The Annals of Statistics

The statistical work of Lucien Le Cam

Aad van der Vaart

Full-text: Open access

Abstract

We give an overview and appraisal of the scientific work in theoretical statistics, and its impact, by Lucien Le Cam. The references to Le Cam's papers refer to the Le Cam bibliography. The reference is the first paper for the given year if not stated.

Article information

Source
Ann. Statist., Volume 30, Number 3 (2002), 631-682.

Dates
First available in Project Euclid: 6 August 2002

Permanent link to this document
https://projecteuclid.org/euclid.aos/1028674836

Digital Object Identifier
doi:10.1214/aos/1028674836

Mathematical Reviews number (MathSciNet)
MR1922537

Zentralblatt MATH identifier
1103.62301

Subjects
Primary: 62G15: Tolerance and confidence regions 62G20: Asymptotic properties 62F25: Tolerance and confidence regions

Keywords
Limit experiment deficiency LAN contiguity metric entropy comparison of experiments sufficiency

Citation

Vaart, Aad van der. The statistical work of Lucien Le Cam. Ann. Statist. 30 (2002), no. 3, 631--682. doi:10.1214/aos/1028674836. https://projecteuclid.org/euclid.aos/1028674836


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References

  • BAHADUR, R. R. (1964). On Fisher's bound for asy mptotic variances. Ann. Math. Statist. 35 1545- 1552.
  • BASAWA, I. V. and SCOTT D. J. (1983). Asy mptotic Optimal Inference for Nonergodic Models. Lecture Notes in Statist. 17. Springer, New York.
  • BEGUN, J. M., HALL, W. J., HUANG, W. M. and WELLNER, J. A. (1983). Information and asy mptotic efficiency in parametric-nonparametric models. Ann. Statist. 11 432-452.
  • BERGER, J. O. and WOLPERT, R. L. (1988). The Likelihood Principle, 2nd ed. IMS, Hay ward, CA.
  • BICKEL, P. J., KLAASSEN, C. A. J., RITOV, Y. and WELLNER, J. A. (1993). Efficient and Adaptive Estimation for Semiparametric Models. Johns Hopkins Univ. Press.
  • BIRGÉ, L. (1983). Approximation dans les espaces métriques et théorie de l'estimation. Z. Wahrsch. Verw. Gebiete 65 181-238.
  • BIRGÉ, L. (1986). On estimating a density using Hellinger distance and some other strange facts. Probab. Theory Related Fields 71 271-291.
  • BIRGÉ, L. and MASSART, P. (1993). Rates of convergence for minimum contrast estimators. Probab. Theory Related Fields 97 113-150.
  • BIRGÉ, L. and MASSART, P. (1998). Minimum contrast estimators on sieves: Exponential bounds and rates of convergence. Bernoulli 4 329-375.
  • BLACKWELL, D. (1951). Comparison of experiments. Proc. Second Berkeley Sy mp. Math. Statist. Probab. 93-102. Univ. California Press, Berkeley.
  • BLACKWELL, D. (1953). Equivalent comparisons of experiments. Ann. Math. Statist. 24 265-272.
  • BOHNENBLUST, H. F., SHAPLEY, L. S. and SHERMAN, S. (1949). Reconnaissance in game theory. RAND Research Memorandum RM-208 1-18.
  • BOLL, C. (1955). Comparison of experiments in the infinite case. Ph.D. dissertation, Dept. Statist., Stanford Univ.
  • BOURBAKI, N. (1955). Espaces vectoriels topologiques. Hermann, Paris.
  • BROWN, L. D. and LOW, M. G. (1996). Asy mptotic equivalence of nonparametic regression and white noise. Ann. Statist. 24 2384-2398.
  • CHERNOFF, H. (1956). Large sample theory: Parametric case. Ann. Math. Statist. 27 1-22.
  • DONOHO, D. L. and LIU, R. C. (1991). Geometrizing rates of convergence. II, III. Ann. Statist. 19 633-667, 668-701.
  • DUDLEY, R. M. (1967). The sizes of compact subsets of Hilbert spaces and continuity of Gaussian processes. J. Funct. Anal. 1 290-330.
  • FISHER, R. A. (1922). On the mathematical foundations of theoretical statistics. Philos. Trans. Roy. Soc. London Ser. A 222 309-368.
  • FISHER, R. A. (1925). Theory of statistical estimation. Proc. Cambridge Philos. Soc. 22 700-725.
  • FISHER, R. A. (1935). The Design of Experiments. Oliver and Boy d, Edinburgh.
  • GHOSAL, S., GHOSH, J. K. and VAN DER VAART, A. W. (2000). Convergence rates of posterior distributions. Ann. Statist. 28 500-531.
  • GRENANDER, U. (1981). Abstract Inference. Wiley, New York.
  • GUSHCHIN, A. A. (1995). Asy mptotic optimality of parameter estimators under the LAQ condition. Theory Probab. Appl. 40 261-272.
  • HÁJEK, J. (1962). Asy mptotically most powerful rank-order tests. Ann. Math. Statist. 33 1124-1147.
  • HÁJEK, J. (1970). A characterization of limiting distributions of regular estimates. Z. Wahrsch. Verw. Gebiete 14 323-330.
  • HÁJEK, J. (1972). Local asy mptotic minimax and admissibility in estimation. Proc. Sixth Berkeley Sy mp. Math. Statist. Probab. 1 175-194. Univ. California Press, Berkeley.
  • HÁJEK, J. and SIDÁK, Z. (1967). Theory of Rank Tests. Academic Press, New York.
  • HEy ER, H. (1973). Mathematische Theorie statistischer Experimente. Springer, Berlin.
  • IBRAGIMOV, I. A. and KHASMINSKII, R. Z. (1977). On the estimation of an infinite dimensional parameter in Gaussian white noise. Soviet Math. Dokl. 236 1035-1055.
  • IBRAGIMOV, I. A. and HAS'MINSKII, R. Z. (1981). Statistical Estimation: Asy mptotic Theory. Springer, New York.
  • JANSSEN, A., MILBRODT, H. and STRASSER, H. (1985). Infinitely Divisible Statistical Experiments. Lecture Notes in Statist. 27. Springer, New York.
  • JEGANATHAN, P. (1982). On the asy mptotic theory of estimation when the limit of the log likelihood ratios is mixed normal. Sankhy¯a Ser. A 44 173-212.
  • JEGANATHAN, P. (1995). Some aspects of asy mptotic theory with applications to time series models. Econometric Theory 11 818-887.
  • KOLMOGOROV, A. N. and TIKHOMIROV, V. M. (1961). -entropy and -capacity of sets in function spaces. Amer. Math. Soc. Trans. Ser. 2 17 277-364.
  • KOSHEVNIK, YU. A. and LEVIT, B. YA. (1976). On a nonparametric analogue of the information matrix. Theory Probab. Appl. 21 738-753.
  • KOUL, H. L. and PFLUG, G. C. (1990). Weakly adaptive estimators in explosive autoregression. Ann. Statist. 18 939-960.
  • LUXEMBURG, W. A. J. and ZAANEN, A. C. (1971). Riesz Spaces. North-Holland, Amsterdam.
  • MILLAR, P. W. (1979). Asy mptotic minimax theorems for the sample distribution function. Z. Wahrsch. Verw. Gebiete 48 233-252.
  • MILLAR, P. W. (1983). The minimax principle in asy mptotic statistical theory. École d'Été de Probabilités de St. Flour XI. Lecture Notes in Math. 976 76-267. Springer, New York.
  • MILLAR, P. W. (1985). Non-parametric applications of an infinite-dimensional convolution theorem. Z. Wahrsch. Verw. Gebiete 68 545-556.
  • NEy MAN, J. (1934). On the two different aspects of the representative method: The method of stratified sampling and the method of purposive selection. J. Roy. Statist. Soc. 97 558- 625.
  • NUSSBAUM, M. (1996). Asy mptotic equivalence of density estimation and Gaussian white noise. Ann. Statist. 24 2399-2430.
  • PINSKER, M. S. (1980). Optimal filtering of square integrable signals in Gaussian white noise. Problems Inform. Transmission 16 120-133.
  • PFANZAGL, J. and WEFELMEy ER, W. (1982). Contributions to a General Asy mptotic Statistical Theory. Lecture Notes in Statist. 13. Springer, New York.
  • PFLUG, G. C. (1983). The limiting loglikelihood process for discontinuous density families. Z. Wahrsch. Verw. Gebiete 64 15-35.
  • POLLARD, D., TORGERSEN, E. and YANG, G. L. (eds.) (1997). Festschrift for Lucien Le Cam: Research Papers in Probability and Statistics. Springer, New York.
  • PRAKASA RAO, B. L. S. (1968). Estimation of the location of the cusp of a continuous density. Ann. Math. Statist. 39 76-87.
  • RAO, C. R. (1965). Linear Statistical Inference and Its Applications. Wiley, New York.
  • ROUSSAS, G. G. (1965). Asy mptotic inference in Markov processes. Ann. Math. Statist. 36 978- 992.
  • ROUSSAS, G. G. (1972). Contiguity of Probability Measures: Some Applications in Statistics. Cambridge Univ. Press.
  • SCHAEFER, H. H. (1974). Banach Lattices and Positive Operators. Springer, New York.
  • SHERMAN, S. (1951). On a theorem of Hardy, Littlewood, Poly a, and Blackwell. Proc. Natl. Acad. Sci. U.S.A. 37 826-831.
  • STEIN, C. (1956). Inadmissibility of the usual estimator for the mean of a multivariate normal distribution. Proc. Third Berkeley Sy mp. Math. Statist. Probab. 1 197-206. Univ. California Press, Berkeley.
  • STRASSER, H. (1985). Mathematical Theory of Statistics: Statistical Experiments and Asy mptotic Theory. de Gruy ter, Berlin.
  • TORGERSEN, E. (1968). Comparison of experiments when the parameter space is finite. Ph.D. dissertation, Dept. Statistics, Univ. California, Berkeley.
  • TORGERSEN, E. (1970). Comparison of experiments when the parameter space is finite. Z. Wahrsch. Verw. Gebiete 16 219-249.
  • TORGERSEN, E. (1972). Comparison of translation experiments. Ann. Math. Statist. 43 1383-1399.
  • TORGERSEN, E. (1991). Comparison of Statistical Experiments. Cambridge Univ. Press.
  • VAN DE GEER, S. (1993). Hellinger-consistency of certain nonparametric maximum likelihood estimators. Ann. Statist. 21 14-44.
  • VAN DER VAART, A. W. (1994). Limits of experiments. Lecture notes, Yale Univ.
  • VAN DER VAART, A. W. and WELLNER, J. A. (1996). Weak Convergence and Empirical Processes. With Applications to Statistics. Springer, New York.
  • WALD, A. (1939). Contributions to the theory of statistical estimation and testing hy potheses. Ann. Math. Statist. 10 299-326.
  • WALD, A. (1943). Tests of statistical hy potheses concerning several parameters when the number of observations is large. Trans. Amer. Math. Soc. 54 426-482.
  • WALD, A. (1950). Statistical Decision Functions. Wiley, New York.
  • WONG, W. H. and SHEN, X. (1995). Probability inequalities for likelihood ratios and convergence rates of sieve MLE's. Ann. Statist. 23 339-362.