Theses and Dissertations from UMD

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New submissions to the thesis/dissertation collections are added automatically as they are received from the Graduate School. Currently, the Graduate School deposits all theses and dissertations from a given semester after the official graduation date. This means that there may be up to a 4 month delay in the appearance of a give thesis/dissertation in DRUM

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Subject: search.filters.subject.Semiparametric

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    Selected Problems in Multi-Sample Statistical Inference
    (2012) Franco, Carolina; Kagan, Abram M; Applied Mathematics and Scientific Computation; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)
    In Chapter 1, a natural semiparametric model for case control study data is discussed, and the asymptotic properties of two simple methods of estimation are explored. The probability element of the model can be factored into a known positive function h involving the finite dimensional structural parameter, an infinite dimensional nuisance parameter in the form of the probability element dP of a distribution, and a normalizing constant. In the setup of interest, a sample of size n is available from a population with a distribution from the aforementioned model . A second, independent sample provides information only about the infinite-dimensional nuisance parameter P. The methods of estimation involve replacing the infinite-dimensional parameter with the empirical distribution function based on the second sample, and constructing semiparametric analogs of the maximum likelihood estimator and the method of moment estimator. The simplicity of these semiparametric estimators permits analysis of their asymptotic distribution even when n and m grow at different rates, yielding very natural and interpretable asymptotic results. In the case where n=o(m), the analog of the maximum likelihood estimator is asymptotically efficient. Chapter 2 explores a related parametric asymptotic statistics problem. Suppose a sample of size m is available from a population with density fY(y; lambda), and an independent sample of size n is available from a population with density fX(x;lambda,alpha). Here &lambda is regarded as a nuisance parameter and &alpha is the structural parameter, where &lambda and &alpha are scalars. One approach to estimation of &alpha would be to compute the maximum likelihood estimator based on both samples. A second approach would be to first find the maximum likelihood estimator of &lambda from the first sample, and to then treat it as the true parameter when using maximum likelihood estimation based on the second sample. Chapter 2 compares the asymptotic behavior of these two estimators under different assumptions about the rate of growth of m relative to n. In chapter 3 we consider interval estimation for small area proportions based on data collected under stratified random sampling. We focus on the case where the stratum sample sizes and the true proportions are small for all strata, and for simplicity we assume equal stratum sample sizes. The objective is to construct a confidence interval for each of the true stratum proportions, Pi. A commonly used small area empirical Bayes model for a single stratum's true proportion Pi assumes that the distributions of the sampled stratum proportions and the prior distribution of the true stratum proportions are normal. The well-documented problems of the normal approximation to the binomial, particularly when the sample size is small and the probability of success is close to 0 or 1, raise questions about the adequacy of such a model when the Pi and the stratum sample sizes are small. We argue that a more reasonable model in this setting is to assume that the sampled stratum counts have binomial distributions and that the prior distribution of the true stratum proportions follows a beta distribution. We propose a new empirical Bayes confidence interval based on this model, and examine related simulation results.
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    SEMIPARAMETRIC AND NONPARAMETRIC ANALYSIS FOR LONGITUDINAL DATA ON THE RELATIONSHIP BETWEEN CHILDHOOD EXTERNALIZING BEHAVIOR AND BODY MASS INDEX
    (2011) Wang, Kejia; He, Xin; Epidemiology and Biostatistics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)
    This thesis is an extension of the longitudinal data analysis of the association between externalizing behavior in early childhood and body mass index (BMI) from age 2 to 12 years conducted in Anderson et al. (2010). Externalizing behaviors problems are characterized by aggressive, oppositional, disruptive, or inattentive behaviors beyond those that would be expected given a child's age and development. The aim of the thesis is to estimate the children's BMI trajectory and to evaluate to what extent the externalizing behavior is related to BMI using semiparametric and nonparametric time-varying coefficient models. Some valuable insights into how the externalizing behavior and BMI are associated will be provided.
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    Asymptotic Theory for Multiple-Sample Semiparametric Density Ratio Models and Its Application to Mortality Forecasting
    (2007-10-03) Lu, Guanhua; Kedem, Benjamin; Mathematical Statistics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)
    A multiple-sample semiparametric density ratio model, which is equivalent to a generalized logistic regression model, can be constructed by multiplicative exponential distortions of a reference distribution. Distortion functions are assumed to be nonnegative and of a known finite-dimensional parametric form, and the reference distribution is left as nonparametric. The combined data from all the samples are used in the semiparametric large sample problem of estimating each distortion and the reference distribution. The large sample behavior for both the parameters and the unknown reference distribution are studied. The estimated reference cumulative distribution function is proved to converge weakly to a zero-mean Gaussian process, whose covariance structure provides confidence bands for the reference distribution function. A Kolmogorov-Smirnov type statistic for a goodness-of-fit test of the density ratio model is also studied. In the second part, an approach to modeling and forecasting age-specific mortality in the United States is provided. The approach is based on an extension of a class of semiparametric models to time series. The method combines information from several time series and estimates their predictive distributions conditional on past data. The conditional expectation, the most common predictor, is obtained as a by product from the first moment of the predictive distribution. The confidence band of the predictor is obtained by applying the asymptotic results of the semiparametric density ratio model. A comparison of short term prediction is made between the semiparametric method and the well known method of Lee and Carter \cite{LC(1992)}. Judging by the mean square error (MSE) of prediction for all ages, the semiparametric method reduces the overall MSE appreciably.
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    Generalized Volatility Model And Calculating VaR Using A New Semiparametric Model
    (2005-12-05) Guo, Haiming; Kedem, Benjamin; Applied Mathematics and Scientific Computation; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)
    The first part of the dissertation concerns financial volatility models. Financial volatility has some stylized facts, such as excess kurtosis, volatility clustering and leverage effects. A good volatility model should be able to capture all these stylized facts. Among the volatility models, ARCH, GARCH, EGARCH and stochastic volatility models are the most important. We propose a generalized volatility model or GVM in this part, which is a generalization of all the ARCH family and stochastic volatility models. The GVM adopts the structure of the generalized linear model (GLM). GLM was originally intended for independent data. However, using partial likelihood, GLM can be extended to time series, and can then be applied to predict financial volatility. Interestingly, the family of ARCH models are special cases of GVM. Also, any covariates can be added easily to a GVM model. As an example, we use GVM to predict the realized volatility. Because of the availability of high frequency data in today's market, we can calculate realized volatility directly. We compare the prediction results of GVM with that of other classical models. By the measure of mean square error, GVM is the best among these the models. The second part of this dissertation is about value at risk (VaR). The most common methods to compute VaR are GARCH, historical simulation, and extreme value theory. A new semiparametric model based on density ratio is developed in Chapter three. By assuming that the density of the return series is an exponential function times the density of another reference return series, we can derive the density function of the portfolio's distribution. Then, we can compute the corresponding quantile or the VaR. We ran a monte carlo simulation to compare the semiparametric model and the traditional VaR models under many different scenarios. In several cases, the semiparametric model performs quite satisfactorily. Furthermore, when applied to real data, the semiparametric model performs best among all the considered models using the metric of failure rate.