《天龙八部》中的因果之说

《天龙八部》是金庸作品中和佛教关系最紧密的一部小说。金庸通过三位主角引出了芸芸众生相以及纷繁复杂的故事发展,而这一切到最后,全部都是有因可循的。通过分析主角及配角的经历和结局,来揭示《天龙八部》中所体现的因果之说。     

二次型与(半)稳定矩阵的判定

对二次型与（半）稳定矩阵之间的相互关系进行了讨论，得到了二者之间的相互判定方法，且利用二次型的不同配方法得到判定（半）稳定矩阵的一些条件     

Some Results on Modeling Biological Sequences and Web Navigation with a Semi Markov Chain

In the article, the entrance probabilities and the probability distribution of the number of transitions to a state are studied to provide some answers to questions related to state occupancies for the semi Markov model. Biological sequences and Web navigation are two cases that initially seem to be different but to a certain extent they do have similarities. Two main aspects of word occurrences in biological sequences are: (a) where do they occur and (b) how many times do they occur. In Web navigation the similar questions are (a) when a node is visited and (b) how many times a node is visited. So, the theoretical results of this study are applied to model these two cases and derive distributions of word location or node occurrence and frequency of occurrences. Rewards/costs are included in the Web navigation model and analytic forms for the means, variances, and moments of total interval rewards/costs are provided.     

Efficiency and productivity of the cement industry: Pakistani experience of deregulation and privatisation

This study evaluates the impact of privatisation on efficiency and productivity of the Pakistani cement industry. To address some of the serious concerns about the problem of dimension and outlier, we use a newly developed unconditional hyperbolic α-quantile estimator of Wheelock and Wilson to estimate efficiency (Wheelock DC, Wilson PW. Non-parametric, unconditional quantile estimation for efficiency analysis with an application to Federal Reserve check processing operations. Journal of Econometrics; 2008: 209–25). Subsequently, we use these efficiency estimates to calculate the Malmquist productivity growth and its components. The results show that deregulation and privatisation had the desired positive effect on productivity growth due to technological progress. We conclude that this improvement in the post reform period could be linked to political stability, improved economic conditions and a competitive industry.     

Asymptotic normality of kernel type regression estimators for random fields

The asymptotic normality of the Nadaraya–Watson regression estimator is studied for α-mixing$\alpha \text{-}\mathrm{mixing}$ random fields. The infill-increasing setting is considered, that is when the locations of observations become dense in an increasing sequence of domains. This setting fills the gap between continuous and discrete models. In the infill-increasing case the asymptotic normality of the Nadaraya–Watson estimator holds, but with an unusual asymptotic covariance structure. It turns out that this covariance structure is a combination of the covariance structures that we observe in the discrete and in the continuous case.     

Semi Varying Coefficient Zero-Inflated Generalized Poisson Regression Model

In this paper, the semi varying coefficient zero-inflated generalized Poisson model is discussed based on penalized log-likelihood. All the coefficient functions are fitted by penalized spline (P-spline), and Expectation-maximization algorithm is used to drive these estimators. The estimation approach is rapid and computationally stable. Under some mild conditions, the consistency and the asymptotic normality of these resulting estimators are given. The score test statistics about dispersion parameter is discussed based on the P-spline estimation. Both simulated and real data example are used to illustrate our proposed methods.     

Bivariate semi α-Laplace distribution and processes

The Laplace distribution is considered as a better choice for modeling whenever data exhibit high kurtosis and heavier tails than Gaussian tails. Even though this is the case, not much work has been done on bivariate Laplace distribution. In this work, we introduce and study a new class of bivariate distributions called bivariate semi α-Laplace distribution, containing bivariate Laplace distributions. Three characterizations of bivariate semi α-Laplace distribution are obtained. Relation with bivariate semi stable distribution is established. An autoregressive model with bivariate semi α-Laplace marginal distributions is developed.     

A surprising property of uniformly best linear affine estimation in linear regression when prior information is fuzzy

It is already shown in Arnold and Stahlecker (2009) that, in linear regression, a uniformly best estimator exists in the class of all Γ-compatible$\Gamma \text{-compatible}$ linear affine estimators. Here, prior information is given by a fuzzy set Γ$\Gamma$ defined by its ellipsoidal α-cuts$\alpha \text{-cuts}$. Surprisingly, such a uniformly best linear affine estimator is uniformly best not only in the class of all Γ-compatible$\Gamma \text{-compatible}$ linear affine estimators but also in the class of all estimators satisfying a very weak and sensible condition. This property of a uniformly best linear affine estimator is shown in the present paper. Furthermore, two illustrative special cases are mentioned, where a generalized least squares estimator on the one hand and a general ridge or Kuks–Olman estimator on the other hand turn out to be uniformly best.     

Rates of Posterior Convergence for iid Observations

By means of the Hausdorff α-entropy introduced by Xing and Ranneby (2009 Xing , Y. , Ranneby , B. ( 2009 ). Sufficient conditions for Bayesian consistency . J. Statist. Plann. Inference. 139 : 2479 – 2489 . [Google Scholar]), we give two theorems on rates of in-probability convergence of posterior distributions. The result is applied in study of the Bernstein polynomial priors.