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We consider a critical branching process with $\psi$-mixing immigration and prove a functional limit theorem, improving the results in previous literatures. As applications, we obtain central limit theorems for an estimator of the offspring mean.
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A new method for estimating high-dimensional covariance matrix based on network structure with heteroscedasticity of response variables is proposed in this paper. This method greatly reduces the computational complexity by transforming the high-dimensional covariance matrix estimation problem into a low-dimensional linear regression problem. Even if the size of sample is finite, the estimation method is still effective. The error of estimation will decrease with the
increase of matrix dimension. In addition, this paper presents a method of identifying influential nodes in network via covariance matrix. This method is very suitable for academic cooperation networks by taking into account both the contribution of the node itself and the impact of the node on other nodes.
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In this article we study test of sphericity for high-dimensional covariance matrix in the general population based on random matrix theory. When the sample size is less than data dimension, the classical likelihood ratio test has poor performance for test of sphericity. Thus, we propose a new statistic for test of sphericity by
using the higher moments of spectral distribution of the sample covariance matrix, and derive the asymptotic distribution of the statistic under the null hypothesis. Simulation results show that the proposed statistics can effectively improve the power of the test of sphericity for high dimensional data, and have especially significant effects for Spiked model, on the basis of controlling the type-one error probability.
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Based on Fourier transform, we obtain properties of the analytical solution of quantum walk on finite graphs. It mainly includes properties of the analytical solution of general state of quantum walk on cycle, the unbiasedness of special quantum walk on two-dimensional lattice and the relationship between the initial condition of quantum walk on hypercube and a set of basis in an invariant subspace.
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In this paper, the complete qth moment convergence for weighted sums of sequences of negatively orthant dependent random variables is investigated. By applying moment inequality and truncation methods, the equivalent conditions of complete qth moment convergence for weighted sums of sequences of negatively orthant dependent random variables are established. These results not only extend the corresponding results obtained by Li and Sp\v{a}taru\ucite{4}, Liang et al.\ucite{5}, Guo\ucite{6} and Gut\ucite{21} to sequences of negatively orthant dependent random variables, but also improve them.
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In this paper we consider the integral-typefunctional downward of single death processes in the finite state space, including the Laplace transformation of its distribution and its polynomial moments as well as the distribution of staying times. As applications, a new proof for the recursive and explicit representation of high order moments of the first hitting times in the denumerable state space is presented; meanwhile, the estimates on the lower bound and the upper one of convergence rate in strong ergodicity are obtained.
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Mortality forecasting is the basis of population forecasting. In recent years, new progress has been made in mortality models. From the earliest static mortality models, mortality models have been developed into dynamic forecasting models including time terms, such as Lee-Carter model family, CBD model family and so on. This paper reviews and sorts out relevant literature on mortality forecasting models. With the development of dynamic models, some scholars have developed a series of mortality improvement models based on the level of mortality improvement. In addition, with the progress of mortality research, multi-population mortality modeling attracted the attention of researchers, and the multi-population forecasting models have been constantly developed and
improved, which play an important role in the mortality forecasting. With the continuous enrichment and innovation of mortality model research methods, new statistical methods (such as machine learning) have been applied in mortality modeling, and the accuracy of fitting and prediction has been improved. In addition to the extension of classical modeling methods, issues such as small-area population or missing data of the population, the elderly population, the related population mortality modeling are still worth studying.
