个j时刻的回归变量,β0是回归常数项,β是回归参数列向量。
(1)求Y的条件期望和无条件期望,说明相差一个常数截距项之外,回归参数β有相同的条件期望和期望并作出解释。
(2)求{Yj}的方差var(yj)和协方差cov(yi,yj).(求方差过程中用到VAR(U)=E(var(U/V))+VAR(E(U/V)),求协方差过程中用到E(UV)=E(E(UV/W,Z))和特征函数)
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