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Multivariate Statistics and Probability: Essays in Memory of Paruchuri R. Krishnaiah is a collection of essays on multivariate statistics and probability in memory of Paruchuri R. Krishnaiah (1932-1987), who made significant contributions to the fields of multivariate statistical analysis and stochastic theory. The papers cover the main areas of multivariate statistical theory and its applications, as well as aspects of probability and stochastic analysis. Topics range from finite sampling and asymptotic results, including aspects of decision theory, Bayesian analysis, classical estimation, regression, and time-series problems. Comprised of 35 chapters, this book begins with a discussion on the joint asymptotic distribution of marginal quantiles and quantile functions in samples from a multivariate population. The reader is then introduced to kernel estimators of density function of directional data; moment conditions for valid formal edgeworth expansions; and ergodicity and central limit theorems for a class of Markov processes. Subsequent chapters focus on minimal complete classes of invariant tests for equality of normal covariance matrices and sphericity; normed likelihood as saddlepoint approximation; generalized Gaussian random fields; and smoothness properties of the conditional expectation in finitely additive white noise filtering. This monograph should be of considerable interest to researchers as well as to graduate students working in theoretical and applied statistics, multivariate analysis, and random processes.
Language
Place of publication
Publishing group
Elsevier Science & Techn.
ISBN-13
978-1-4832-6383-0 (9781483263830)
Schweitzer Classification
PrefaceContributorsIn MemoriamJoint Asymptotic Distribution of Marginal Quantiles and Quantile Functions in Samples from a Multivariate PopulationKernel Estimators of Density Function of Directional DataOn Determination of the Order of an Autoregressive ModelAdmissible Linear Estimation in a General Gauss-Markov Model with an Incorrectly Specified Dispersion MatrixOn Moment Conditions for Valid Formal Edgeworth ExpansionsErgodicity and Central Limit Theorems for a Class of Markov ProcessesConditionally Ordered DistributionsA Discounted Cost RelationshipStrong Consistency of M-Estimates in Linear ModelsMinimal Complete Classes of Invariant Tests for Equality of Normal Covariance Matrices and SphericityInvariance Principles for Changepoint ProblemsOn the Area of the Circles Covered by a Random WalkNormed Likelihood as Saddlepoint ApproximationNon-uniform Error Bounds for Asymptotic Expansions of Scale Mixtures of DistributionsEmpirical and Hierarchical Bayes Competitors of Preliminary Test Estimators in Two Sample ProblemsOn Confidence Bands in Nonparametric Density Estimation and RegressionA Note on Generalized Gaussian Random FieldsSmoothness Properties of the Conditional Expectation in Finitely Additive White Noise FilteringEquivariant Estimation of a Mean Vector µ of N(µ,S) with 'S-1=1 or S-1/2µ=c or S = s2µ'µ1A Generalized Cauchy-Binet Formula and Applications to Total Positivity and MajorizationIsotonic M-Estimation of Location: Union-Intersection Principle and Preliminary Test VersionsSome Asymptotic Inferential Problems Connected with Elliptical DistributionsStochastic Integrals of Empirical-Type Processes with Applications to Censored RegressionNonminimum Phase Non-Gaussian DeconvolutionInference in a Model with at Most One Slope-Change PointMaximum Likelihood Principle and Model Selection when the True Model is UnspecifiedAn Asymptotic Minimax Theorem of Order n-1/2An Improved Estimation Method for Univariate Autoregressive ModelsParadoxes in Conditional ProbabilityInference Properties of a One-Parameter Curved Exponential Family of Distributions with Given MarginalsAsymptotically Precise Estimate of the Accuracy of Gaussian Approximation in Hubert SpaceThe Estimation of the Bispectral Density Function and the Detection of Periodicities in a SignalAnalysis of Odds Ratios in 2xn Ordinal Contingency TablesAsymptotic Expansions of the Distributions of Some Test Statistics for Gaussian ARMA ProcessesEstimating Multiple Rater Agreement for a Rare DiagnosisAuthor IndexSubject Index