无失效数据的多层Bayes分析

本文对无效数据（ｔ,ｎｉ）,在时刻ｔｉ的失效概率ｐｉ＝ｐ的先验分布不为完全Ｂｅｔａ分布Ｂｅｔａ（ｐｉ－１,λ;ａ,１）时,给出了ｐｉ多层Ｂａｙｅｓ估计,从而可以得到无失铲数据情形可靠度的估计。     

Poisson分布参数的渐近最优和可容许的经验Bayes估计

设Ｘ及（Ｘ１，Ｘ２…，Ｘｎ）分别为取自Ｐｏｉｓｓｏｎ分布Ｐ（θ）的当前样本和历史样本，参数θ的先验分布族Ｆ＝｛Γ（ｍ，β）：β＞０｝，其中ｍ＞０已知，Γ（ｍ，β）表示参数为（ｍ，β）的伽玛分布．对ｐ＞０，ｑ＞２的任意两个实数，记ｔｎ＝Ｘ＋∑ｎｉ＝１Ｘｉ＋ｐＸ＋∑ｎｉ＝１Ｘｉ＋ｐ＋ｑ＋（ｎ＋１）ｍ（Ｘ＋ｍ）则在平方损失函数ｌ（θ，ｄ）＝（θ－ｄ）２下，ｔｎ是θ的渐近最优和可容许的经验Ｂａｙｅｓ估计，而且收敛速度为Ｏ（１ｎ）．     

增长曲线模型的参数估计及其性质

考虑增长曲线模型：Ｙｐ×ｎ＝ＡＢＣ＇＋εｐ×ｎ，Ｅε＝０．其中，ε＝（ε１，ε２，…，εｎ），ε１，ε２…，εｎ独立同分布，Ｅεｉεｉ＇＝Σｐ×ｐ＞０．该文利用协差阵的Σ的（一定意义下的）最小二乘估计Σ，分别给出了参数Ｂ，参数的线性函数ＡＢ，ｔｒ（Ｄ１’Ｂ）＋（Ｄ２Σ）（Ｄ２＝Ｄ‘２）（Ｄ２＝Ｄ２’）的估计Ｂｎ，Ｚｎ和ｔｒ（Ｄ１＇Ｂｎ）＋ｔｒ（Ｄ２Σｎ）．在ε１服从正态分布的情形下，给出了Ｚｎ，Σｎ的分布．并在ε１分布比较一般的情形和一定条件下给出了Ｚｎ，Ｂｎ，Σｎ和ｔｒ（Ｄ１’Ｂｎ）＋ｔｒ（Ｄ２Σｎ）的极限分布皆为正态分布（ｎ→∞）．而且Ｚｎ，和Σｎ，Ｂｎ，和Σｎ都是渐近独立的（ｎ→∞）．从而可构造参数Ｂ的置信区域和更好地进行判别分析，相关分析等．     

各向异性Besov类的最优恢复

本文讨论各向异性 Ｂｅｓｏｖ类 ＳＢ（Ｒd）在 Ｌp （Ｒd ）（１＜ p<∞）中及在Ｌｑ（Ｒｄ）（１＜ｐ≤ｑ≤２）中的最优恢复,得到了相应误差的弱渐近估计．     

工序能力Bayes推断

本文从Ｂａｙｅｓ观点研究工序能力，对无信息先验和共轭先验，给出了Ｃｐ的后验分布、条件期望估计和最大后验估计、Ｂａｙｅｓ置信下限和判断工序是否有能力的临界值，适于对相似工序作统计推断。     

删失场合半参数回归模型的二阶段估计

对于半参数回归模型ｙｉ＝ｘ′ｉβ＋ｇ（ｔｉ）＋ｅｉ，１≤ｉ≤ｎ，ｇ为Ｒ１上未知函数，β为ｐ×１维待估参数向量．本文考虑当ｙｉ被随机删失时β和ｇ的估计．基于模型的可加性，利用综合数据法得到β的二阶段估计β～＊ｎ和ｇ的估计ｇ＊ｎ，并证明了它们的强相合性．     

Banach空间的型与B值随机元和的完全收敛性

本文讨论了Ｂ值随机元非随机足标与随机足标和的完全收敛性．当０＜ｔ＜１时，得到了任意随机元完全收敛性的一般性结论；当１≤ｔ＜ｐ≤２时，揭示了独立零均值随机元的完全收敛性与Ｂａｎａｃｈ空间ｐ型性质的关系．推广并加强了许多熟知的结果     

B值广义αK_p鞅空间上极大算子与均方算子的有界性

该文引入了一类Ｂ值广义αＫｐ鞅空间（１≤ａ≤Ｐ≤＋∞，且ａ＜＋∞），并获得如下主要结果：①当ａ＞１时，极大算子在这类空间上总是有界的．②当ａ≥２时，ａ－均方算子在这类空间上为有界的充要条件是：状态空间Ｂ是α一凸的．     

非参数回归函数估计的随机加权逼近

本文应用随机加权法的思想构造了回归函数的最近邻估计和核估计的随机加权统计量,并证明了用随机加权统计量的分布逼近两类估计量的分布之精度可达到ｏ（ｎ~（－１／２Ｐ）,其中１＜ｐ ≤ ２．     

二项分布无失效数据可靠度的多层Bayes估计

文章对二次分布无失效数据的可靠度,在先验分布为Ｂｅｔａ分布时,给出了可靠度的多层Ｂａｙｅｓ估计。最后,结合实际问题进行了计算。     

斑须蝽种群空间分布格局Weibull分布的拟合

Weibull分布的概率密度函数为f(x) =(c/b) [(x -a) /b]c -1exp [(x a) /b]c ,x≥a。本文首次用于拟合班须蝽三代卵块的空间分布 ,8批抽样数据拟合结果表明班须蝽三代卵块在烟田的空间分布遵循Weibull分布。从而丰富了班须蝽种群空间格局的分布理论。同时 ,利用斑须蝽种群空间格局的资料探讨了Weibull分布的参数b、c与种群密度及种群聚集度之间的关系 ,结果表明 ,尺度参数b与种群密度、种群聚集度间均分别存在极显著的线性相关关系 ,形状参数c与种群密度存在极显著的正幂函数相关关系 ,与种群聚集度之间存在极显著负幂函数关系。     

A concentrated Cauchy distribution with finite moments

The Cauchy distribution $$\mathfrak {C}(a,b)(x)=\frac{1}{\pi b(1+(\frac{x-a}{b})^2)},\quad -\infty < x <\infty,$$ with a,b real, b>0, has no moments (expected value, variance, etc.), because the defining integrals diverge. An obvious way to “concentrate” the Cauchy distribution, in order to get finite moments, is by truncation, restricting it to a finite domain. An alternative, suggested by an elementary problem in mechanics, is the distribution $${\mathfrak {C}}_g(a,b)(x)=\frac{\sqrt{1+2 b g}}{\pi b (1+(\frac{x-a}{b})^2)\sqrt{1-2 b g(\frac{x-a}{b})^2}},\quad a-\sqrt{\frac{b}{2g}}<x<a+\sqrt{\frac{b}{2g}},$$ with a,b as above and a third parameter g≥0. It has the Cauchy distribution C(a,b) as the special case with g=0, and for any g>0, ? _g (a,b) has finite moments of all orders, while keeping the useful “fat tails” property of ?(a,b).     

Test of association between multivariate stable vectors

Based on observations of d-dimensional random vectors in the domain of attraction of a stable distribution with (multi-)index α = (α₁, …, α_d), an estimator for the dependence function of the α_i-stable variables is constructed. The estimator utilizes the α-tail-estimator and an estimator of the spectral measure of the α-stable law. This estimator gives rise to a test of association of the stable components and various quantitative measures of association.     

关于两个均匀分布总体标准差比的估计

考虑取两个均匀分布总体样本数不同时,两个均匀分布总体标准差比的估计,给出了两个均匀分布总体标准差比的区间估计.     

Discrete time parametric models with long memory and infinite variance

We study a large class of infinite variance time series that display long memory. They can be represented as linear processes (infinite order moving averages) with coefficients that decay slowly to zero and with innovations that are in the domain of attraction of a stable distribution with index 1 < α < 2 (stable fractional ARIMA is a particular example). Assume that the coefficients of the linear process depend on an unknown parameter vector β which is to be estimated from a series of length n. We show that a Whittle-type estimator β_n for β is consistent (β_n converges to the true value β₀ in probability as n → ∞), and, under some additional conditions, we characterize the limiting distribution of the rescaled differences (n/logn)^1/ga(β_n − β₀).     

Work-Conserving Tandem Queues

Consider a tandem queue of two single-server stations with only one server for both stations, who may allocate a fraction α of the service capacity to station 1 and 1−α to station 2 when both are busy. A recent paper treats this model under classical Poisson, exponential assumptions.Using work conservation and FIFO, we show that on every sample path (no stochastic assumptions), the waiting time in system of every customer increases with α. For Poisson arrivals and an arbitrary joint distribution of service times of the same customer at each station, we find the average waiting time at each station for α = 0 and α = 1. We extend these results to k ≥ 3 stations, sample paths that allow for server breakdown and repair, and to a tandem arrangement of single-server tandem queues.This revised version was published online in June 2005 with corrected coverdate     

Asymptotic properties of Cramér-Smirnov statistics—A new approach

Let Y₁,…, Y_n be independent identically distributed random variables with distribution function F(x, θ), θ = (θ′₁, θ′₂), where θ_i (i = 1, 2) is a vector of p_i components, p = p₁ + p₂ and for θI, an open interval in ^p, F(x, θ) is continuous. In the present paper the author shows that the asymptotic distribution of modified Cramér-Smirnov statistic under H_n: θ₁ = θ₁₀ + n^−1/2γ, θ₂ unspecified, where γ is a given vector independent of n, is the distribution of a sum of weighted noncentral χ₁² variables whose weights are eigenvalues of a covariance function of a Gaussian process and noncentrality parameters are Fourier coefficients of the mean function of the Gaussian process. Further, the author exploits the special form of the covariance function by using perturbation theory to obtain the noncentrality parameters and the weights. The technique is applicable to other goodness-of-fit statistics such as U² [G. S. Watson, Biometrika 48 (1961), 109–114].     

e~(ax+bx~2)(a,b∈R)参数平面上的骚动区域

本文将参数（ａ，ｂ）平面分为七个区域，然后讨论在每一个区域中ｅａｘ＋ｂｘ２的不动点分布（§１）．在§２中，我们得到一个定理：在Ｄ∞１∪Ｄ∞Ｃ中ｅａｘ＋ｂｘ２是骚动的（在扩充意义下）．     

Efficient robust estimation of parameter in the random censorship model

For an open set Θ of ^k, let \s{P_θ: θ Θ\s} be a parametric family of probabilities modeling the distribution of i.i.d. random variables X₁,…, X_n. Suppose X_i's are subject to right censoring and one is only able to observe the pairs (min(X_i, Y_i), [X_i Y_i]), i = 1,…, n, where [A] denotes the indicator function of the event A, Y₁,…, Y_n are independent of X₁,…, X_n and i.i.d. with unknown distribution Q₀. This paper investigates estimation of the value θ that gives a fitted member of the parametric family when the distributions of X₁ and Y₁ are subject to contamination. The constructed estimators are adaptive under the semi-parametric model and robust against small contaminations: they achieve a lower bound for the local asymptotic minimax risk over Hellinger neighborhoods, in the Hájel—Le Cam sense. The work relies on Beran (1981). The construction employs some results on product-limit estimators.