Weak Consistency of Quasi-Maximum Likelihood Estimates in Generalized Linear Models
Pengyan Wang · Journal of Chongqing Institute of Technology · 2009
In this paper,we study the solutionβ-n of quasi-maximum likelihood equation ni=1XiHX′iβΛX′iβyi-hX′iβ=0for generalized linear models(GLMs),Under the assumption an unnatural link function and other some mild conditions,we prover the weak consistency of the solution β-nto the above equation and present its convergence rate,which is as the same as under the natural link condition,that is β^n-β0=Opλ——1/2n,where β0is the true value of parameterβ andλ-n(λ-n)denotes the smallest eigervalue of the matrixSn=ni=1XiX′i.