共查询到20条相似文献,搜索用时 15 毫秒
1.
Peter D. Hoff 《Journal of computational and graphical statistics》2013,22(4):633-641
Abstract This article discusses a new technique for calculating maximum likelihood estimators (MLEs) of probability measures when it is assumed the measures are constrained to a compact, convex set. Measures in such sets can be represented as mixtures of simple, known extreme measures, and so the problem of maximizing the likelihood in the constrained measures becomes one of maximizing in an unconstrained mixing measure. Such convex constraints arise in many modeling situations, such as empirical likelihood and estimation under stochastic ordering constraints. This article describes the mixture representation technique for these two situations and presents a data analysis of an experiment in cancer genetics, where a partial stochastic ordering is assumed but the data are incomplete. 相似文献
2.
N. Balakrishnan G. Iliopoulos 《Annals of the Institute of Statistical Mathematics》2009,61(3):753-772
In this paper, we present a general method which can be used in order to show that the maximum likelihood estimator (MLE)
of an exponential mean θ is stochastically increasing with respect to θ under different censored sampling schemes. This propery is essential for the construction of exact confidence intervals for
θ via “pivoting the cdf” as well as for the tests of hypotheses about θ. The method is shown for Type-I censoring, hybrid censoring and generalized hybrid censoring schemes. We also establish the
result for the exponential competing risks model with censoring. 相似文献
3.
《Optimization》2012,61(9):1719-1747
ABSTRACTBy utilizing a min-biaffine scalarization function, we define the multivariate robust second-order stochastic dominance relationship to flexibly compare two random vectors. We discuss the basic properties of the multivariate robust second-order stochastic dominance and relate it to the nonpositiveness of a functional which is continuous and subdifferentiable everywhere. We study a stochastic optimization problem with multivariate robust second-order stochastic dominance constraints and develop the necessary and sufficient conditions of optimality in the convex case. After specifying an ambiguity set based on moments information, we approximate the ambiguity set by a series of sets consisting of discrete distributions. Furthermore, we design a convex approximation to the proposed stochastic optimization problem with multivariate robust second-order stochastic dominance constraints and establish its qualitative stability under Kantorovich metric and pseudo metric, respectively. All these results lay a theoretical foundation for the modelling and solution of complex stochastic decision-making problems with multivariate robust second-order stochastic dominance constraints. 相似文献
4.
We prove convex ordering results for random vectors admitting a predictable representation in terms of a Brownian motion and
a non-necessarily independent jump component. Our method uses forward-backward stochastic calculus and extends the results
proved in Klein et al. (Electron J Probab 11(20):27, 2006) in the one-dimensional case. We also study a geometric interpretation of convex ordering for discrete measures in connection
with the conditions set on the jump heights and intensities of the considered processes.
The work described in this paper was partially supported by a grant from City University of Hong Kong (Project No. 7200108). 相似文献
5.
We consider a load-sharing problem for a multiprocessor system in which jobs have real-time constraints: if the waiting time of a job exceeds a given random amount (called the laxity of the job), then the job is considered lost. To minimize the steady-state probability of loss with respect to the load-sharing parameters, we propose to use the likelihood ratio derivative estimate approach, which has recently been studied for sensitivity analysis of stochastic systems. We formulate a recursive stochastic optimization algorithm using likelihood ratio estimates to solve the optimization problem and provide a proof for almost sure convergence of the algorithm. The algorithm can be used for on-line optimization of the real-time system and does not require a priori knowledge of the arrival rate of customers to the system or the service time and laxity distributions. To illustrate our results, we provide simulation examples.This research was partially supported by an IBM Graduate Fellowship and by the National Science Foundation through Grant No. ECS-87-15217. 相似文献
6.
The hybrid censoring scheme is a mixture of type-I and
type-II censoring schemes. It is a popular censoring scheme in the literature
of life data analysis. Mixed exponential distribution (MED) models is a class
of favorable models in reliability statistics. Nevertheless, there is no much
discussion to focus on parameters estimation for MED models with hybrid
censored samples. We will address this problem in this paper. The EM
(Expectation-Maximization) algorithm is employed to derive the closed form of
the maximum likelihood estimators (MLEs). Finally, Monte Carlo simulations and
a real-world data analysis are conducted to illustrate the proposed method. 相似文献
7.
We consider stochastic optimization problems where risk-aversion is expressed by a stochastic ordering constraint. The constraint requires that a random vector depending on our decisions stochastically dominates a given benchmark random vector. We identify a suitable multivariate stochastic order and describe its generator in terms of von Neumann–Morgenstern utility functions. We develop necessary and sufficient conditions of optimality and duality relations for optimization problems with this constraint. Assuming convexity we show that the Lagrange multipliers corresponding to dominance constraints are elements of the generator of this order, thus refining and generalizing earlier results for optimization under univariate stochastic dominance constraints. Furthermore, we obtain necessary conditions of optimality for non-convex problems under additional smoothness assumptions. 相似文献
8.
We generalize stochastic mathematical programs with equilibrium constraints (SMPEC) introduced by Patriksson and Wynter (Ref. 1) to allow for the inclusion of joint upper-level constraints and to change the continuity assumptions with respect to the uncertainty parameters assumed before by measurability assumptions. For this problem, we prove the existence of solutions. We discuss also algorithmic aspects of the problem, in particular the construction of an inexact penalty function for the SMPEC problem. We apply the theory to the problem of structural topology optimization. 相似文献
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11.
Under the assumption of dependent identically distributed components and redundant (spares) components, the problem of stochastic comparison of component and system redundancies have been considered. This study has been carried out under the criteria of the likelihood ratio ordering, the reversed failure rate ordering, the failure rate ordering and the usual stochastic ordering. 相似文献
12.
《Journal of computational and graphical statistics》2013,22(3):403-421
This article presents methods for finding the nonparametric maximum likelihood estimate (NPMLE) of the distribution function of time-to-event data. The basic approach is to use graph theory (in particular intersection graphs) to simplify the problem. Censored data can be represented in terms of their intersection graph. Existing combinatorial algorithms can be used to find the important structures, namely the maximal cliques. When viewed in this framework there is no fundamental difference between right censoring, interval censoring, double censoring, or current status data and hence the algorithms apply to all types of data. These algorithms can be extended to deal with bivariate data and indeed there are no fundamental problems extending the methods to higher dimensional data. Finally this article shows how to obtain the NPMLE using convex optimization methods and methods for mixing distributions. The implementation of these methods is greatly simplified through the graph-theoretic representation of the data. 相似文献
13.
Hsien-Chung Wu 《Fuzzy Optimization and Decision Making》2003,2(1):13-29
The solution concepts of the fuzzy optimization problems using ordering cone (convex cone) are proposed in this paper. We introduce an equivalence relation to partition the set of all fuzzy numbers into the equivalence classes. We then prove that this set of equivalence classes turns into a real vector space under the settings of vector addition and scalar multiplication. The notions of ordering cone and partial ordering on a vector space are essentially equivalent. Therefore, the optimality notions in the set of equivalence classes (in fact, a real vector space) can be naturally elicited by using the similar concept of Pareto optimal solution in vector optimization problems. Given an optimization problem with fuzzy coefficients, we introduce its corresponding (usual) optimization problem. Finally, we prove that the optimal solutions of its corresponding optimization problem are the Pareto optimal solutions of the original optimization problem with fuzzy coefficients. 相似文献
14.
??In this paper, we concern with the estimation problem for the Pareto
distribution based on progressive Type-II interval censoring with random removals. We discuss
the maximum likelihood estimation of the model parameters. Then, we show the consistency and
asymptotic normality of maximum likelihood estimators based on progressive Type-II interval
censored sample. 相似文献
15.
《高校应用数学学报(英文版)》2019,34(4)
One of the most powerful algorithms for obtaining maximum likelihood estimates for many incomplete-data problems is the EM algorithm. However, when the parameters satisfy a set of nonlinear restrictions, It is difficult to apply the EM algorithm directly. In this paper,we propose an asymptotic maximum likelihood estimation procedure under a set of nonlinear inequalities restrictions on the parameters, in which the EM algorithm can be used. Essentially this kind of estimation problem is a stochastic optimization problem in the M-step. We make use of methods in stochastic optimization to overcome the difficulty caused by nonlinearity in the given constraints. 相似文献
16.
概率分布间随机序在实践中已经得到了广泛的应用,而且似然比检验是用以检验涉及随机序问题的最普遍的检验方法.但是,关于多个多项式总体间的增凸序约束的统计推断问题并没有得到充分发展.多样本的增凸序对无约束的检验问题已被研究.然而,多总体的相等性对增凸序的假设检验问题似乎更有研究意义.并且分布的相等对随机序的假设检验问题往往是统计学家最为普遍地考虑.对多样本的情况,本文考虑了分布的相等对增凸序的假设检验问题,并且获得似然比检验统计量的零渐近分布,它是一组x~2分布随机变量的加权和,即■~2分布. 相似文献
17.
In this paper, we develop an empirical likelihood-based test for the presence of stochastic ordering under censoring in the k-sample case. The proposed test statistic is formed by taking the supremum of localized empirical likelihood ratio test statistics. Its asymptotic null distribution has a simple representation in terms of a standard Brownian motion process. Through simulations, we show that it outperforms in terms of power existing methods for the same problem at all the distributions that we consider. A real-life example is used to illustrate the applicability of this new test.
相似文献18.
A problem that is frequently encountered in statistics concerns testing for equality of multiple probability vectors corresponding to independent multinomials against an alternative they are not equal. In applications where an assumption of some type of stochastic ordering is reasonable, it is desirable to test for equality against this more restrictive alternative. Similar problems have been considered heretofore using the likelihood ratio approach. This paper aims to generalize the existing results and provide a unified technique for testing for and against a set of linear inequality constraints placed upon on any probability vectors corresponding to r independent multinomials. The paper shows how to compute the maximum likelihood estimates under all hypotheses of interest and obtains the limiting distributions of the likelihood ratio test statistics. These limiting distributions are of chi bar square type and the expression of the weighting values is given. To illustrate our theoretical results, we use a real life data set to test against second-order stochastic ordering. 相似文献
19.
逐步区间删失是获取高可靠性产品相关信息的一种重要方法.文章研究了产品寿命服从Weibull分布,带有随机移除逐步区间删失寿命试验的最优设计问题.采用极大似然方法获取模型参数的估计及其信息矩阵.利用Bayesian方法处理模型参数未知情况下设计准则对模型参数的依赖问题,获得了模型参数估计的Bayesian稳健设计准则.在考虑试验费用有限制的条件下,给出了获得最优稳健设计非线性混合整数算法.同时对先验选取及约束参数设定的敏感性做了分析.数值结果表明文章提出的方法是有效可行的. 相似文献