Limit Distribution Of Maxima Of Strongly Dependent Gaussian Vector Sequences Under Complete And Incomplete Samples

There are three main parts in this thesis. In the first part of the thesis, we discuss the rates of convergence of maxima of discrete random variables. For the second part, we study the limit distribution of maxima of strongly dependent gaussian vector sequences under complete and incomplete samples. Finally, we obtain the almost sure convergence for the maxima of strongly dependent stationary gaussian vector sequences under complete and incomplete samples for the third part.Let X1, X2,…, Xn be a sequence of independent and identically distributed discrete random variables and Mn=max(X1,…, Xn). we have known the limiting behavior of (Mn-bn)/an as nâ†'∞. However, by tuning the parameter of the discrete distribution to vary as nâ†'∞, it is possible to obtain the non-degenerate rate of convergence for (Mn-bn)/an. We have given the the rates of convergence of maxima of three families of discrete random variables.Secondly, let{Xn,n≥1} be a sequence of d-dimensional stationary Gaussian vectors, and let Mn denote the maxima of{Xk,1≤k≤n}. Suppose that there are missing data in each component of Xk and let Mn denote the partial maxima of the observed variables. In the second part, we study the asymptotic distribution of the random vector (Mn,Mn) as the correlation and cross-correlation satisfy strongly dependent condition.In the third part, we discuss the almost sure convergence for the maxima of strongly dependent stationary Gaussian vector sequences under complete and in-complete samples.