Spatial Clustering Tests Based on the Domination Number of a New Random Digraph Family

We use the domination number of a parametrized random digraph family called proportional-edge proximity catch digraphs (PCDs) for testing multivariate spatial point patterns. This digraph family is based on relative positions of data points from various classes. We extend the results on the distribution of the domination number of proportional-edge PCDs, and use the domination number as a statistic for testing segregation and association against complete spatial randomness. We demonstrate that the domination number of the PCD has binomial distribution when size of one class is fixed while the size of the other (whose points constitute the vertices of the digraph) tends to infinity and has asymptotic normality when sizes of both classes tend to infinity. We evaluate the finite sample performance of the test by Monte Carlo simulations and prove the consistency of the test under the alternatives. We find the optimal parameters for testing each of the segregation and association alternatives. Furthermore, the methodology discussed in this article is valid for data in higher dimensions also.     

Precise Asymptotics in Complete Moment Convergence of Parameter Estimator in the Gaussian Autoregressive Process

In this article, we study the precise asymptotic behaviors of the least-squares estimator in the Gaussian autoregressive process. Two kinds of complete moment convergence of this estimator can be obtained by the methods of deviation inequalities for this estimator and nonuniform Berry-Esseen bound for martingales.     

Complete convergence of the non-identically distributed pairwise NQD random sequences

ABSTRACT

In this article, we study complete convergence of the nonidentically distributed pairwise negatively quadrant dependent (NQD) random sequences by the moment inequality and terminating random variables,which extend and improve the previous relevant results.     

Optimal block designs for double cross experiments

ABSTRACT

This paper presents systematic methods of construction of optimal block designs for a double cross experiments for both even and odd values of “p” parental lines. The both even and odd values of designs are derived by using initial block of unreduced balanced incomplete block designs and initial block of row–column designs given by Bose et al. (1953 Bose, R.C., Shrikhande, S.S., Bhattacharya, K.N. (1953). On the construction of group divisible incomplete block design. Ann. Math. Stat. 24:167–195.[Crossref] , [Google Scholar]) and Gupta and Choi (1998 Gupta, S., Choi, K.C. (1998). Optimal row-column designs for complete diallel crosses. Commun. Stat. Theory Methods 27(11):2827–2835.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]), respectively. In this attempt we have found some new universally optimal block designs for double cross experiments.     

General results of complete convergence and complete moment convergence for weighted sums of some class of random variables

ABSTRACT

In the article, the complete convergence and complete moment convergence for weighted sums of sequences of random variables satisfying a maximal Rosenthal type inequality are studied. As an application, the Marcinkiewicz–Zygmund type strong law of large numbers is obtained. Our partial results generalize and improve the corresponding ones of Shen (2013 Shen, A.T. (2013). On strong convergence for weighted sums of a class of random variables. Abstr. Appl. Anal.2013, Article ID 216236: 1–7. [Google Scholar]).     

《全本新注〈聊斋志异〉》若干问题商榷

朱其铠主编的《全本新注〈聊斋志异〉》是一本好书,但在注释方面也存在一些值得商榷的问题。文章对注释方面存在的问题,逐一提出了补正意见,并提出了若干新的看法。     

《全清词·雍乾卷》辑补74首

《全清词·雍乾卷》共收词人近1000家,词作35000多首。然由于清代词籍的复杂性,遗漏在所难免。今翻检清人诗文集及地方志等,为之补录4家词作74首,以备续编采择之需。     

功在当代,泽被后学——《宋诗话全编》对古代文学研究的学术价值

《宋诗话全编》涵盖了诗论、诗话专著和主要的诗论家及主要的论诗名著,更蒐集到了至今还远未为研究者所知晓的散见于浩瀚载籍中的论诗片言只语,对治古代文学者具有莫大的参考意义和学术价值.一是补阙、正误的重要资料价值.二是为作家、作品研究提供事实支撑（含生平事迹补遗;宋代僧诗和诗僧的材料补充;弥补某些人物关系的重要史事）.三是为文学史上的某些专门问题提供佐证材料.四是艺术风格的品评,文论观点的概括,则更具有直接的理论意义.     

《全清词·雍乾卷》辑补61首

《全清词·雍乾卷》共收词人约1000多家,词作35000多首。然由于清代词籍的复杂性,遗漏在所难免。今翻检清人诗文集及地方志等,为之补录靳之隆、康载、王天发、王翰青、张礼等五家凡61首,以备续编采择之需。     

On Complete Convergence for an Extended Negatively Dependent Sequence

In this article, the Rosenthal-type maximal inequality for extended negatively dependent (END) sequence is provided. By using the Rosenthal type inequality, we present some results of complete convergence for weighted sums of END random variables under mild conditions.