Risk is one of the important indicators in the epidemiology and usually used to compare the effectiveness of two therapeutics or diagnostics. Therefore, accurate estimate of the risk difference interval is important for the diagnosis of disease and selection of therapeutic scheme. Combining with the characteristics of chronic whose diseases cycle is long and the incidence is low and the advantages of Poisson sampling, the paper uses the saddle point approximation method to construct the risk difference confidence interval under the Poisson distribution. At the same time, five traditional kinds of interval estimation method are assessed through examples and monte carlo simulation. Simulation results show that under the condition of small samples, the saddle point approximation is a kind of very good confidence interval estimation method. In most cases it can guarantee the coverage rate being equal to the desired confidence level and make the shortest length.

In applications, there are many different statistical characteristics among diverse categories, so it is very necessary to study the heterogeneous population. This paper is based on the existence of the first order and second order moments of the distribution function, and the mixture of double generalized linear models is used to build mean and variance models in different population. After constructing the extended quasi-likelihood and pseudo-likelihood functions, the EM algorithm is used to estimate the mean parameter, dispersion parameter and mixture proportion. Finally, a Monte Carlo experiment and a real example prove that the model and the method are effective.

In this paper, inspired by the paper of Shao and Su (2006), the Berry-Esseen bound for equilibrium distribution is obtained by Stein method.

Consider a bidimensional risk model, in which two insurance companies divide between them the claims in some specified proportions, and every main claim induces a delayed by-claim. Suppose that the surpluses of the two companies are invested into portfolios whose returns follow a geometric Levy process. When the claim-size distribution is consistently-varying tailed, and the inter-arrival time and claim-size follow some dependence structure, asymptotic estimates for the ruin probabilities of this bidimensional risk model are derived.

In this paper, the estimations for the parameters of fractional diffusion models and their applications are presented. Fractional diffusion models satisfy the stochastic differential equations driven by fractional Brownian motions. The paper’s main results are: (1) An estimator for the diffusion parameter by the method of quadratic variation and estimators for the drift parameters by least squares method are given; (2) These estimators are proved to be strong consistent and asymptotically normal; (3) These estimators are examined via the MCMC method and applied to empirical data of SHIBOR.

Classical penalized regression model is inadequate of adaptivity for fitting complex data because that the spatial heterogeneity of observation data is not considered by the penalized term. According to the geometric meaning of radial basis, the local penalization vector based on the ranges of the data around each knot is constructed and added into the penalized term of the model. This new adaptive penalized spline regression model via radial basis gives less penalization to fitted curve where the observation data is volatile and more penalization to fitted curve where the observation data is flat, which makes the model adaptive to the local characterization of the sample points. Simulations and application show the fitting effect based on new model outperforms classical penalized spline regression model.

This paper introduces and characterizes rough continuity and topological continuity of maps between generalized approximation spaces. Properties and relationships of rough continuity and topological continuity are considered. It is proved that compositions of rough continuous maps are also rough continuous, and every rough continuous map is topological continuous. With these two continuities, concepts of rough homeomorphism properties and topological homeomorphism properties are defined. It is proved that every topological homeomorphism property is a rough homeomorphism property. Besides, some properties such as separation axioms, connectedness and compactness of generalized approximation spaces are shown to be rough or topological homeomorphism properties.

The concept of $L$-fuzzy ideals of semirings is first introduced in this paper. Based on this new concept, some properties of the category of $L$-fuzzy ideal of semirings are investigated, the result that the category of $L$-fuzzy ideals of semirings is a topological construct on the category of semirings is also proved. Meanwhile, the equalizer, pullback and product are all discussed. On the other hand, the notion of inverse systems of category of $L$-fuzzy ideals of semirings is proposed and the inverse limit of the category of $L$-fuzzy ideals of semirings is constructed. Particularly, the limit mapping has been obtained by means of presenting the mapping between two inverse systems.

This paper focuses on the feature extraction and variable selection of massive data which is divided and stored in different linked computers, and studies the distributed $L_{1/2}$ regularization. Based on Alternating Direction Method of Multipliers algorithm(ADMM), distributed $L_{1/2}$ regularization algorithm which communicates information between the neighborhood computers has been proposed and the convergence of the algorithm has been proved. The variable selection results of the approach are the same with the entire data set by using $L_{1/2}$ regularization. Numerical studies show that this method is both effective and practical which performs well in distributed data analysis.

In this paper, according to the dynamic change regulation of pregnant mother and fetus growth, a pharmacokinetic model of maternal fetal oral digoxin in the treatment of tachyarrhythmia is established, reasonable regimens on the basis of the gestational age changes and the digoxin therapeutic window of clinical react blood drug concentration are designed, and MATLAB program for simulation, analysising the feasibility of the scheme is used.

By using the spectrum theory of the linear completely continuous fields and transition theory, the bifurcation and transition of the solar granulation are studied and the existence of granulation is verified. With certain assumption, the eigenvalues, eigenvectors and bifurcation solution are obtained. Finally, the estimation of diameter for granulation is obtained from the model, which can fit the actual data approximately.

By using $k$-partition of matrices index set and the spectral radius for its sub-matrices, some new determinant conditions for generalized $H$-matrices under positive definite matrix conditions were presented. When a block matrix reduces a point matrix, these conditions then become the sufficient conditions for nonsingular $H$-matrices, and improve some recent related results. Numerical examples are given to show the effectiveness of the corresponding results.

Due to the high segmentation accuracy and robustness, the multi-atlas based image segmentation method is currently a hot topic. It consists of two main components which are the image registration and the label fusion. The most of current multi-atlas based image segmentation methods consider the situation that the atlas images and the target image have the same resolution. But, we will always obtain the low-resolution target images because of the restriction on the acquisition time and collecting equipment. On the other hand, the atlases are generated before the target images, and we often use high-resolution images to obtain high-resolution atlases. Since the registration from high-resolution atlases to the low-resolution target image may not obtain the exact results, the accuracy of the multi-atlas based image segmentation methods will be reduced when applied to segment the low-resolution target images. In order to solve this problem, we present an accurate and robust image segmentation method for low-resolution target images by combining the advantages of the image super-resolution method and the multi-atlas segmentation method. The experiment results show that the proposed method significantly improves the accuracy of the original multi-atlas based image segmentation method.