A new estimator is proposed based on the ideas of AIC(Akaike Information Criterion) and gave asymptotic distribution of the estimator.

The asymptotic distribution of parameter estimated matrix , for vector autoregressive models is discussed.

Moreover, the asymptotic distribution of the maxima in disjoint intervals is obtained.

For a measure of information discrepancy B, in this paper we investigate the asymptotic distributions of B(u1 ,u2,…, us), where u1,u2,…, us are sample-based estimators of a common probability distribution.

On certain conditions of assumption, we build the mathematical model in imitation of distribution of population in two spaces, and according to the mathematical model we make a study of the asymptotic distribution of population in two spaces, obtain several important results, announce .

According to the hypothesis of parameters in random effect model with equilibrium design and one-way classification H0:μ=μ0,σ2α=σ2α0,σ2=σ20H1:μ≠μ0,or σ2α≠σ2α0 or σ2≠σ20,a statistical estimator to test H0 is presented by using maximum likelihood ratio method,and then the asymptotic distribution of test statistics and its rule are given.

In view of the problems,according to the time correlation of exponent forgetting distribution,this paper modified the Morlet wavelet function,and derived a fast algorithm for modified Morlet wavelet transform to reduce the computation.