During the second half of the 20th century, Murray Rosenblatt was one of the most celebrated and leading figures in probability and statistics. Among his many contributions, Rosenblatt conducted seminal work on density estimation, central limit theorems under strong mixing conditions, spectral domain methodology, long memory processes and Markov processes. He has published over 130 papers and 5 books, many as relevant today as when they first appeared decades ago. Murray Rosenblatt was one of the founding members of the Department of Mathematics at the University of California at San Diego (UCSD) and served as advisor to over twenty Ph D students. He maintains a close association with UCSD in his role as Professor Emeritus.
This volume is a celebration of Murray Rosenblatt’s stellar research career that spans over six decades, and includes some of his most interesting and influential papers. Several leading experts provide commentary and reflections on various directions of Murray’s research portfolio.
Table des matières
Commentary: Discussion of Rosenblatt’s work on Global Measures of Deviations for Density Estimates.- Commentary: Murray Rosenblatt’s contributions to strong mixing.- Commentary: Murray Rosenblatt and cumulant/higher-order/polyspectra.- Commentary: Rosenblatt’s Contribution to Deconvolution.- Commentary: Rosenblatt’s Contributions to Random Walks on Compact Semigroups.- Commentary: The Rosenblatt Process.- On spectral analysis of stationary time series.- Remarks on a multivariate transformation.- Statistical spectral analysis of time series arising from stationary stochastic processes.- Recurrence-time moments in random walks.- A class of stationary processes and a central limit theorem.- A central limit theorem and a strong mixing condition.- Remarks on some nonparametric estimates of a density function.- Some regression problems in time series analysis.- Some purely deterministic processes.- Functions of a Markov process that are Markovian.- Stationary processes as shifts of functions of independent random variables.- Asymptotic distribution of eigenvalues of block Toeplitz matrices.- Limits of convolution sequences of measures on a compact topological semigroup.- Independence and dependence.- Asymptotic behavior of eigenvalues of Toeplitz forms.- Estimation of the bispectrum.- Asymptotic theory of estimates of kthorder spectra.- Remarks on the Burgers equation.- Density estimates and Markov sequences.- Curve estimates.- On some global measures of the deviations of density function estimates.- Asymptotic behavior of a spline estimate of a density function.- Fractional integrals of stationary processes and the central limit theorem.- Limit theorems for Fourier transforms of functionals of Gaussian sequences.- Deconvolution and estimation of transfer function phase and coefficients for non-Gaussian linear processes.- Asymptotic normality, strong mixing and spectral density estimates.- Deconvolution of non-Gaussian linear processes with vanishing spectralvalues.- Scale renormalization and random solutions of the Burgers equation. On frequency estimation.- Maximum likelihood estimation for noncausal autoregressive processes.- Spectral analysis for harmonizable processes.- Correction: “Spectral analysis for harmonizable processes”.- Estimation for almost periodic processes.- Prolate spheroidal spectral estimates.- Correction: “Estimation for almost periodic processes”.
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