Convergence Properties for Asymptotically almost Negatively Associated Sequence

We get the strong law of large numbers, strong growth rate, and the integrability of supremum for the partial sums of asymptotically almost negatively associated sequence. In addition, the complete convergence for weighted sums of asymptotically almost negatively associated sequences is also studied

Complete Convergence for Moving Average Process of Martingale Differences

Under some simple conditions, by using some techniques such as truncated method for random variables (see e.g., Gut (2005)) and properties of martingale differences, we studied the moving process based on martingale differences and obtained complete convergence and complete moment convergence for this moving process. Our results extend some related ones

Genetic Structure of Daphnia galeata Populations in Eastern China

This study presents the first examination of the genetic structure of Daphnia longispina complex populations in Eastern China. Only one species, D. galeata, was present across the eight investigated lakes; as identified by taxon assignment using allelic variation at 15 microsatellite loci. Three genetically differentiated D. galeata subgroups emerged independent of the type of statistical analysis applied. Thus, Bayesian clustering, discriminant analysis based on results from factorial correspondence analysis, and UPGMA clustering consistently showed that populations from two neighbouring lakes were genetically separated from a mixture of genotypes found in other lakes, which formed another two subgroups. Clonal diversity was high in all D. galeata populations, and most samples showed no deviation from Hardy-Weinberg equilibrium, indicating that clonal selection had little effect on the genetic diversity. Overall, populations did not cluster by geographical origin. Further studies will show if the observed pattern can be explained by natural colonization processes or by recent anthropogenic impact on predominantly artificial lakes

Convergence Rates in the Strong Law of Large Numbers for Martingale Difference Sequences

We study the complete convergence and complete moment convergence for martingale difference sequence. Especially, we get the Baum-Katz-type Theorem and Hsu-Robbins-type Theorem for martingale difference sequence. As a result, the Marcinkiewicz-Zygmund strong law of large numbers for martingale difference sequence is obtained. Our results generalize the corresponding ones of Stoica (2007, 2011)

Complete Consistency of the Estimator of Nonparametric Regression Models Based on ∼ ρ-Mixing Sequences

We study the complete consistency for estimator of nonparametric regression model based on ∼ ρ-mixing sequences by using the classical Rosenthal-type inequality and the truncated method. As an application, the complete consistency for the nearest neighbor estimator is obtained