It is considered that penalized empirical likelihood for parameter estimation and variable selection in partially linear models with measurement errors in non-parametric part. By using adaptive Lasso penalty function, it is shown that the proposed estimator has the oracle property.Also, the problem of testing hypothesis is considered. Some simulations are given to illustrate the performance of the proposed method.

By using moment inequality and maximum inequality of NQD random variable sequences, this paper mainly discuss the large deviation of partial sum of NQD sequences and convergence of weighted sum of NQD sequences.

It is considered that the asymptotic properties for the drift estimations of the Ornstein-Uhlenbeck process under discrete observations.By using the deviation properties of multiple Wiener-It integrals and asymptotic analysis techniques,the Cramér-type moderate deviations for the estimators are obtained.For applications, a test statistic which can be used to construct confidence intervals and rejection regions in the hypothesis testing for the drift coefficient is proposed. It is shown that the Type II errors tendto zero exponentially.

The parameter estimation and hypothesis testing problem in the tensor linear regression model are studied. Firstly, the point estimator of the parameter is obtained based on the least squares, and the consistency is proved. Then the approximative algorithm of the estimation is given by the CP(CANDECOMP/PARAFAC) decomposition structure of the coefficient tensor-alternating least-square; secondly, the quasi-likelihood ratio test statistic of parameter linear hypothesis test is established, and its large sample property is proved. The Mote Carlo simulation results show that the alternating least-square estimation performs well and the quasi-likelihood ratio test is no significant difference between the empirical distribution of the statistics and the theoretical distribution. Finally, the method is applied to the English alphabet counting problem in text data analysis, and the more accurate prediction results are obtained.

The region structure learning of haze pollution is studied by using the complex network analysis method. The PM2.5 data of each hour from 2015 to 2018 in 363 cities of China are collected. Then the change of concentration of PM2.5 in those cities in the recent four years is analyzed. Based on the complex graphical model method, the change of hubs and structure of the haze pollution network among the 363 cities is studied. The results show that: after the haze governance, the effect of nationwide haze control has been significantly improved, but the haze control effect in Beijing and northeast China is better than that in northwest China. Haze control needs to focus on the central cities and the regions that they locate in; to carry out haze governance, we should not only consider the differences among different communities, but also cooperate with each other within the same community to achieve better haze governance results.

For generalized linear models with adaptive designs, the variable selection method based on the adaptive Lasso penalized least squared method is considered. Under certain conditions, the consistency and oracle properties of the adaptive Lasso penalized least squared estimator are established, which extend the corresponding results from the fixed designs to the adaptive designs for generalized linear models. The simulation results show that the adaptive Lasso penalty method is better than Lasso punishment.

Dimensions of graphical models are important for test, model selection and classification. There are two definitions of dimension for discrete undirected graphical models in literature, and one of them provides a formula for calculating the dimensions of discrete undirected graphical models. It isshown that the consistency of the two definitions for all discrete undirected graphical models.