Nonlinear Model Parameters Of Unknown Error Variances, Quasi Likelihood Estimates Of Progressive Qualitative Research

The thesis mainly studies the properties of quasi-maximum likelihood estimatorin nonlinear models , many results in literatures are extended.Focus on the consistency and the convergence rate of maximumquasi-likelihood estimates of quasi-likelihood estimate model, The thesis summarizesvarious methods previously, then studies the large sample properties of maximumquasi-likelihood estimates of QMLE in nonlinear models which variance is unknown.The thesis is divided into three chapters. In the first chapter, we introduce thehistory of generalize linear mode at first, we introduce GLM, Link Function, MLEand QMLE etc. Then we introduce the quasi-likelihood estimate model and the resultsof previous studies, we get the definition of maximum quasi-likelihood estimate andquasi-likelihood equation. At last the article briefly introduce the main researchachievement of quasi-likelihood nonlinear models.In the second chapter, we discuss the week consistency of maximumquasi-likelihood estimation in quasi-likelihood nonlinear models when the variancefunction is unknown. During the derivation, the article mainly applies the Lemma 2.2（Ortega J M, Rheinboldt W C (1970), deduction 6.3.4，p.162-163）.In the third chapter, we study the asymptotic properties of quasi-likelihoodnonlinear models with a random design when the variance function is unknown, thenwe discuss the existence, consistency and asymptotic normality of maximumquasi-likelihood estimation. In this part, the thesis mainly applies the Strong Law ofLarge Numbers and the Lemma 3.2(Wu（1981）).