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31 
On uniform consistency of confidence regions based on shrinkagetype estimatorsTang, Tianyuan., 唐田园. January 2011 (has links)
published_or_final_version / Statistics and Actuarial Science / Master / Master of Philosophy

32 
Maximum likelihood estimation of parameters with constraints in normaland multinomial distributionsXue, 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 doseresponse 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 doseresponse relationship can be modeled by a shaperestricted
normal regression. We develop an iterative twostep 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 radioimmunological 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

33 
Hybrid bootstrap procedures for shrinkagetype estimatorsChan, Tszhin., 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. Shrinkagetype 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 JamesStein 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 noutofn bootstrap, moutofn bootstrap and the proposed methods are derived under a moving parameter framework. The problem of the lack of uniform consistency of the noutofn and the moutofn 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

34 
Adaptive jacknife estimators for stochastic programmingPartani, 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. Samplingbased 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 previouslyavailable estimators. Our estimators adapt to problemspecific 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.

35 
M out of n bootstrap for nonstandard Mestimation: consistency and robustnessPun, Manchi., 潘敏芝. January 2004 (has links)
published_or_final_version / abstract / toc / Statistics and Actuarial Science / Master / Master of Philosophy

36 
Estimating the join point of two regression regimesSchwarz, Marion Janet, 1949 January 1978 (has links)
No description available.

37 
Some numerical computations in linear estimationBhattacharya, Binay K. January 1978 (has links)
No description available.

38 
The combination of biased and robust estimation techniques in multiple regression modelsAskin, Ronald Gene 08 1900 (has links)
No description available.

39 
Equality of minimum variance unbiased estimator under two different modelsToh, Keng Choo. January 1975 (has links)
No description available.

40 
A discrete nonlinear recursive estimatorBryan, Richard Erwin 08 1900 (has links)
No description available.

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