J. K. Ghosh’s contribution to statistics: A brief outline
Bertrand Clarke, Subhashis Ghosal
Abstract
Professor Jayanta Kumar Ghosh has contributed massively to various areas of Statistics over the last five decades. Here, we survey some of his most important contributions. In roughly chronological order, we discuss his major results in the areas of sequential analysis, foundations, asymptotics, and Bayesian inference. It is seen that he progressed from thinking about data points, to thinking about data summarization, to the limiting cases of data summarization in as they relate to parameter estimation, and then to more general aspects of modeling including prior and model selection.
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Primary Subjects: 62
Secondary Subjects: 62
Keywords: Bartlett corrections; Bayesian nonparametrics; Edgeworth expansions; foundations of statistics; model selection; noninformative prior; posterior convergence; second order efficiency; semiparametric inference; sequential analysis
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Permanent link to this document: http://projecteuclid.org/euclid.imsc/1209398456
Digital Object Identifier: doi:10.1214/074921708000000011
References
[1] Amewou-Atisso, M., Ghosal, S., Ghosh, J. K. and Ramamoorthi, R. V. (2003). Posterior consistency for semi-parametric regression problems. Bernoulli 9 291–312.
Mathematical Reviews (MathSciNet):
MR1997031
Digital Object Identifier: doi:10.3150/bj/1068128979
Project Euclid: euclid.bj/1068128979
[2] Basu, D. and Ghosh, J. K. (1969). Sufficient statistics in sampling from a finite universe. Bull. Inst. Internat. Statist. 42 850–858.
Mathematical Reviews (MathSciNet):
MR286197
[3] Berger, J. O., Ghosh, J. K. and Mukhopadhyay, N. (2003). Approximations and consistency of Bayes factors as model dimension grows. J. Statist. Plann. Inference 112 241–258.
Mathematical Reviews (MathSciNet):
MR1961733
Zentralblatt MATH:
1026.62018
Digital Object Identifier: doi:10.1016/S0378-3758(02)00336-1
[4] Bhanja, J. and Ghosh, J. K. (1992). Efficient estimation with many nuisance parameters. I. Sankhyā Ser. A 54 1–39.
Mathematical Reviews (MathSciNet):
MR1189781
[5] Bhanja, J. and Ghosh, J. K. (1992). Efficient estimation with many nuisance parameters. II. Sankhyā Ser. A 54 135–156.
Mathematical Reviews (MathSciNet):
MR1192091
[6] Bhanja, J. and Ghosh, J. K. (1992). Efficient estimation with many nuisance parameters. III. Sankhyā Ser. A 54 297–308.
Mathematical Reviews (MathSciNet):
MR1216288
[7] Bhattacharya, R. N. and Ghosh, J. K. (1978). On the validity of the formal Edgeworth expansion. Ann. Statist. 6 434–451.
Mathematical Reviews (MathSciNet):
MR471142
Zentralblatt MATH:
0396.62010
Digital Object Identifier: doi:10.1214/aos/1176344134
Project Euclid: euclid.aos/1176344134
[8] Bhattacharya, R. N. and Ghosh, J. K. (1988). On moment conditions for valid formal Edgeworth expansions. J. Multivariate Anal. 27 68–79.
Mathematical Reviews (MathSciNet):
MR971173
Zentralblatt MATH:
0672.62030
Digital Object Identifier: doi:10.1016/0047-259X(88)90116-9
[9] Bickel, P. J. and Ghosh, J. K. (1990). A decomposition for the likelihood ratio statistic and the Bartlett correction – a Bayesian argument. Ann. Statist. 18 1070–1090.
Mathematical Reviews (MathSciNet):
MR1062699
Zentralblatt MATH:
0727.62035
Digital Object Identifier: doi:10.1214/aos/1176347740
Project Euclid: euclid.aos/1176347740
[10] Chakrabarti, A. and Ghosh, J. K. (2006). Optimality of AIC in inference about Brownian motion. Ann. Inst. Statist. Math. 58 1–20.
Mathematical Reviews (MathSciNet):
MR2281204
Zentralblatt MATH:
1095.62102
Digital Object Identifier: doi:10.1007/s10463-005-0007-7
[11] Chakrabarti, A. and Ghosh, J. K. (2006). A generalization of BIC for the general exponential family. J. Statist. Plann. Inference 136 2847–2872.
Mathematical Reviews (MathSciNet):
MR2281234
Zentralblatt MATH:
1094.62031
Digital Object Identifier: doi:10.1016/j.jspi.2005.01.005
[12] Chandra, T. K. and Ghosh, J. K. (1978). Comparison of tests with same Bahadur efficiency. Sankhyā Ser. A 40 253–277.
Mathematical Reviews (MathSciNet):
MR589281
[13] Chandra, T. K. and Ghosh, J. K. (1979). Valid asymptotic expansions for the likelihood ratio statistic and other perturbed chi-square variables. Sankhyā Ser. A 41 22–47.
Mathematical Reviews (MathSciNet):
MR615038
[14] Chandra, T. K. and Ghosh, J. K. (1980). Valid asymptotic expansions for the likelihood ratio and other statistics under contiguous alternatives. Sankhyā Ser. A 42 170–184.
Mathematical Reviews (MathSciNet):
MR656254
[15] Clarke, B. and Ghosh, J. K. (1995). Posterior convergence given the mean. Ann. Statist. 23 2116–2144.
Mathematical Reviews (MathSciNet):
MR1389868
Zentralblatt MATH:
0854.62023
Digital Object Identifier: doi:10.1214/aos/1034713650
Project Euclid: euclid.aos/1034713650
[16] DasGupta, A. and Ghosh, J. K. (1983). Some remarks on second-order admissibility in the multiparameter case. Sankhyā Ser. A 45 181–190.
Mathematical Reviews (MathSciNet):
MR748457
[17] Datta, G. S. and Ghosh, J. K. (1995). On priors providing frequentist validity for Bayesian inference. Biometrika 82 37–45.
Mathematical Reviews (MathSciNet):
MR1332838
Digital Object Identifier: doi:10.2307/2337625
JSTOR: links.jstor.org
[18] Datta, G. S. and Ghosh, J. K. (1995). Noninformative priors for maximal invariant parameter in group models. Test 4 95–114.
Mathematical Reviews (MathSciNet):
MR1365042
Zentralblatt MATH:
0851.62002
Digital Object Identifier: doi:10.1007/BF02563105
[19] Ghosal, S., Ghosh, J. K. and Ramamoorthi, R. V. (1997). Non-informative priors via sieves and packing numbers. In Advances in Statistical Decision Theory and Applications 119–132. Stat. Ind. Technol. Birkhäuser, Boston.
Mathematical Reviews (MathSciNet):
MR1479180
Zentralblatt MATH:
0904.62007
[20] Ghosal, S., Ghosh, J. K. and Ramamoorthi, R. V. (1999). Consistent semiparametric Bayesian inference about a location parameter. J. Statist. Plann. Inference 77 181–193.
Mathematical Reviews (MathSciNet):
MR1687955
Zentralblatt MATH:
1054.62528
Digital Object Identifier: doi:10.1016/S0378-3758(98)00192-X
[21] Ghosal, S., Ghosh, J. K. and Ramamoorthi, R. V. (1999). Posterior consistency of Dirichlet mixtures in density estimation. Ann. Statist. 27 143–158.
Mathematical Reviews (MathSciNet):
MR1701105
Zentralblatt MATH:
0932.62043
Digital Object Identifier: doi:10.1214/aos/1018031105
Project Euclid: euclid.aos/1018031105
[22] Ghosal, S., Ghosh, J. K. and Ramamoorthi, R. V. (1999). Consistency issues in Bayesian nonparametrics. In Asymptotics, Nonparametrics, and Time Series 639–667. Statist. Textbooks Monogr. 158. Dekker, New York.
Mathematical Reviews (MathSciNet):
MR1724711
Zentralblatt MATH:
1069.62516
[23] Ghosal, S., Ghosh, J. K. and Samanta, T. (1995). On convergence of posterior distributions. Ann. Statist. 23 2145–2152.
Mathematical Reviews (MathSciNet):
MR1389869
Zentralblatt MATH:
0858.62024
Digital Object Identifier: doi:10.1214/aos/1034713651
Project Euclid: euclid.aos/1034713651
[24] Ghosal, S., Ghosh, J. K. and Samanta, T. (1999). Approximation of the posterior distribution in a change-point problem. Ann. Inst. Statist. Math. 51 479–497.
Mathematical Reviews (MathSciNet):
MR1722841
Zentralblatt MATH:
0938.62023
Digital Object Identifier: doi:10.1023/A:1003998005295
[25] Ghosal, S., Ghosh, J. K. and van der Vaart, A. W. (2000). Convergence rates of posterior distributions. Ann. Statist. 28 500–531.
Mathematical Reviews (MathSciNet):
MR1790007
Digital Object Identifier: doi:10.1214/aos/1016218228
Project Euclid: euclid.aos/1016218228
[26] Ghosh, J. K. (1960). On some properties of sequential t-test. Calcutta Statist. Assoc. Bull. 9 77–86.
Mathematical Reviews (MathSciNet):
MR114277
Zentralblatt MATH:
0091.30804
[27] Ghosh, J. K. (1960). On the monotonicity of the OC of a class of sequential probability ratio tests. Calcutta Statist. Assoc. Bull. 9 139–144.
Mathematical Reviews (MathSciNet):
MR117849
Zentralblatt MATH:
0108.31702
[28] Ghosh, J. K. (1961). On the optimality of probability ratio tests in sequential and multiple sampling. Calcutta Statist. Assoc. Bull. 10 73–92.
Mathematical Reviews (MathSciNet):
MR130774
Zentralblatt MATH:
0104.12301
[29] Ghosh, J. K. (1964). Bayes solutions in sequential problems for two or more terminal decisions and related results. Calcutta Statist. Assoc. Bull. 13 101–122.
Mathematical Reviews (MathSciNet):
MR172422
Zentralblatt MATH:
0203.20403
[30] Ghosh, J. K. (1971). A new proof of the Bahadur representation of quantiles and an application. Ann. Math. Statist. 42 1957–1961.
Mathematical Reviews (MathSciNet):
MR297071
Zentralblatt MATH:
0235.62006
Digital Object Identifier: doi:10.1214/aoms/1177693063
Project Euclid: euclid.aoms/1177693063
[31] Ghosh, J. K. (1991). Higher order asymptotics for the likelihood ratio, Rao’s and Wald’s tests. Statist. Probab. Lett. 12 505–509.
Mathematical Reviews (MathSciNet):
MR1143747
[32] Ghosh, J. K. (1994). Higher Order Asymptotics. NSF-CBMS Regional Conference in Probability and Statistics 4. IMS, Hayward, CA.
[33] Ghosh, J. K. and Chaudhuri, A. R. (1984). An invariant SPRT for identification. Sequential Anal. 3 99–120.
Mathematical Reviews (MathSciNet):
MR767249
[34] Ghosh, J. K., Delampady, M. and Samanta, T. (2007). An Introduction to Bayesian Analysis, Theory and Methods. Springer, New York.
Mathematical Reviews (MathSciNet):
MR2247439
Zentralblatt MATH:
1135.62002
[35] Ghosh, J. K., Ghosal, S. and Samanta, T. (1994). Stability and convergence of the posterior in non-regular problems. In Statistical Decision Theory and Related Topics V 183–199. Springer, New York.
Mathematical Reviews (MathSciNet):
MR1286304
Zentralblatt MATH:
0798.62037
[36] Ghosh, J. K., Hjort, N. L., Messan, C. and Ramamoorthi, R. V. (2006). Bayesian bivariate survival estimation. J. Statist. Plann. Inference 136 2297–2308.
Mathematical Reviews (MathSciNet):
MR2235060
Zentralblatt MATH:
1088.62040
Digital Object Identifier: doi:10.1016/j.jspi.2005.08.023
[37] Ghosh, J. K., Morimoto, H. and Yamada, S. (1981). Neyman factorization and minimality of pairwise sufficient subfields. Ann. Statist. 9 514–530.
Mathematical Reviews (MathSciNet):
MR615428
Zentralblatt MATH:
0475.62003
Digital Object Identifier: doi:10.1214/aos/1176345456
Project Euclid: euclid.aos/1176345456
[38] Ghosh, J. K. and Mukerjee, R. (1989). Some optimality results on Stein’s two-stage sampling. In Statistical Data Analysis and Inference 251–256. North-Holland, Amsterdam.
Mathematical Reviews (MathSciNet):
MR1089640
Zentralblatt MATH:
0738.62033
[39] Ghosh, J. K. and Mukerjee, R. (1990). Improvement in Stein’s procedure using a random confidence coefficient. Calcutta Statist. Assoc. Bull. 40 145–152.
Mathematical Reviews (MathSciNet):
MR1172640
Zentralblatt MATH:
0744.62045
[40] Ghosh, J. K. and Mukerjee, R. (1991). Characterization of priors under which Bayesian and frequentist Bartlett corrections are equivalent in the multiparameter case. J. Multivariate Anal. 38 385–393.
Mathematical Reviews (MathSciNet):
MR1131727
Zentralblatt MATH:
0728.62020
Digital Object Identifier: doi:10.1016/0047-259X(91)90052-4
[41] Ghosh, J. K. and Mukerjee, R. (1992). Bayesian and frequentist Bartlett corrections for likelihood ratio and conditional likelihood ratio tests. J. Roy. Statist. Soc. Ser. B 54 867–875.
Mathematical Reviews (MathSciNet):
MR1185228
JSTOR: links.jstor.org
[42] Ghosh, J. K. and Mukerjee, R. (1992). Non-informative priors. In Bayesian Statistics 4 195–210. Oxford Univ. Press, New York.
Mathematical Reviews (MathSciNet):
MR1380277
Zentralblatt MATH:
0904.62007
[43] Ghosh, J. K. and Mukerjee, R. (1993). On priors that match posterior and frequentist distribution functions. Canad. J. Statist. 21 89–96.
Mathematical Reviews (MathSciNet):
MR1221860
Digital Object Identifier: doi:10.2307/3315661
JSTOR: links.jstor.org
[44] Ghosh, J. K. and Mukerjee, R. (1993). Frequentist validity of highest posterior density regions in the multiparameter case. Ann. Inst. Statist. Math. 45 293–302.
Mathematical Reviews (MathSciNet):
MR1232496
Zentralblatt MATH:
0778.62024
Digital Object Identifier: doi:10.1007/BF00775815
[45] Ghosh, J. K. and Mukerjee, R. (1994). Adjusted versus conditional likelihood: power properties and Bartlett-type adjustment. J. Roy. Statist. Soc. Ser. B 56 185–188.
Mathematical Reviews (MathSciNet):
MR1257806
JSTOR: links.jstor.org
[46] Ghosh, J. K. and Mukerjee, R. (1995). Frequentist validity of highest posterior density regions in the presence of nuisance parameters. Statist. Decisions 13 131–139.
Mathematical Reviews (MathSciNet):
MR1342734
[47] Ghosh, J. K. and Mukerjee, R. (1995). On perturbed ellipsoidal and highest posterior density regions with approximate frequentist validity. J. Roy. Statist. Soc. Ser. B 57 761–769.
Mathematical Reviews (MathSciNet):
MR1354080
JSTOR: links.jstor.org
[48] Ghosh, J. K. and Mukerjee, R. (2001). Test statistics arising from quasi likelihood: Bartlett adjustment and higher-order power. J. Statist. Plann. Inference 97 45–55.
Mathematical Reviews (MathSciNet):
MR1851373
Zentralblatt MATH:
0982.62013
Digital Object Identifier: doi:10.1016/S0378-3758(00)00344-X
[49] Ghosh, J. K., Mukerjee, R. and Sen, P. K. (1996). Second-order Pitman admissibility and Pitman closeness: the multiparameter case and Stein-rule estimators. J. Multivariate Anal. 57 52–68.
Mathematical Reviews (MathSciNet):
MR1392577
Zentralblatt MATH:
0863.62020
Digital Object Identifier: doi:10.1006/jmva.1996.0021
[50] Ghosh, J. K., Purkayastha, S. and Samanta, T. (2004). Sequential probability ratio tests based on improper priors. Sequential Anal. 23 585–602.
Mathematical Reviews (MathSciNet):
MR2103910
[51] Ghosh, J. K. and Ramamoorthi, R. V. (1995). Consistency of Bayesian inference for survival analysis with or without censoring. In Analysis of Censored Data. IMS Lecture Notes Monogr. Ser. 27. IMS, Hayward, CA.
Mathematical Reviews (MathSciNet):
MR1483342
Zentralblatt MATH:
0876.62021
Digital Object Identifier: doi:10.1214/lnms/1215452215
[52] Ghosh, J. K. and Ramamoorthi, R. V. (2003). Bayesian Nonparametrics. Springer, New York.
Mathematical Reviews (MathSciNet):
MR1992245
[53] Ghosh, J. K., Ramamoorthi, R. V. and Srikanth, K. R. (1999). Bayesian analysis of censored data. Statist. Probab. Lett. 41 255–265.
Mathematical Reviews (MathSciNet):
MR1672393
[54] Ghosh, J. K. and Roy, K. K. (1972). Families of densities with non-constant carriers which have finite dimensional sufficient statistics. Sankhyā Ser. A 34 205–226.
Mathematical Reviews (MathSciNet):
MR378158
[55] Ghosh, J. K. and Samanta, T. (2001). Model selection – an overview. Current Science 80 (9), 1135–1144.
[56] Ghosh, J. K. and Samanta, T. (2002). Nonsubjective Bayes testing – an overview. J. Statist. Plann. Inference 103 205–223.
Mathematical Reviews (MathSciNet):
MR1896993
Zentralblatt MATH:
0989.62017
Digital Object Identifier: doi:10.1016/S0378-3758(01)00222-1
[57] Ghosh, J. K. and Samanta, T. (2002). Towards a nonsubjective Bayesian paradigm. Uncertainty and Optimality 1–69. World Sci. Publ., River Edge, NJ.
Mathematical Reviews (MathSciNet):
MR1955963
Zentralblatt MATH:
1078.62004
Digital Object Identifier: doi:10.1142/9789812777010_0001
[58] Ghosh, J. K., Sen, P. K. and Mukerjee, R. (1994). Second-order Pitman closeness and Pitman admissibility. Ann. Statist. 22 1133–1141.
Mathematical Reviews (MathSciNet):
MR1311968
Zentralblatt MATH:
0817.62017
Digital Object Identifier: doi:10.1214/aos/1176325621
Project Euclid: euclid.aos/1176325621
[59] Ghosh, J. K. and Sinha, B. K. (1981). A necessary and sufficient condition for second order admissibility with applications to Berkson’s bioassay problem. Ann. Statist. 9 1334–1338.
Mathematical Reviews (MathSciNet):
MR630116
Zentralblatt MATH:
0484.62047
Digital Object Identifier: doi:10.1214/aos/1176345650
Project Euclid: euclid.aos/1176345650
[60] Ghosh, J. K. and Sinha, B. K. (1982). Third order efficiency of the MLE – a counterexample. Calcutta Statist. Assoc. Bull. 31 151–158.
Mathematical Reviews (MathSciNet):
MR702402
Zentralblatt MATH:
0509.62028
[61] Ghosh, J. K., Sinha, B. K. and Joshi, S. N. (1982). Expansions for posterior probability and integrated Bayes risk. In Statistical Decision Theory and Related Topics III 1 403–456. Academic Press, New York.
Mathematical Reviews (MathSciNet):
MR705299
Zentralblatt MATH:
0585.62062
[62] Ghosh, J. K., Sinha, B. K. and Subramanyam, K. (1979). Edgeworth expansions for Fisher-consistent estimators and second order efficiency. Calcutta Statist. Assoc. Bull. 28 1–18.
Mathematical Reviews (MathSciNet):
MR586079
Zentralblatt MATH:
0445.62041
[63] Ghosh, J. K., Sinha, B. K. and Wieand, H. S. (1980). Second order efficiency of the MLE with respect to any bounded bowl-shaped loss function. Ann. Statist. 8 506–521.
Mathematical Reviews (MathSciNet):
MR568717
Zentralblatt MATH:
0436.62031
Digital Object Identifier: doi:10.1214/aos/1176345005
Project Euclid: euclid.aos/1176345005
[64] Ghosh, J. K. and Subramanyam, K. (1974). Second order efficiency of maximum likelihood estimators. Sankhyā Ser. A 36 325–358.
Mathematical Reviews (MathSciNet):
MR428572
[65] Hall, W. J., Wijsman, R. A. and Ghosh, J. K. (1965). The relationship between sufficiency and invariance with applications in sequential analysis. Ann. Math. Statist. 36 575–614.
Mathematical Reviews (MathSciNet):
MR178552
Zentralblatt MATH:
0227.62007
Digital Object Identifier: doi:10.1214/aoms/1177700169
Project Euclid: euclid.aoms/1177700169
[66] Mukhopadhyay, N. and Ghosh, J. K. (2003). Parametric empirical Bayes model selection – some theory, methods and simulation. In Probability, Statistics and Their Applications: Papers in Honor of Rabi Bhattacharya 229–245. IMS Lecture Notes Monogr. Ser. 41. IMS, Beachwood, OH.
Mathematical Reviews (MathSciNet):
MR1999424
Zentralblatt MATH:
1044.62008
Digital Object Identifier: doi:10.1214/lnms/1215091667
[67] Mukhopadhyay, N., Ghosh, J. K. and Berger, J. O. (2005). Some Bayesian predictive approaches to model selection. Statist. Probab. Lett. 73 369–379.
Mathematical Reviews (MathSciNet):
MR2187852
[68] Tokdar, S. T. and Ghosh, J. K. (2007). Posterior consistency of logistic Gaussian process priors in density estimation. J. Statist. Plann. Inference 137 34–42.
Mathematical Reviews (MathSciNet):
MR2292838
Zentralblatt MATH:
1098.62041
Digital Object Identifier: doi:10.1016/j.jspi.2005.09.005
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