Selected works of E. L. Lehmann

Cover......Page 1
Selected Works of E. L. Lehmann......Page 4
Preface to the Series......Page 6
PREFACE......Page 10
References......Page 12
Acknowledgements......Page 14
Contents......Page 16
CONTRIBUTORS......Page 24
Erich Leo Lehmann......Page 26
References......Page 30
ARTICLES......Page 32
TECHNICAL REPORTS......Page 39
BOOKS AND THEIR TRANSLATIONS......Page 40
INTERVIEWS, RECORDED LECTURES, AND BIOGRAPHIES/OBITUARIES......Page 42
MISCELLANEOUS......Page 43
ERICH L. LEHMANN\'S PH.D. STUDENTS......Page 46
Erich L. Lehmann\'s Work on Decision Theory......Page 50
References......Page 53
2. Introduction......Page 54
3. Determination of the family F......Page 55
4. The effect on F of assumptions about the alternatives......Page 59
REFERENCES......Page 61
2. Introduction......Page 62
3. Randomization......Page 64
4. General properties of minimax estimation......Page 68
5. Binomial and hypergeometric distributions......Page 70
6. Non parametric problems......Page 73
7. Prediction problems......Page 75
REFERENCES......Page 77
2. Estimates based on samples of fixed size......Page 78
3. Estimates based on sequential procedures......Page 84
REFERENCES......Page 86
NOTES......Page 88
REFERENCES......Page 92
ONE-SIDED CONFIDENCE CONTOURS FOR PROBABILITY DISTRIBUTION FUNCTIONS......Page 93
2. Introduction......Page 94
3. Restricted Bayes solutions......Page 95
4. A continuity theorem......Page 98
5. Extensions......Page 100
6. Examples......Page 101
REFERENCES......Page 105
3. Least favorable distributions for problems of hypothesis testing......Page 106
4. Testing against a simple alternative......Page 110
5. Some extensions......Page 112
REFERENCES......Page 114
1. Introduction......Page 115
2. The principal theorem......Page 116
REFERENCES......Page 121
1. A counter example......Page 122
2. The connection between subfields and statistics......Page 124
A NOTE ON CONFIDENCE SETS FOR RANDOM VARIABLES......Page 125
1. Introduction......Page 126
2. The Bahadur-Goodman theorem......Page 127
þÿ......Page 130
REFERENCES......Page 131
On Testing of Hypotheses......Page 132
References......Page 136
1. Introduction......Page 138
2.1 One-sided tests......Page 139
3. Testing for circular serial correlation in a normal population......Page 142
4. Similar regions......Page 146
5. Testing exponential and rectangular distributions......Page 150
REFERENCES......Page 158
1. Introduction......Page 160
2. Sufficient conditions for a most powerful test......Page 162
3. Testing the values of one or several variances......Page 165
4. Testing equality of variances and the value of the circular serial correlation coefficient......Page 167
5. Student\'s hypothesis and some generalizations......Page 170
REFERENCES......Page 180
1. The likelihood ratio principle......Page 182
2. Formulation of the problem......Page 183
3. Testing against a simple alternative......Page 185
4. Sufficient statistics......Page 187
5. The principle of invariance......Page 189
6. The principle of unbiasedness......Page 192
7. Tests whose power increases with the distance from the hypothesis......Page 194
8. Most stringent tests......Page 195
9. Tests that minimize the maximum loss......Page 198
10. Applications to sequential analysis......Page 200
11. Two sided tests considered as 3-decision problems......Page 204
REFERENCES......Page 205
1. Introduction......Page 208
2. Some Parametric Problems......Page 209
3. Student\'s Problem......Page 211
4. Testing for Goodness of Fit......Page 214
References......Page 215
2. A compJete class theorem......Page 216
3. Significance level and power......Page 218
4. Conditional tests......Page 221
5. Examples......Page 222
REFERENCES......Page 224
1. Order relations among tests......Page 226
2. Consequences of the Hunt-Stein theorem......Page 227
3. Applications......Page 228
REFERENCES......Page 229
10. SEQUENTIAL PROBABILITY RATIO TESTS......Page 230
11. POWER AND EXPECTED SAMPLE SIZE OF SEQUENTIAL PROBABILITY RATIO TESTS......Page 233
12. OPTIMUM PROPERTY OF SEQUENTIAL PROBABILITY RATIO TESTS......Page 237
2. TESTING STATISTICAL HYPOTHESES......Page 244
þÿ......Page 245
5. POWER......Page 246
6. CONDITIONAL INFERENCE......Page 247
7. TWO EXAMPLES......Page 248
8. ONE THEORY OR TWO?......Page 249
REFERENCES......Page 250
1. The popularity of likelihood ratio tests......Page 252
2. The case of two alternatives......Page 253
3. A finite number of alternatives......Page 254
4. Location-scale families......Page 256
5. The failure of intuition......Page 257
References......Page 258
Professor Erich Lehmann\'s Contributionsto Testing of Hypotheses and Estimation......Page 260
References......Page 262
2. Introduction......Page 263
3. A necessary condition for completeness......Page 264
4. The binomial case......Page 268
REFERENCES......Page 272
1. INTRODUCTION......Page 273
2. TERMINOLOGY AND NOTATION......Page 276
3. COMPLETENESS OF A FAMILY OF MEASURES......Page 279
4 . SIMILAR REGIONS......Page 285
5. UNBIASED ESTIMATION......Page 288
6. CONSTRUCTION AND EXISTENCE OF MINIMAL SUFFICIENT STATISTICS......Page 295
APPENDIX......Page 305
REFERENCES......Page 307
7. SOME FURTHER RESULTS ON COMPLETENESS......Page 309
8. UNIFORMLY MOST POWERFUL UNBIASED TESTS......Page 314
9. SOME EXAMPLES......Page 322
MEASURABILITY OF PROPOSED CRITICAL FUNCTIONS......Page 324
REFERENCES......Page 326
2. Point estimates based on test statistics......Page 327
3. A class of estimates for the two-sample problem......Page 329
4. Estimates based on the Wilcoxon and normal scores statistics......Page 330
5. Some estimates for the one-sample problem......Page 332
6. Regularity properties......Page 333
8. Symmetry properties......Page 334
9. Median unbiasedness......Page 336
10. Asymptotic normality......Page 337
11. Asymptotic efficiency......Page 338
REFERENCES......Page 339
1. Introduction and summary......Page 341
2. Degree......Page 342
3. Degree: Two-sample problem......Page 347
4. Existence of unbiased estimates......Page 349
REFERENCES......Page 353
2. AN EXAMPLE AND BASU\'S THEOREM......Page 354
3. SOME ADAPTATIONS OF BASU\'S THEOREM......Page 355
4. INTERPRETATION OF COMPLETENESS......Page 356
5. ANCILLARY STATISTICS AND THE PRINCIPLE OF CONDITIONALITY......Page 357
REFERENCES......Page 358
1. Introduction......Page 360
3. A symmetry property......Page 361
4. Some extensions......Page 362
REFERENCES......Page 363
2. PROBLEMS WITH INADEQUATE INFORMATION......Page 364
3. SOME FURTHER EXAMPLES......Page 365
4. CONCLUDING REMARKS......Page 366
REFERENCES......Page 367
Erich Lehmann on rank methods......Page 368
1 On the theory of some non-parametric hypotheses......Page 369
3 The power of rank tests......Page 370
5 Rank methods for combination of independent experimentsin analysis of variance......Page 372
6 Robust estimation in analysis of variance......Page 373
8 Parametrics versus nonparametrics: two alternative methodologies......Page 374
References......Page 375
1. Generalities......Page 376
2. Most powerful tests and most stringent tests......Page 381
3. Normal alternatives......Page 383
4. Binomial and other non-normal alternatives......Page 386
5. Hypotheses of invariance for independent variables......Page 389
6. Extension to infinite equivalence classes......Page 390
REFERENCES......Page 393
3. Two-sample problem: specific classes of alternatives......Page 394
4. Two-sample problem: general class of alternatives......Page 400
6. Discontinuous distributions......Page 404
6. Existence of unbiased tests for the hypothesis of independence and some other nonparametrlc problems......Page 405
REFERENCES......Page 407
2. Introduction......Page 409
3. The hypothesis of randomness......Page 410
4.. The two-sample problem......Page 411
5. Large sample power......Page 416
6. Optimum rank tests for the two-sample problem......Page 420
7. The hypothesis of independence......Page 423
REFERENCES......Page 425
1. Minimum Pitman efficiency of the Wilcoxon and sign tests......Page 427
2. Alternative notions of asymptotic efficiency......Page 432
3. Limiting efficiencies for the sign test......Page 434
REFERENCES......Page 438
2. Tests based on independent rankings......Page 439
3. Ranking after alignment......Page 442
4. Rank sum analysis of two treatments in a block design......Page 444
5. Nornnal approximation to the null distribution of W......Page 447
6. Asymptotic null distribution of the blocked Wilcoxon statistic......Page 448
8. Several treatments......Page 452
REFERENCES......Page 454
2. A compatible set of difference estimates......Page 455
3. The estimation of contrasts......Page 456
4. Asymptotic distribution and efficiency......Page 458
5. An alternative approach......Page 461
6. Appendix: generalized U-statistics......Page 462
REFERENCES......Page 463
A Class of Selection Procedures Based on Ranks......Page 465
References......Page 472
1. Introduction......Page 473
4. Asymptotic relative efficiency......Page 474
ARE of Wilcoxon and normal scores to t......Page 475
9. Comparison of the four tests......Page 476
11. Asymptotic versus small-sample results......Page 477
13. Using more than one test......Page 478
16. The advantage of simplicity......Page 479
References......Page 480
3. Multiple comparisons......Page 482
References......Page 483
2 Nonparametric confidence intervals for a shift parameter......Page 484
3.1 The literature before Bickel and Lehmann......Page 485
3.3 Partial orderings of distributions......Page 486
3.4 Equivariance of the measures under linear transformations......Page 487
4 Final comments......Page 488
References......Page 489
Summary......Page 491
REFERENCE......Page 496
2. Nonparametric neighbourhood models......Page 497
4. Neighbourhoods of nonparametric models with natural parameters......Page 498
REFERENCES......Page 502
1. Conditions for a location parameter......Page 504
2. Some examples......Page 507
3. Three classes of location parameters......Page 510
4. Robustness......Page 513
5. Estimation......Page 516
5 A. Linear functions of order statistics......Page 517
5 B. R-estimators......Page 522
5 C. M-estimators......Page 525
REFERENCES......Page 527
1. Measures of dispersion......Page 529
2. Estimation......Page 531
3. The doubly trimmed standard deviation......Page 533
4. Nonexistence of a lower bound......Page 535
5. The pth power deviations......Page 539
6. Measuring the scale of positive random variables......Page 542
7. Unknown center of symmetry......Page 543
REFERENCES......Page 548
1. Ordering by spread......Page 549
2. Measures of spread......Page 552
3. Choice of measure......Page 555
References......Page 556
Erich Lehmann\'s Work on Asymptotics......Page 557
Chernoff and Lehmann (1954)......Page 558
Fix, Hodges and Lehmann (1959)......Page 559
Lehmann (1963a) and Lehmann (1964)......Page 560
Hodges and Lehmann (1970)......Page 564
Lehmann and Lob (1990)......Page 565
References......Page 567
1. Introduction......Page 569
2. Introduction......Page 578
3. Linear models with several observations per cell......Page 580
4. An example......Page 584
6. Asymptotic efficiency......Page 586
REFERENCES......Page 589
2. Estimation of a single contrast......Page 591
3. A compatible set of estimates for all contrasts......Page 594
4. Tests and confidence procedures......Page 596
5. Several observations per cell......Page 598
REFERENCES......Page 599
2. General properties of deficiency......Page 600
3. Further examples of point estimation......Page 602
4. Confidence sets for normal means......Page 605
5. Student\'s t-test versus the X-test......Page 608
6. Bayes versus unbiased estimation of a normal mean......Page 613
7. Further possibilities......Page 617
REFERENCES......Page 618
1. Introduction......Page 619
2.1. Kolmogorov-Smirnov neighbourhoods......Page 621
2.3. Uniformly bounded standardized moments......Page 622
2.3.1. Symmetric distributions defined by shape......Page 624
3. Intervals for binomial p......Page 625
3.1. Normal-approximation interval......Page 626
4. Conclusion......Page 627
References......Page 629
1 Introduction......Page 630
2 The 1957 papers......Page 631
3 Optimum significance levels for multistage companson procedures......Page 632
4.1 Previous related work......Page 633
5 Generalizations of the Family-wise Error Rate......Page 634
References......Page 636
1. Introduction......Page 638
2. A class of multiple decision procedures......Page 640
3. Some classification problems......Page 643
4. Estimation......Page 646
5. Some nonparametric problems......Page 648
6. Restricted products of decision problems......Page 650
8. Optimality of the procedures of Sections 4 and 5......Page 656
REFERENCES......Page 662
9. Decision procedures permitting partial conclusions......Page 663
10. Partial classification of one or more parameters......Page 666
11. Decision problems with simple loss functions......Page 671
12. Consecutive decisions in a single experiment......Page 673
13. Some examples of conditional procedures......Page 676
14. Minimizing the maximum risk......Page 682
REFERENCES......Page 688
I. Introduction......Page 689
2. Multistage procedures......Page 690
3. Separability......Page 692
4. Significance levels......Page 695
5. Most powerful test when s is odd......Page 699
þÿ......Page 700
7. Applications and further extensions......Page 702
REFERENCES......Page 707
1. Introduction......Page 708
2. The case k = 2......Page 711
3. General k stepdown......Page 715
4. General k stepup......Page 718
6. Proofs and auxiliary results......Page 720
REFERENCES......Page 731
1. Introduction......Page 733
2. Control of the k-FWER......Page 736
3. Control of the false discovery proportion......Page 741
Acknowledgments......Page 748
REFERENCES......Page 749
Testing multiparameter hypotheses......Page 750
Comparing location experiments......Page 751
Invariant directional orderings......Page 752
References......Page 753
2. Introduction......Page 755
3. Unbiasedness and the minimax principle......Page 756
4. Monotone regions......Page 758
5. Examples......Page 760
6. A multidecision problem......Page 762
7. Convex regions......Page 763
9. A general concept of monotonicity......Page 765
REFERENCES......Page 766
2. Some definitions of order......Page 767
3. Monotonicity of the power function of some sequential tests......Page 773
4. Tests with guaranteed power......Page 776
5. Comparability of experiments......Page 783
6. Appendix. A property of the sign test......Page 785
REFERENCES......Page 787
1. Introduction......Page 788
2. Comparing two location experiments......Page 789
3. The uniform case......Page 791
4. Monotone decision problems......Page 792
5. Relative effectiveness of location families......Page 794
6. Scale-free comparisons and a tail-ordering......Page 796
7. The case of n observations......Page 798
REFERENCES......Page 799
1. Introduction......Page 801
2. Invariant directional preorderings......Page 803
3. Characterization of sets of k-functions defining preorders......Page 805
4. Extension to a larger class of distribution functions......Page 806
5. Ordering the orbits......Page 807
6. Distances between ordered distributions......Page 808
REFERENCES......Page 810
1 Comments on Lehmann [19]......Page 812
2 Comments on Lehmann and Shaffer [20]......Page 816
References......Page 817
2. Quadrant dependence......Page 819
3. A property of quadrant dependent distributions......Page 821
4. Application to slippage problems......Page 824
5. Regression dependence......Page 825
6. Unbiasedness of tests of independence......Page 828
7. Unbiasedness of tests of independence based on normal and other scores......Page 830
8. Likelihood ratio dependence......Page 832
REFERENCES......Page 834
2. THE SHAPE OF INVERTED DISTRIBUTIONS......Page 836
3. A LIMITING RESULT......Page 837
4. TWO KINDS OF LIMITS......Page 838
REFERENCES......Page 839
Erich L. Lehmann\'s Biographical Work......Page 840
References......Page 842
THE LIFE OF ABRAHAM W ALD......Page 843
PAO-LU HSU 1909-1970......Page 844
PAo-Lu Hsu: PuBucAnoNs......Page 845
Papers by Balm CbeDg as represeatadve for a seminar CODducted by Pao-l.AJ Hsu.......Page 847
HSU\'S WORK ON INFERENCE......Page 848
REFERENCES......Page 850
HENRY SCHEFFE 1907-1977......Page 851
Work in Statistics......Page 853
The publications of Henry Scheffe......Page 862
REFERENCES......Page 863
JERZY NEYMAN......Page 864
EARLY YEARS......Page 865
SURVEY SAMPLING AND CONFIDENCE ESTIMATION......Page 871
STATISTICAL PHILOSOPHY......Page 873
MOVING TO AMERICA......Page 875
THE BERKELEY DEPARTMENT OF STATISTICS......Page 876
APPLIED STATISTICS......Page 879
EPILOGUE......Page 882
NOTES......Page 884
HONORS AND DISTINCTIONS......Page 885
SELECTED BIBLIOGRAPHY......Page 886
18.1 Early Life......Page 890
18.2 University and Scientific Administration......Page 891
18.3 Research......Page 894
18.4 REFERENCES......Page 895
€(;)\'\' calisphere......Page 898
HAROLD HOTELLING......Page 900
CONTRIBUTIONS TO ECONOMICS......Page 902
CONTRIBUTIONS TO STATISTICS......Page 905
REFERENCES......Page 908
Erich L. Lehmann\'s Work on the History of Classical Statistics......Page 913
References......Page 917
SOME EARLY INSTANCES OF CONFIDENCE STATEMENTS......Page 918
FOOTNOTES......Page 930
\"THE ONE THING IN WHICH I WAS REALLY INTERESTED WAS GERMAN LITERATURE\"......Page 931
\"I HAD A TRIPLE OF Ph.D. SUPERVISORS\"......Page 933
\"NEYMAN GOT RUMORS THAT I WAS NOT FOllOWING THE SCRIPT CLOSELY ENOUGH\"......Page 934
FAVORITE PAPERS......Page 935
\"I WANTED TO BECOME A WRITER\"......Page 937
\"THE PENDULUM WILL SWING BACK AGAIN\"......Page 939
\"I DON\'T THINK EXACT NONPARAMETRICS WILL PROVE TO BE VERY VIABLE IN THE LONG RUN\"......Page 940
\"WHY DO PEOPLE USE .05?\"......Page 942
\"STATISTICS TOTALLY DOMINATES MY SOCIAL LIFE\"......Page 944
\"COMING TO AMERICA WAS A VERY GOOD THING FOR ME\"......Page 945
1. THE VIEWS OF FISHER AND NEYMAN......Page 947
2.1 A Reservoir of Models......Page 948
2.2 Model Selection......Page 949
3.2 Environment......Page 950
3.5 Validating the Model......Page 951
4. A SPECTRUM OF POSSIBILITIES......Page 952
REFERENCES......Page 953
1 Introduction......Page 956
2 Bertrand\'s views......Page 957
3 Borel\'s reply......Page 959
4 Circonstances remarquables......Page 960
5 The Bertrand-Borel debate and the Neyman-Pearson theory......Page 962
REFERENCES......Page 964
2. GRIFFITH C. EVANS (1887-1973)......Page 966
3. JERZY NEYMAN (1894-1981)......Page 967
4. ABRAHAM WALD (1902-1950)......Page 970
5. HENRY SCHEFFE (1907-1977)......Page 971
6. CHARLES STEIN (1920-)......Page 972
7. JOSEPH L. HODGES, JR. (1922-)......Page 973
Neyman......Page 974
REFERENCES......Page 975
1. The Beginning......Page 977
i) Faculty......Page 978
iii) The Symposia......Page 979
3. From Lab to Department......Page 980
4. Two Crises......Page 981
REFERENCES......Page 983
2. THE BLYTH NOTES......Page 985
4. FROM NOTES TO BOOK......Page 986
7. REVIEWS......Page 987
9. AN ODYSSEY......Page 988
REFERENCES......Page 989
2.1 Gosset\'s 1908 Papers......Page 990
2.2 Fisher\'s Proof......Page 991
2.3 Extensions......Page 992
3.1 Student\'s Questions......Page 993
3.2 A Fisher- Gosset Debate......Page 994
4. CHOICE OF TEST......Page 995
5.1 Gosset and Pearson......Page 996
REFERENCES......Page 997
1. INTRODUCTION......Page 998
2. THE BIRTH OF OPTIMALITY THEORY......Page 1000
3. THE MOVE TO AMERICA......Page 1003
4. THE BERKELEY SYMPOSIA......Page 1004
REFERENCES......Page 1006
1. Introduction......Page 1008
2. The assumption of normality in the 19th century......Page 1010
3. Fisher and the assumption of normality......Page 1011
4. The role of normality after Fisher......Page 1013
5. The assumption of independence......Page 1014
6. The linear model......Page 1015
7. Conclusions......Page 1017
References......Page 1018
2. Maximum Likelihood Estimation......Page 1021
4. The Neyman-Pearson Theory of Hypothesis Testing......Page 1022
6. The Hunt-Stein Theorem......Page 1023
iii) Multiple Testing......Page 1024
10. A Culture Clash......Page 1025
References......Page 1026
Erich L. Lehmann\'s Work on the Philosophy of Statistics......Page 1028
References......Page 1030
1 . INTRODUCTION......Page 1031
2. ROBUSTNESS AND ADAPTATION......Page 1033
3. RELATION WITH DATA ANALYSIS......Page 1036
4. RELATION WITH BAYESIAN INFERENCE......Page 1038
5. CONCLUSIONS AND ACKNOWLEDGMENTS......Page 1040
REFERENCES......Page 1042
2. Model-free data analysis......Page 1045
4. Model-based inference......Page 1046
5. Common ground......Page 1047
5. Conclusions......Page 1048
References......Page 1049
1. Inductive behavior vs. inductive inference: Neyman and Fisher......Page 1050
2. Deductivism: Neyman and Popper......Page 1051
3. The impact of Neyman\'s work......Page 1053
REFERENCES......Page 1055
1. Data, Models, and Inference......Page 1057
2. Some Simple Models......Page 1059
3. Inference Methods......Page 1060
3.2 Point Estimation......Page 1061
3.4 Confidence Regions......Page 1062
3.6 Model Selection......Page 1063
Frequentist Interpretation of Probability......Page 1064
2. Education and Early Interests......Page 1066
The Books......Page 1067
References......Page 1069
Abstract......Page 1071
References......Page 1074
Writing TPE2......Page 1075
Nonparametrics: Statistical Methods Basedon Ranks and Its Impact on the Field of Nonparametric Statistics......Page 1078
References......Page 1080
REFERENCES......Page 1081
REFERENCES......Page 1087
Elements of Large-Sample Theory......Page 1088
Mathematical Statistics......Page 1089
Reminiscences of a Statistician: The Company I Kept......Page 1090