Statistical Science

A Conversation with Murray Rosenblatt

David R. Brillinger and Richard A. Davis

Full-text: Open access

Abstract

On an exquisite March day in 2006, David Brillinger and Richard Davis sat down with Murray and Ady Rosenblatt at their home in La Jolla, California for an enjoyable day of reminiscences and conversation. Our mentor, Murray Rosenblatt, was born on September 7, 1926 in New York City and attended City College of New York before entering graduate school at Cornell University in 1946. After completing his Ph.D. in 1949 under the direction of the renowned probabilist Mark Kac, the Rosenblatts’ moved to Chicago where Murray became an instructor/assistant professor in the Committee of Statistics at the University of Chicago. Murray’s academic career then took him to the University of Indiana and Brown University before his joining the University of California at San Diego in 1964. Along the way, Murray established himself as one of the most celebrated and leading figures in probability and statistics with particular emphasis on time series and Markov processes. In addition to being a fellow of the Institute of Mathematical Statistics and American Association for the Advancement of Science, he was a Guggenheim fellow (1965–1966, 1971–1972) and was elected to the National Academy of Sciences in 1984. Among his many contributions, Murray conducted seminal work on density estimation, central limit theorems under strong mixing, spectral domain methods and long memory processes. Murray and Ady Rosenblatt were married in 1949 and have two children, Karin and Daniel.

Article information

Source
Statist. Sci. Volume 24, Number 1 (2009), 116-140.

Dates
First available in Project Euclid: 8 October 2009

Permanent link to this document
http://projecteuclid.org/euclid.ss/1255009014

Digital Object Identifier
doi:10.1214/08-STS267

Mathematical Reviews number (MathSciNet)
MR2561129

Zentralblatt MATH identifier
1327.01036

Keywords
Murray Rosenblatt time series Markov processes density estimation strong mixing central limit theorem long range dependence Chicago Indiana Brown University of California at San Diego

Citation

Brillinger, David R.; Davis, Richard A. A Conversation with Murray Rosenblatt. Statist. Sci. 24 (2009), no. 1, 116--140. doi:10.1214/08-STS267. http://projecteuclid.org/euclid.ss/1255009014.


Export citation

References

  • [1] Blum, R. and Rosenblatt, M. (1956). A class of stationary processes and a central limit theorem. Proc. Natl. Acad. Sci. 42 412–413.
  • [2] Bogert, R., Healey, M. and Tukey, J. (1963). The quefrency analysis of time series for echoes: Cepstrum, pseudo-autocovariances, cross-cepstrum and saphe cracking. In Time Series Analysis (M. Rosenblatt, ed.) 209–243. Wiley, New York.
  • [3] Bradley, R. (2008). Introduction to Strong Mixing Conditions, Vol. 1–3. Kendrick Press, Heber City, UT.
  • [4] Brillinger, D. (1977). The identification of a particular nonlinear time series system. Biometrika 64 509–515.
  • [5] Brillinger, D. R. and Rosenblatt, M. (1967). Computation and interpretation of kth order spectra. In Spectral Analysis of Time Series 189–232. Wiley, New York.
  • [6] Brillinger, D. R. and Rosenblatt, M. (1967). Asymptotic theory of estimates of kth order spectra. Proc. Natl. Acad. Sci. 57 206–210.
  • [7] Burke, C. J. and Rosenblatt, M. (1958). A Markovian function of a Markov chain. Ann. Math. Statist. 29 1112–1122.
  • [8] Burke, C. J. and Rosenblatt, M. (1959). Consolidation of probability matrices. Theorie Statistique 7–8.
  • [9] Einstein, A. (1914). Méthode pour la détermination de valeurs statistiques d’observations concernant des gradeurs soumises à des fluctuations irrégulières. Arch. Sci. Phys. et Natur. Ser. 4 37 254–256.
  • [10] Fix, E. and Hodges, J. L. (1989). Discriminatory Analysis. Nonparametric Discrimination: Consistency Properties. Republished International Statistical Review 57 238–247. (Originally appeared as Report Number 4, Project Number 21-49-004, USAF School of Aviation Medicine, Randolph Field, Texas, in February 1951.)
  • [11] Freiberger, W., Rosenblatt, M. and Van Ness, J. (1962). Regression analysis of vector-valued random processes. J. of Soc. for Indust. Appl. Math. 10 89–102.
  • [12] Grenander, U. (1950). Stochastic processes and statistical inference. Arkiv Mat. 1 195–277.
  • [13] Grenander, U. and Rosenblatt, M. (1957). Statistical Analysis of Time Series. Wiley, New York.
  • [14] Ibragimov, I. and Rozanov, Y. (1978). Gaussian Random Processes. Applications of Mathematics 9. Springer, New York.
  • [15] Kolmogorov, A. and Rozanov, Y. (1960). On a strong mixing condition for stationary Gaussian processes. Teor. Verojatnost. i Primenen 5 222–227.
  • [16] Lii, K. S. and Rosenblatt, M. (1980). Deconvolution and estimation of transfer function phase and coefficients for non-Gaussian linear processes. Ann. Statist. 10 1195–1208.
  • [17] Lii, K. S. and Rosenblatt, M. (2006). Estimation for almost periodic processes. Ann. Statist. 34 1115–1139.
  • [18] Poussin, C. de la Vallée (1916). Intégrales de Lebesgue, Fonctions d’Ensemble, Classes de Baire. Gauthier-Villars, Paris.
  • [19] Rosenblatt, M. (1951). On a class of Markov processes. Trans. Amer. Math. Soc. 71 120–135.
  • [20] Rosenblatt, M. (1952). Remarks on a multivariate transformation. Ann. Math. Statist. 23 470–472.
  • [21] Rosenblatt, M. (1954). An inventory problem. Econometrica 22 244–247.
  • [22] Rosenblatt, M. (1956). A central limit theorem and a strong mixing condition. Proc. Natl. Acad. Sci. USA 42 43–47.
  • [23] Rosenblatt, M. (1956). Remarks on some nonparametric estimates of a density function. Ann. Math. Statist. 27 832–837.
  • [24] Rosenblatt, M. (1959). Functions of a Markov process that are Markovian. J. Math. Mech. 8 585–596.
  • [25] Rosenblatt, M. (1959). Stationary processes as shifts of functions of independent random variables. J. Math. Mech. 8 665–682.
  • [26] Rosenblatt, M. (1960). Asymptotic distribution of eigenvalues of block Toeplitz matrices. Bull. Amer. Math. Soc. 66 320–321.
  • [27] Rosenblatt, M. (1960). Stationary Markov chains and independent random variables. J. Math. Mech. 9 945–950.
  • [28] Rosenblatt, M. (1960). Independence and dependence. In Fourth Berkeley Symposium on Mathematical Statistics and Probability 1 431–443. Univ. California Press, Berkeley.
  • [29] Rosenblatt, M. (1961). Some comments on narrow band-pass filters. Quart. Appl. Math. 18 387–393.
  • [30] Rosenblatt, M. (1962). Asymptotic behavior of eigenvalues of Toeplitz forms. J. Math. Mech. 11 941–950.
  • [31] Rosenblatt, M. (1964). Equicontinuous Markov operators. Teoriya Veroyatnostei 9 205–222.
  • [32] Rosenblatt, M. (2006). An example and transition function equicontinuity. Statist. Probab. Lett. 76 1961–1964.
  • [33] Rosenblatt, M. and Slepian, D. (1962). N order Markov chains with every N variables independent. J. Soc. Indust. Appl. Math. 10 537–549.
  • [34] Rosenblatt, M. and Van Atta, C., ed. (1971). Statistical Models and Turbulence. Lecture Notes in Physics 12. Springer, New York.
  • [35] Segal, I. (1938). Fiducial distribution of several parameters with application to a normal system. Proc. Camb. Philos. Soc. 34 41–47.
  • [36] Wiener, N. (1958). Nonlinear Problems in Random Theory. The Technology Press of Massachusetts Institute of Technology, New York.