Let F denote the life distribution of a coherent structure of independent components. Suppose that we have a sample of independent systems, each having the structure (phi). Each system is continuously observed until it fails. For every component in each system, either a failure time or a censoring time is recorded. A failure time is recorded if the component fails before or at the time of system failure; otherwise a censoring time is recorded. We introduce a method for finding estimates for F(t), quantiles, and other functionals of F, based on the censorship of the component lives by system failure. We present limit theorems that enable the construction of confidence intervals for large samples. / Source: Dissertation Abstracts International, Volume: 47-02, Section: B, page: 0688. / Thesis (Ph.D.)--The Florida State University, 1986.

Markov Random Fields (MRF's) have been extensively applied in Statistical Mechanics as well as in Bayesian Image Analysis. MRF's are a special class of dependent random variables located at the vertices of a graph whose joint distribution includes a parameter called the temperature. When the number of vertices of the graph tends to infinity, the normalized distribution of statistics based on these random variables converge in distribution. It can happen that for certain values of the temperature, that the rate of growth of these normalizing constants change drastically. This feature is generally used to explain the phenomenon of phase transition as understood by physicists. In this dissertation we will show that this drastic change in normalizing constants occurs even in the relatively smooth case when all the random variables are Gaussian. Hence any image analytic MRF ought to be checked for such discontinuous behavior before any analysis is performed. / Mixed limit theorems in Bayesian Image Analysis seek to replace intensive simulations of MRF's with limit theorems that approximate the distribution of the MRF's as the number of sites increases. The problem of deriving mixed limit theorems for MRF's on a one dimensional lattice graph with an acceptor function that has a second moment has been studied by Chow. A mixed limit theorem for the integer lattice graph is derived when the acceptor function does not have a second moment as for instance when the acceptor function is a symmetric stable density of index 0 $<$ $\alpha$ $<$ 2. / Source: Dissertation Abstracts International, Volume: 52-08, Section: B, page: 4297. / Major Professor: Jayaram Sethuraman. / Thesis (Ph.D.)--The Florida State University, 1991.

One may estimate a conditional hazard function from grouped (and possibly censored) survival data by the time and covariate specific occurrence/exposure rate. Asymptotic results for cumulative versions of this estimator are developed, utilizing the general framework of counting processes. In particular, a grouped data based goodness-of-fit test for Cox's proportional hazard model is given. Various constraints on the asymptotic behavior of the widths of the calendar periods and covariate strata employed in grouping the data are needed to prove the results. Actual performance of the estimators and test statistics is evaluated by Monte Carlo methods. / We also consider the problem of identifying the class of time series model to which a series belongs based on observation of part of the series. Techniques of nonparametric estimation have been applied to this problem by Auestad and Tjostheim (Biometrika 77(1990):669-687) who used kernel estimates of the one-step lagged conditional mean and variance functions. We study cumulative versions of such estimates. These are more stable than the kernel estimates and can be used to construct confidence bands for the underlying cumulative mean and variance functions. Goodness-of-fit tests for specific parametric models are also developed. / Source: Dissertation Abstracts International, Volume: 52-08, Section: B, page: 4300. / Major Professor: Ian McKeague. / Thesis (Ph.D.)--The Florida State University, 1991.

The purpose of the study was to investigate the relative performance of two estimation procedures, the restricted maximum likelihood (REML) and the bootstrap via MINQUE, for a two-level hierarchical linear model under a variety of conditions. Specific focus lay on observing whether the bootstrap via MINQUE procedure offered improved accuracy in the estimation of the model parameters and their standard errors in situations where normality may not be guaranteed. Through Monte Carlo simulations, the importance of this assumption for the accuracy of multilevel parameter estimates and their standard errors was assessed using the accuracy index of relative bias and by observing the coverage percentages of 95% confidence intervals constructed for both estimation procedures. The study systematically varied the number of groups at level-2 (30 versus 100), the size of the intraclass correlation (0.01 versus 0.20) and the distribution of the observations (normal versus chi-squared with 1 degree of freedom). The number of groups and intraclass correlation factors produced effects consistent with those previously reported—as the number of groups increased, the bias in the parameter estimates decreased, with a more significant effect observed for those estimates obtained via REML. High levels of the intraclass correlation also led to a decrease in the efficiency of parameter estimation under both methods. Study results show that while both the restricted maximum likelihood and the bootstrap via MINQUE estimates of the fixed effects were accurate, the efficiency of the estimates was affected by the distribution of errors with the bootstrap via MINQUE procedure outperforming the REML. Both procedures produced less efficient estimators under the chi-squared distribution, particularly for the variance-covariance component estimates. / A Dissertation submitted to the Department of Statistics in partial fulfillment of the requirements for the degree of Doctor of Philosophy. / Degree Awarded: Summer Semester, 2006. / Date of Defense: June 5, 2006. / Reml, Minque / Includes bibliographical references. / Xu-Feng Niu, Professor Directing Dissertation; Richard L. Tate, Outside Committee Member; Fred W. Huffer, Committee Member; Douglas Zahn, Committee Member.

This dissertation introduces and assesses an algorithm to generate confidence bands for a regression function or a main effect when multiple data sets are available. In particular it proposes to construct confidence bands for different trajectories and then aggregate these to produce an overall confidence band for a mean function. An estimator of the regression function or main effect is also examined. First, nonparametric estimators and confidence bands are formed on each data set separately. Then each data set is in turn treated as a testing set for aggregating the preliminary results from the remaining data sets. The criterion used for this aggregation is either the least squares (LS) criterion or a BIC type penalized LS criterion. The proposed estimator is the average over data sets of these aggregates. It is thus a weighted sum of the preliminary estimators. The proposed confidence band is the minimum L1 band of all the M aggregate bands when we only have a main effect. In the case where there is some random effect we suggest an adjustment to the confidence band. In this case, the proposed confidence band is the minimum L1 band of all the M adjusted aggregate bands. Desirable asymptotic properties are shown to hold. A simulation study examines the performance of each technique relative to several alternate methods and theoretical benchmarks. An application to seismic data is conducted. / A Dissertation submitted to the Department of Statistics in partial fulfillment of the requirements for the degree of Doctor of Philosophy. / Degree Awarded: Summer Semester, 2006. / Date of Defense: March 29, 2006. / Confidence Bands, Confidence Intervals, Nonparametric / Includes bibliographical references. / Florentina Bunea, Professor Directing Dissertation; Patrick Mason, Outside Committee Member; Myles Hollander, Committee Member; Fred Huffer, Committee Member.

The minimal repair process assumes that upon repair a system is restored to its functioning condition just before failure. For systems with few vulnerable components it is more reasonable to assume that repair actually brings the state of the system to a level that is between "completely new" and "prior to failure". Kijima (1989) introduced models for such a repair process based on the notion of age reduction. Under age reduction, the system, upon repair, is functionally the same as an identical system of lesser age. An alternative to age reduction is the notion of extra life. Under this notion, the system, upon repair, enjoys a longer expected remaining life than it would have had under a minimal repair. / In this dissertation, we introduce a repair model that generalizes Kijima's models so as to include both the notions of age reduction and extra life. We then look at the problem of estimating system reliability based on observations of the repair process from several systems working independently. We make use of counting processes and martingales to derive large sample properties of the estimator. / Source: Dissertation Abstracts International, Volume: 56-07, Section: B, page: 3837. / Major Professors: Myles Hollander; Jayaram Sethuraman. / Thesis (Ph.D.)--The Florida State University, 1995.

Source: Dissertation Abstracts International, Volume: 29-02, Section: B, page: 0806. / Thesis (Ph.D.)--The Florida State University, 1968.

Source: Dissertation Abstracts International, Volume: 30-11, Section: B, page: 5284. / Thesis (Ph.D.)--The Florida State University, 1969.

Source: Dissertation Abstracts International, Volume: 31-09, Section: B, page: 5696. / Thesis (Ph.D.)--The Florida State University, 1970.

Source: Dissertation Abstracts International, Volume: 29-05, Section: B, page: 1872. / Thesis (Ph.D.)--The Florida State University, 1968.