PREFACELIST OF CONTRIBUTORSLIST OF TABLESLIST OF FIGURESTHEOPHILOS N. CACOULLOS - A VIEW OF HIS CAREER PUBLICATIONS OF THEOPHILOS N. CACOULLOSTHE TEN COMMANDMENTS FOR A STATISTICIANPART I APPROXIMATION, BOUNDS AND INEQUALITIES. NON-UNIFORM BOUNDS IN PROBABILITY APPROXIMATIONS USING STEIN'S METHODIntroductionPoisson ApproximationBinomial Approximation: Binary Expansion of a Random IntegerNormal ApproximationConclusionPROBABILITY INEQUALITIES FOR MULTIVARIATE DISTRIBUTIONS WITH APPLICATIONS TO STATISTICSIntroduction and SummaryPositive Dependence and Product-Type InequalitiesNegative Dependence and Product-Type InequalitiesBonferroni-Type InequalitiesApplicationsAPPLICATIONS OF COMPOUND POISSON APPROXIMATION IntroductionFirst ApplicationsWord CountsDiscussion and Numerical ExamplesCOMPOUND POISSON APPROXIMATION FOR SUMS OF DEPENDENT RANDOM VARIABLESIntroductionPreliminaries and NotationsMain ResultsExamples of ApplicationsUNIFIED VARIANCE BOUNDS AND A STEIN-TYPE IDENTITY IntroductionProperties of the TransformationApplication to Variance Bounds PROBABILITY INEQUALITIES FOR U-STATISTICS IntroductionPreliminariesProbability InequalitiesPART II PROBABILITY AND STOCHASTIC PROCESSES THEORY AND APPLICATIONS OF DECOUPLING Complete Decoupling of Marginal Laws and One-Sided BoundsTangent Sequences and Conditionally Independent VariablesBasic Decoupling Inequalities for Tangent SequencesApplications to Martingale Inequalities and Exponential Tail Probability BoundsDecoupling of Multilinear Forms, U-Statistics and U-ProcessesTotal Decoupling of Stopping TimesPrinciple of Conditioning in Weak ConvergenceConclusionA NOTE ON THE PROBABILITY OF RAPID EXTINCTION OF ALLELES IN A WRIGHT-FISHER PROCESSIntroductionThe Lower Bound for Boundary Sets STOCHASTIC INTEGRAL FUNCTIONALS IN AN ASYMPTOTIC SPLIT STATE SPACE IntroductionPreliminariesPhase Merging Scheme for Markov Jump ProcessesAverage of Stochastic Integral FunctionalDiffusion Approximation of Stochastic Integral FunctionIntegral Functional with Perturbed KernelBUSY PERIODS FOR SOME QUEUES WITH DETERMINISTIC INTERARRIVAL OR SERVICE TIMESIntroductionPreliminaries: A Basic Class of PolynomialsThe Dg/M(Q)/1 QueueThe M(Q)/Dg /1 QueueTHE EVOLUTION OF POPULATION STRUCTURE OF THE PERTURBED NON-HOMOGENOUS SEMI-MARKOV SYSTEMIntroductionThe Perturbed Non-Homogeneous Semi-Markov SystemThe Expected Population Structure with Respect to the First Passage Time ProbabilitiesThe Expected Population Structure with Respect to the Duration of a Membership in a StateThe Expected Population Structure with Respect to the State Occupancy of a MembershipThe Expected Population Structure with Respect to the Counting Transition ProbabilitiesPART III DISTRIBUTIONS, CHARACTERIZATIONS, AND APPLICATIONSCHARACTERIZATIONS OF SOME EXPONENTIAL FAMILIES BASED ON SURVIVAL DISTRIBUTIONS AND MOMENTSIntroductionAn Auxiliary LemmaCharacterizations Based on Survival DistributionsCharacterizations Based on MomentsBIVARIATE DISTRIBUTIONS COMPATIBLE OR NEARLY COMPATIBLE WITH GIVEN CONDITIONAL INFORMATION IntroductionImprecise SpecificationPrecise SpecificationAn ExampleA CHARACTERIZATION OF A DISTRIBUTION ARISING FROM ABSORPTION SAMPLING IntroductionThe Characterization TheoremAn ApplicationREFINEMENTS OF INEQUALITIES FOR SYMMETRIC FUNCTIONS GENERAL OCCUPANCY DISTRIBUTIONS IntroductionA General Random Occupancy ModelSpecial Occupancy DistributionsA SKEW t Distribution IntroductionDerivation of Skew t DensityProperties of Skew t DistributionA First Bivariate Skew t DistributionA Second Bivariate Skew t DistributionON THE POSTERIOR MOMENTS FOR TRUNCATION PARAMETER DISTRIBUTIONS AND IDENTIFIABILITY BY POSTERIOR MEAN FOR EXPONENTIAL DISTRIBUTION WITH LOCATION PARAMETERS IntroductionPosterior MomentsExamplesIdentifiability by Posterior MeanAn Illustrative ExampleDISTRIBUTIONS OF RADON VOLUMES WITHOUT USING INTEGRAL GEOMETRY TECHNIQUES IntroductionEvaluation of Arbitrary Moments of the Random VolumesPART IV TIME SERIES, LINEAR, AND NON-LINEAR SERIES COINTEGRATION OF ECONOMIC TIME SERIES IntroductionRegression ModelsSimultaneous Equation ModelsCanonical Analysis and the Reduced Rank Regression EstimatorAutoregressive ProcessesNonstationary ModelsCointegrated ModelsAsymptotic Distribution of Estimators and Test CriterionON SOME POWER PROPERTIES OF GOODNESS-OF-FIT TESTS IN TIME SERIES ANALYSIS Testing Spectral Density FitsLocal Power ConsiderationsComparisonLINEAR CONSTRAINTS ON A LINEAR MODELIntroductionGeometric Interpretation of the Role of the Linear ConstraintsM-METHODS IN GENERALIZED NONLINEAR MODELSIntroductionDefinitions and AssumptionsAsymptotic ResultsTest of Significance and Computational AlgorithmPART V INFERENCE AND APPLICATIONS EXTENTIONS OF A VARIATION OF THE ISOPERIMETRIC PROBLEM IntroductionInformation Retrieval ProblemInformation Retrieval without Measurement ErrorUseful Information in a VariableAllocation of Storage SpaceThe Isoperimetric ProblemExtensionsON FINDING A SINGLE POSITIVE UNIT IN GROUP-TESTINGIntroductionDescription of Properties, Numerical ResultsSome Formulas for Procedure RDHThe Greedy Procedure RGConclusionsChanging the Prior with Procedure RDHRobustness of Procedure RDH for q KnownTESTING HYPOTHESES ON VARIANCES IN THE PRESENCE OF CORRELATIONSBivariate Normal PopulationModifying the HypothesisNon-Null MomentsNull CaseThe Conditional HypothesisESTIMATING THE SMALLEST SCALE PARAMETER: UNIVERSAL DOMINATION RESULTSIntroductionMain ResultsON SENSITIVITY OF EXPONENTIAL RATE OF CONVERGENCE FOR THE MAXIMUM LIKELIHOOD ESTIMATORIntroductionMain ResultsSome ApplicationsDiscussionA CLOSER LOOK AT WEIGHTED LIKELIHOOD IN THE CONTEXT OF MIXTURESIntroductionBackgroundSimulation Experiments and ResultsModel SelectionConclusionsON NONPARAMETRIC FUNCTION ESTIMATION WITH INFINITE-ORDER FLAT-TOP KERNELS Introduction: A General Family of Flat-Top Kernels of Infinite OrderMultivariate Density Estimation: A ReviewFurther Issues on Density EstimationMULTIPOLISHING LARGE TWO-WAY TABLESIntroductionBilinear MultipolishersMatrix ApproximationsDisplaysExamplelConcluding RemarksON DISTANCES AND MEASURES OF INFORMATION: A CASE OF DIVERSITYIntroductionMeasuring Information-Measures of InformationProperties of Measures of InformationMeasures of Information and InferenceApplicationsConclusionsREPRESENTATION FORMULAE FOR PROBABILITIES OF CORRECT CLASSIFICATIONIntroductionVector Algebraic PreliminariesDistributional ResultsESTIMATION OF CYCLING EFFECT ON RELIABILITY ModelsSemiparametric EstimationPART VI APPLICATIONS TO BIOLOGY AND MEDICINEA NEW TEST FOR TREATMENT VS. CONTROL IN AN ORDERED 2 X 3 CONTINGENCY TABLEIntroductionNew Test, Implementation and ExampleSimulation StudyTheoretical PropertiesAppendixAN EXPERIMENTAL STUDY OF THE OCCURRENCE TIMES OF RARE SPECIESStatement of the ProblemThe Design of the ExperimentStage 2 of the ExperimentFindingsA DISTRIBUTION FUNCTIONAL ARISING IN EPIDEMIC CONTROLIntroductionProperties of the FunctionalProof of the TheoremApplication to Epidemic ControlBIRTH AND DEATH URN FOR TERNARY OUTCOMES: STOCHASTIC PROCESSES APPLIED TO URN MODELS IntroductionA Birth and Death Urn with Immigration for Ternary OutcomesEmbedding the Urn Scheme in a Continuous-Time Birth and Death ProcessThe Probabiity Generating Function for the Number of Success on Treatment i in the Continuous-Time Birth and Death ProcessThe Probability Generating Function for the Number of Trials on Treatment i in the Continuous-Time Birth and Death ProcessThe Number of Trials on Treatment i in the Continuous -Time Birth and Death ProcessThe Joint Probability Generating Function for the Number of Successes and the Number of Trials in the Continuous-Time Birth and Death ProcessAdopting a Stopping Rule to Convert Continuous-Time Statistics to the Urn DesignLimiting Results for the Proportion of Trials on Treatment iAUTHOR INDEXSUBJECT INDEXNOTE: References at the end of each chapter.
