NONNULL DISTRIBUTION OF THE LIKELIHOOD RATIO CRITERION FOR TESTING THE EQUALITY OF DIAGONAL BLOCKS WITH BLOCKWISE INDEPENDENCE

In this paper, the nonnull moments and the distributions of the likelihood ratio criterion for testing the equality of diagonal blocks with blockwise independence under certain alternatives have derived.

The Effectiveness of Cyclic Blockwise Distribution

In spite of the wealth Of existing data distribution methods, most parallel programming languages support only some form of cyclic blockwise distribution. The main reason why only this single method is supported is that it is relatively simple to implement. However, it is as yet nuclear whether cyclic blockwise distribution is sufficiently powerful for a wide class of distribution problems. In this paper the method will be analysed, showing that for a wide range of problems it is indeed sufficient. It will also be shown in which cases cyclic blockwise distribution can be effected to fail. From this analysis, it is possible to formulate practical guidelines to assist Programmers in choosing the cycle frequency for cyclic blockwise distribution that leads to an optimal result.

On the Strong Limit Theorems for Double Arrays of Blockwise M-dependent Random Variables

For a double array of blockwise M-dependent random variables {Xmn,m ≥ 1,n ≥ 1}, ∑i^m=1 ∑^nj=1 strong laws of large numbers are established for double sums ∑m i=1 ∑j^n=1 ij, m≥ 1, n 〉 1. The main results are obtained for （i） random variables {Xmn, m≥ 1, n ≥ 1} being non-identically distributed but satisfy a condition on the summability condition for the moments and （ii） random variables {Xmn, m ≥ 1, n ≥ 1} being stochastically dominated. The result in Case （i） generalizes the main result of M6ricz et al. [J. Theoret. Probab., 21, 660-671 （2008）] from dyadic to arbitrary blocks, whereas the result in Case （ii） extends a result of Gut [Ann. Probab., 6, 469-482 （1978）] to the bockwise M-dependent setting. The sharpness of the results is illustrated by some examples.

Some Strong Laws of Large Numbers for Blockwise Martingale Difference Sequences in Martingale Type p Banach Spaces

For a blockwise martingale difference sequence of random elements {Vn, n ≥ 1} taking values in a real separable martingale type p （1 ≤ p ≤ 2） Banach space, conditions are provided for strong laws of large numbers of the form limn→∞ Vi/gn = 0 almost surely to hold where the constants gn ↑∞. A result of Hall and Heyde [Martingale Limit Theory and Its Application, Academic Press, New York, 1980, p. 36] which was obtained for sequences of random variables is extended to a martingale type p （1〈 p ≤2） Banach space setting and to hold with a Marcinkiewicz-Zygmund type normalization. Illustrative examples and counterexamples are provided.

The Inductive Blockwise Alperin Weight Condition for PSL（3, q）

The blockwise Alperin weight conjecture assets that for any finite group G and any prime l, the number of the Brauer characters in an l-block B equals the number of the G-conjugacy classes of l-weights belonging to B. Recently, the inductive blockwise Alperin weight condition has been introduced such that the blockwise Alperin weight conjecture holds if all non-abelian simple groups satisfy these conditions. We will verify the inductive blockwise Alperin weight condition for the finite simple groups PSL（3, q） in this paper.

The Inductive Blockwise Alperin Weight Condition for PSp4(q)

Let G be a finite group and ι be any prime dividing|G|.The blockwise Alperin weight conjeeture states that the number of the irreducible Brauer characters in an E-block B of G equals the number of the G-conjugacy classes of ι-weights belonging to B.Recently,this conjeeture has been reduced to the simple groups,which means that to prove the blockwise Alperin weight conjeeture,it suffices to prove that all non-abelian simple groups satisfy the inductive blockwise Alperin weight condition.In this paper,we verify this inductive cond计ion for the finite simple groups PSp4(g)and non-defining characteristic,where q is a power of an odd prime.

BLOCKWISE PERTURBATION THEORY FOR 2×2 BLOCK MARKOV CHAINS

Let P be a transition matrix of a Markov chain and be of the form P = qq@. The stationary distribution πT is partitioned conformally in the form (π1T, π2T). This paper establish the relative error bound in πiT (i = 1, 2) when each block Pij get a small relative perturbation.

Empirical Euclidean likelihood for general estimating equations under association dependence

Empirical Euclidean likelihood for general estimating equations for association dependent processes is investigated. The strong consistency and asymptotic normality of the blockwise maximum empirical Euclidean likelihood estimator are presented. We show that it is more efficient than estimator without blocking. The blockwise empirical Euclidean log-likelihood ratio asymptotically follows a chi-square distribution.

Joint empirical likelihood confidence regions for a finite number of quantiles under strong mixing samples

In this paper, we obtain the joint empirical likelihood confidence regions for a finite number of quantiles under strong mixing samples. As an application of this result, the empirical likelihood confidence intervals for the difference of any two quantiles are also obtained.

An Efficient Quadratic Approximation of Simple Singular Solutions——Dedicated to Professor You Zhao-yong on the occasion of his 60-th birthday

We consider a blockwise extended system and an efficient quadratically convergent Newton-like method for approximations of simple (cubic) singular solutions of nonlinear problems with sparse properties.

How to Estimate the Mortality Risk of COVID-19:A New Approach with a Three-Factor Decomposition

Statistical analysis of COVID-19 mortality is challenging due to its non-stationarity and cross-sectional instability.In this paper,the authors introduce a unified method to evaluate the fatality rate of COVID-19 across countries,whose method provides more reliable information for cross-country comparison than the traditional case-fatality rate(CFR).It emerges that the new method,the blockwise case-fatality rate(BCFR),varies for different countries and in different periods.The authors also decompose the COVID-19 fatality data by three factors:1)The virus infection dynamics over population in different countries,2)pure distribution and evolution of instantaneous death rate attributed to different individual’s physical characteristics such as age and health,and 3)individual countries’variations affecting interactions between the virus infection and the instantaneous mortality due to individual’s physical characteristics.Based on the new three-factor model,the authors obtain six key findings of the COVID-19 fatality rate.Our study suggests that,on average,the estimated instantaneous fatality rate contributes about 57.0%to the global BCFR while the time-varying weight contributes about 41.5%in December 2020.The country-specific contribution of instantaneous fatality rate is significantly higher than that of the time-varying weight.Besides,the country-specific characteristics in demographical,social,and economic aspects would affect the relative severity of the disease.

Empirical Likelihood for Partially Linear Models Under Negatively Associated Errors

This paper proposes to use the blockwise empirical likelihood （EL） method to construct the confidence regions for the regression vector β in a partially linear model under negatively associated errors. It is shown that the blockwise EL ratio statistic for β is asymptotically χ^2 distributed. The result is used to obtain an EL-based confidence region for β. Results of a simulation study on the finite sample performance of the proposed confidence regions are reported.

Empirical Likelihood Ratio Confidence Interval for Positively Associated Series

Empirical likelihood is discussed by using the blockwise technique for strongly stationary, positively associated random variables. Our results show that the statistics is asymptotically chi-square distributed and the corresponding confidence interval can be constructed.

Empirical Likelihood for Quantiles Under Associated Samples

The construction of confidence intervals for quantiles of a population under a associated sample is studied by using the blockwise technique. It is shown that the blockwise empirical likelihood （EL） ratio statistic is asymptotically X2-type distributed, which is used to obtain EL-based confidence intervals for quantiles of a population.

Joint Empirical Likelihood Confidence Regions for a Finite Number of Quantiles Under Negatively Associated Samples

In this paper, the authors obtain the joint empirical likelihood confidence regions for a finite number of quantiles under negatively associated samples. As an application of this result, the empirical likelihood confidence intervals for the difference of any two quantiles are also developed.