Preservation of transform orders under a semiparametric model and its mixture

In this paper, sufficient conditions for preservation of several transform orders under a typical family of semiparametric distributions are made. The preservation properties are developed to compare mixture semiparametric distributions. Possible applications of the achieved results to compare scale family of distributions and also compare coherent systems with dependent but identical components and series and parallel systems with randomized number of components are provided.     

Multiplicity of Solutions of the Weighted p-Laplacian with Isolated Singularity and Diffusion Suppressed by Convection

In this paper, the authors study the multiplicity of solutions to the weighted p-Laplacian with isolated singularity and di?usion suppressed by convection ?div(|x|^α|?u|^p?2?u) + λ 1/|x|^β |?u|^p?2?u · x = |x|^γg(|x|) in B \ {0} subject to nonlinear Robin boundary value condition |x|^α|?u|^p?2?u · ?n = A ? ρu on ?B,where λ > 0, B ? R^N(N ≥ 2) is the unit ball centered at the origin, α > 0, p > 1, β ∈ R, γ > ?N, g ∈ C([0,1]) with g(0) > 0, A ∈ R, ρ > 0 and ?n is the unit outward normal. The same problem with di?usion promoted by convection, namely λ ≤ 0, has already been discussed by the last two authors (Song-Yin (2012)), where the existence, nonexistence and classi?cation of singularities for solutions are presented. Completely di?erent from [Song, H. J. and Yin, J. X., Removable isolated singularities of solutions to the weighted p-Laplacian with singular convection, Math. Meth. Appl. Sci., 35, 2012, 1089–1100], in the present case λ > 0, namely the di?usion is suppressed by the convection, non-singular solutions are not only existent but also may be in?nite which vary according only to the values of solutions at the isolated singular point. At the same time, the singular solutions may exist only if the di?usion dominates the convection.     

曲率流的参数化有限元逼近

许多物理现象可以在数学上描述为受曲率驱动的自由界面运动,例如薄膜和泡沫的演变、晶体生长,等等.这些薄膜和界面的运动常依赖于其表面曲率,从而可以用相应的曲率流来描述,其相关自由界面问题的数值计算和误差分析一直是计算数学领域中的难点.参数化有限元法是曲率流的一类有效计算方法,已经能够成功模拟一些曲面在几类基本的曲率流下的演化过程.本文重点讨论曲率流的参数化有限元逼近,它的产生、发展和当前的一些挑战.     

带有随机初值的复值Ginzburg-Landau方程的弱平均动力学*

本文研究了无界域上的带有随机初值的复值Ginzburg-Landau方程.首先, 基于解过程的全局适定性, 建立了带有随机初值的Ginzburg-Landau方程的平均随机动力系统.然后, 证明了弱拉回平均随机吸引子的存在唯一性以及随机吸引子的周期性,并将其进一步推广到加权空间L²(?, L²_σ(R)).     

高维稳健主成分聚类方法及其应用研究

随着信息技术的高速发展,每条数据所包含的信息越来越丰富,使得数据不可避免地含有异常值,且随着维数的增加,异常值出现的可能性更大。传统的主成分聚类分析对异常值特別敏感,基于MCD估计的主成分聚类方法虽然对异常值具有防御作用,但是在高维数据下MCD估计的偏差过大,其稳健性显著降低,而且当维数大于观测值个数时MCD估计失效。为此本文提出了基于MRCD估计的稳健主成分聚类方法,数值模拟和实证分析表明,基于MRCD估计的主成分聚类分析的效果优于传统的主成分聚类分析和基于MCD估计的主成分聚类分析,尤其是在维数大于样本观测值的情况下,MRCD估计更为有效。     

Weighted local polynomial estimations of a non-parametric function with censoring indicators missing at random and their applications

In this paper, we consider the weighted local polynomial calibration estimation and imputation estimation of a non-parametric function when the data are right censored and the censoring indicators are missing at random, and establish the asymptotic normality of these estimators. As their applications, we derive the weighted local linear calibration estimators and imputation estimations of the conditional distribution function, the conditional density function and the conditional quantile function, and investigate the asymptotic normality of these estimators. Finally, the simulation studies are conducted to illustrate the finite sample performance of the estimators.     

LOWLAD: a locally weightedL 1 smoothing spline algorithm with cross validated choice of smoothing parameters

The computation ofL ₁ smoothing splines on large data sets is often desirable, but computationally infeasible. A locally weighted, LAD smoothing spline based smoother is suggested, and preliminary results will be discussed. Specifically, one can seek smoothing splines in the spacesW _m (D), with [0, 1] ⁿ D. We assume data of the formy _i =f(t _i )+ _i ,i=1,..., N with {t _i } _i=1 ^N D, the _i are errors withE( _i )=0, andf is assumed to be inW _m . An LAD smoothing spline is the solution,s , of the following optimization problem

Perturbation analysis of theGI/GI/1 queue

We examine a family ofGI/GI/1 queueing processes generated by a parametric family of service time distributions,F(x,), and we show that under suitable conditions the corresponding customer stationary expectation of the system time is twice continuously differentiable with respect to. Expressions for the derivatives are given which are suitable for single run derivative estimation. These results are extended to parameters of the interarrival time distribution and expressions for the corresponding second derivatives (as well as partial second derivatives involving both interarrivai and service time parameters) are also obtained. Finally, we present perturbation analysis algorithms based on these expressions along with simulation results demonstrating their performance.     

Estimation of Multinomial Probabilities under a Model Constraint

In this paper estimation of the probabilities of a multinomial distribution has been studied. The five estimators considered are: unrestricted estimator (UE), restricted estimator (RE) (under model ), preliminary test estimator (PTE) based on a test of the model , shrinkage estimator (SE) and the positive-rule shrinkage estimator (PRSE). Asymptotic distributions of these estimators are given under Pitman alternatives and the asymptotic risk under a quadratic loss has been evaluated. The relative performance of the five estimators is then studied with respect to their asymptotic distributional risks (ADR). It is seen that neither of the preliminary test and shrinkage estimators dominates the other, though each fares well relative to the other estimators. However, the positive rule estimator is recommended for use for dimension 3 or more while the PTE is recommended for dimension less than 3.     

Measurement scheduling for recursive team estimation

We consider a decentralized LQG measurement scheduling problem in which every measurement is costly, no communication between observers is permitted, and the observers' estimation errors are coupled quadratically. This setup, motivated by considerations from organization theory, models measurement scheduling problems in which cost, bandwidth, or security constraints necessitate that estimates be decentralized, although their errors are coupled. We show that, unlike the centralized case, in the decentralized case the problem of optimizing the time integral of the measurement cost and the quadratic estimation error is fundamentally stochastic, and we characterize the -optimal open-loop schedules as chattering solutions of a deterministic Lagrange optimal control problem. Using a numerical example, we describe also how this deterministic optimal control problem can be solved by nonlinear programming.This research was supported in part by ARPA Grant N00174-91-C-0116 and NSF Grant NCR-92-04419.