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Order of addition designs with conditions are widely used in experiments, but references on this subject are rather primitive. The paper gives the definition of conditional main effect of pair-wise ordering factor, studies the orthogonality of conditional main effects of pair-wise ordering factors, and proposes the model of order of addition designs with conditions. Finally, it gives the methods for data analysis through two examples.
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In this paper we study a Geo/Geo/1 queue with T-IPH vacations, where T-IPH denotes the discrete-time phase type distribution defined on a birth and death process with countably many states. Both the multiple and single vacation strategies are considered. For each case, based on the system of stationary equations and using complex analysis method, we firstly give the probability generating functions (PGFs) of stationary distributions for queue length and sojourn time. Moreover, by analysis the PGFs, recursive and asymptotic formulas for additional queue length and additional delay are also given. Finally, we further give some numerical examples to show the effectiveness of the method.
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A reasonable mortality model is the key to accurately measuring longevity risks. This paper considers the dependence of mortality among different age groups and the autocorrelation and heteroscedastic structure of mortality in each age group. The multivariate Copula and AR(n)-LSV models are used to construct the mortality model. VaR, TVaR, GlueVaR are used to measure longevity risk. The results show that Copula-AR($n$)-LSV characterizes mortality trends and fluctuations better than Lee-Cater model; When mortality in China gradually decline, insurance companies will face increasing longevity risk in the future.
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We study the moderate deviation probability of the position of the rightmost particle in a branching Brownian motion and obtain its moderate deviation function. Firstly, Chauvin and Rouault studied the large deviation probability for the rightmost position in a branching Brownian motion. Recently, Derrida and Shi considered lower deviation for the same model. By contrast, Our main result is more extensive.
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Mean chage-point detection is the groundwork in statistics. The trimmed empirical Euclidean likelihood ratio function is constructed based on the features of change-point in mean model. And the explicit expression is derived. The null limit distribution of the test statistic is investigated with extreme value distribution. And the change-point detection is made. if the change-point exists, it's location and consistency are discussed. Simulations and real analysis of Nile River data show that our proposed method is practicable and effective.
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We consider a branching random walk with bounded steps in random environments, where the particles are produced as a branching process with a random environment in time, and move independently as a random walk with bounded steps on $\mathbb{Z}$ with a random environment in location. We study the speed of the rightmost particle, conditionally on the survival of the branching process.
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With the improvement of data collection and storage capacity, ultra-high dimensional data\ucite{9}, that is, dimensionality with the exponential growth of samples appears in many scientific neighborhoods. At this time, penalized variable selection methods generally encounter three challenges: computational expediency, statistical accuracy, and algorithmic stability, which are limited in handling ultra-high dimensional problems. Fan and Lv\ucite{9} proposed the method of ultra-high dimensional feature screening, and achieved a lot of research results in the past ten years, which has become the most popular field of research in statistics. This paper mainly introduces the related work of ultra-high dimensional screening method from four aspects: the screening methods with model hypothesis, including parametric, non-parametric and semi-parametric model hypothesis, model-free hypothesis, and screening methods for special data. Finally, we briefly discuss the existing problems of ultra-high dimensional screening methods and some future directions.
