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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.

On uniform consistency of confidence regions based on shrinkage-type estimators

Tang, Tianyuan., 唐田园. January 2011 (has links)
published_or_final_version / Statistics and Actuarial Science / Master / Master of Philosophy

Maximum likelihood estimation of parameters with constraints in normaland multinomial distributions

Xue, Huitian., 薛惠天. January 2012 (has links)
Motivated by problems in medicine, biology, engineering and economics, con- strained parameter problems arise in a wide variety of applications. Among them the application to the dose-response of a certain drug in development has attracted much interest. To investigate such a relationship, we often need to conduct a dose- response experiment with multiple groups associated with multiple dose levels of the drug. The dose-response relationship can be modeled by a shape-restricted normal regression. We develop an iterative two-step ascent algorithm to estimate normal means and variances subject to simultaneous constraints. Each iteration consists of two parts: an expectation{maximization (EM) algorithm that is utilized in Step 1 to compute the maximum likelihood estimates (MLEs) of the restricted means when variances are given, and a newly developed restricted De Pierro algorithm that is used in Step 2 to find the MLEs of the restricted variances when means are given. These constraints include the simple order, tree order, umbrella order, and so on. A bootstrap approach is provided to calculate standard errors of the restricted MLEs. Applications to the analysis of two real datasets on radioim-munological assay of cortisol and bioassay of peptides are presented to illustrate the proposed methods. Liu (2000) discussed the maximum likelihood estimation and Bayesian estimation in a multinomial model with simplex constraints by formulating this constrained parameter problem into an unconstrained parameter problem in the framework of missing data. To utilize the EM and data augmentation (DA) algorithms, he introduced latent variables {Zil;Yil} (to be defined later). However, the proposed DA algorithm in his paper did not provide the necessary individual conditional distributions of Yil given (the observed data and) the updated parameter estimates. Indeed, the EM algorithm developed in his paper is based on the assumption that{ Yil} are fixed given values. Fortunately, the EM algorithm is invariant under any choice of the value of Yil, so the final result is always correct. We have derived the aforesaid conditional distributions and hence provide a valid DA algorithm. A real data set is used for illustration. / published_or_final_version / Statistics and Actuarial Science / Master / Master of Philosophy

Hybrid bootstrap procedures for shrinkage-type estimators

Chan, Tsz-hin., 陳子軒. January 2012 (has links)
In statistical inference, one is often interested in estimating the distribution of a root, which is a function of the data and the parameters only. Knowledge of the distribution of a root is useful for inference problems such as hypothesis testing and the construction of a confidence set. Shrinkage-type estimators have become popular in statistical inference due to their smaller mean squared errors. In this thesis, the performance of different bootstrap methods is investigated for estimating the distributions of roots which are constructed based on shrinkage estimators. Focus is on two shrinkage estimation problems, namely the James-Stein estimation and the model selection problem in simple linear regression. A hybrid bootstrap procedure and a bootstrap test method are proposed to estimate the distributions of the roots of interest. In the two shrinkage problems, the asymptotic errors of the traditional n-out-of-n bootstrap, m-out-of-n bootstrap and the proposed methods are derived under a moving parameter framework. The problem of the lack of uniform consistency of the n-out-of-n and the m-out-of-n bootstraps is exposed. It is shown that the proposed methods have better overall performance, in the sense that they yield improved convergence rates over almost the whole range of possible values of the underlying parameters. Simulation studies are carried out to illustrate the theoretical findings. / published_or_final_version / Statistics and Actuarial Science / Master / Master of Philosophy

Adaptive jacknife estimators for stochastic programming

Partani, Amit, 1978- 29 August 2008 (has links)
Stochastic programming facilitates decision making under uncertainty. It is usually impractical or impossible to find the optimal solution to a stochastic problem, and approximations are required. Sampling-based approximations are simple and attractive, but the standard point estimate of optimization and the Monte Carlo approximation. We provide a method to reduce this bias, and hence provide a better, i.e., tighter, confidence interval on the optimal value and on a candidate solution's optimality gap. Our method requires less restrictive assumptions on the structure of the bias than previously-available estimators. Our estimators adapt to problem-specific properties, and we provide a family of estimators, which allows flexibility in choosing the level of aggressiveness for bias reduction. We establish desirable statistical properties of our estimators and empirically compare them with known techniques on test problems from the literature.

M out of n bootstrap for nonstandard M-estimation: consistency and robustness

Pun, Man-chi., 潘敏芝. January 2004 (has links)
published_or_final_version / abstract / toc / Statistics and Actuarial Science / Master / Master of Philosophy

Estimating the join point of two regression regimes

Schwarz, Marion Janet, 1949- January 1978 (has links)
No description available.

Some numerical computations in linear estimation

Bhattacharya, Binay K. January 1978 (has links)
No description available.

The combination of biased and robust estimation techniques in multiple regression models

Askin, Ronald Gene 08 1900 (has links)
No description available.

Equality of minimum variance unbiased estimator under two different models

Toh, Keng Choo. January 1975 (has links)
No description available.

A discrete nonlinear recursive estimator

Bryan, Richard Erwin 08 1900 (has links)
No description available.

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