Nearly optimal tests when a nuisance parameter is present under the null hypothesis

Econometrica

Volumn 83, Issue 2, 2015, Pages 771-811

  Elliott, Graham ^a   Müller, Ulrich K ^b   Watson, Mark W ^b,c  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b PRINCETON UNIVERSITY   (United States)

^c NATIONAL BUREAU OF ECONOMIC RESEARCH   (United States)

Author keywords

composite hypothesis; maximin tests; Least favorable distribution

Indexed keywords

EID: 84961289408     PISSN: 00129682     EISSN: 14680262     Source Type: Journal    
DOI: 10.3982/ECTA10535     Document Type: Article

References (62)

1. Andrews, D. W. K. (2011): "Similar-on-the-Boundary Tests for Moment Inequalities Exist, but Have Poor Power, " Discussion Paper 1815, Cowles Foundation.
2. Andrews, D. W. K., and G. Guggenberger (2010): "Asymptotic Size and a Problem With Subsampling and With the M out of N Bootstrap, " Econometric Theory, 26, 426-468. 10.1017/S0266466609100051
3. Andrews, D. W. K., and W. Ploberger (1994): "Optimal Tests When a Nuisance Parameter Is Present Only Under the Alternative, " Econometrica, 62, 1383-1414. 10.2307/2951753
4. Andrews, D. W. K., M. J. Moreira, and J. H. Stock (2008): "Efficient Two-Sided Nonsimilar Invariant Tests in IV Regression With Weak Instruments, " Journal of Econometrics, 146, 241-254. 10.1016/j.jeconom.2008.08.015
5. Bai, J. (1994): "Least Squares Estimation of a Shift in Linear Processes, " Journal of Time Series Analysis, 15, 453-470. 10.1111/j.1467-9892.1994.tb00204.x
6. Bai, J. (1997): "Estimation of a Change Point in Multiple Regressions, " Review of Economics and Statistics, 79, 551-563. 10.1162/003465397557132
7. Blackwell, D., and M. A. Girshick (1954): Theory of Games and Statistical Decisions. New York: Wiley.
8. Bobkoski, M. J. (1983): "Hypothesis Testing in Nonstationary Time Series, " Ph.D. Thesis, Department of Statistics, University of Wisconsin.
9. Campbell, J. Y., and M. Yogo (2006): "Efficient Tests of Stock Return Predictability, " Journal of Financial Economics, 81, 27-60. 10.1016/j.jfineco.2005.05.008
10. Cavanagh, C. L. (1985): "Roots Local to Unity, " Working Paper, Harvard University.
11. Cavanagh, C. L., G. Elliott, and J. H. Stock (1995): "Inference in Models With Nearly Integrated Regressors, " Econometric Theory, 11, 1131-1147. 10.1017/S0266466600009981
12. Chamberlain, G. (2000): "Econometric Applications of Maximin Expected Utility, " Journal of Applied Econometrics, 15, 625-644. 10.1002/jae.583
13. Chamberlain, G. (2007): "Decision Theory Applied to an Instrumental Variables Model, " Econometrica, 75 (3), 609-652. 10.1111/j.1468-0262.2007.00764.x
14. Chan, N. H., and C. Z. Wei (1987): "Asymptotic Inference for Nearly Nonstationary AR(1) Processes, " The Annals of Statistics, 15, 1050-1063. 10.1214/aos/1176350492
15. Chiburis, R. C. (2009): "Approximately Most Powerful Tests for Moment Inequalities, " in "Essays on Treatment Effects and Moment Inequalities, " Ph.D. Thesis, Department of Economics, Princeton University, Chapter 3.
16. Choi, A., W. J. Hall, and A. Schick (1996): "Asymptotically Uniformly Most Powerful Tests in Parametric and Semiparametric Models, " The Annals of Statistics, 24, 841-861. 10.1214/aos/1032894469
17. Dufour, J.-M., and M. L. King (1991): "Optimal Invariant Tests for the Autocorrelation Coefficient in Linear Regressions With Stationary or Nonstationary AR(1) Errors, " Journal of Econometrics, 47, 115-143. 10.1016/0304-4076(91)90080-W
18. Elliott, G., and U. K. Müller (2007): "Confidence Sets for the Date of a Single Break in Linear Time Series Regressions, " Journal of Econometrics, 141, 1196-1218. 10.1016/j.jeconom.2007.02.001
19. Elliott, G., and U. K. Müller (2012): "Pre and Post Break Parameter Inference, " Working Paper, Princeton University.
20. Elliott, G., and U. K. Müller (2014): "Pre and Post Break Parameter Inference, " Journal of Econometrics, 180, 141-157. 10.1016/j.jeconom.2014.03.007
21. Elliott, G., U. K. Müller, and M. W. Watson (2015): "Supplement to 'Nearly Optimal Tests When a Nuisance Parameter Is Present Under the Null Hypothesis', " Econometrica Supplemental Material, 83, http://dx.doi.org/10.3982/ECTA10535.
22. Elliott, G., T. J. Rothenberg, and J. H. Stock (1996): "Efficient Tests for an Autoregressive Unit Root, " Econometrica, 64, 813-836. 10.2307/2171846
23. Facchinei, F., and J.-S. Pang (2003): Finite-Dimensional Variational Inequalities and Complementarity Problems, Vols. I and II. New York: Springer.
24. Ferguson, T. S. (1967): Mathematical Statistics-A Decision Theoretic Approach. New York: Academic Press.
25. Hahn, J., and G. Ridder (2011): "A Dual Approach to Confidence Intervals for Partially Identified Parameters, " Working Paper, UCLA.
26. Hansen, B. E. (1999): "The Grid Bootstrap and the Autoregressive Model, " Review of Economics and Statistics, 81, 594-607. 10.1162/003465399558463
27. Hillier, G. (1990): "On the Normalization of Structural Equations: Properties of Direction Estimators, " Econometrica, 58, 1181-1194. 10.2307/2938305
28. Ibragimov, R., and U. K. Müller (2010): "T-Statistic Based Correlation and Heterogeneity Robust Inference, " Journal of Business & Economic Statistics, 28, 453-468. 10.1198/jbes.2009.08046
29. Ibragimov, R., and U. K. Müller (2013): "Inference With Few Heterogeneous Clusters, " Working Paper, Princeton University.
30. Imbens, G., and C. F. Manski (2004): "Confidence Intervals for Partially Identified Parameters, " Econometrica, 72, 1845-1857. 10.1111/j.1468-0262.2004.00555.x
31. Jansson, M., and M. J. Moreira (2006): "Optimal Inference in Regression Models With Nearly Integrated Regressors, " Econometrica, 74, 681-714. 10.1111/j.1468-0262.2006.00679.x
32. Kempthorne, P. J. (1987): "Numerical Specification of Discrete Least Favorable Prior Distributions, " SIAM Journal on Scientific and Statistical Computing, 8, 171-184. 10.1137/0908028
33. Kim, S., and A. S. Cohen (1998): "On the Behrens-Fisher Problem: A Review, " Journal of Educational and Behavioral Statistics, 23, 356-377. 10.3102/10769986023004356
34. King, M. L. (1987): "Towards a Theory of Point Optimal Testing, " Econometric Reviews, 6, 169-218. 10.1080/07474938708800129
35. Krafft, O., and H. Witting (1967): "Optimale Tests und ungünstige Verteilungen, " Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete, 7, 289-302. 10.1007/BF01844447
36. Lee, A. F. S., and J. Gurland (1975): "Size and Power of Tests for Equality of Means of Two Normal Populations With Unequal Variances, " Journal of the American Statistical Association, 70, 933-941. 10.1080/01621459.1975.10480326
37. Leeb, H., and B. M. Pötscher (2005): "Model Selection and Inference: Facts and Fiction, " Econometric Theory, 21, 21-59. 10.1017/S0266466605050036
38. Lehmann, E. L., and J. P. Romano (2005): Testing Statistical Hypotheses. New York: Springer.
39. Linnik, Y. V. (1966): "Randomized Homogeneous Tests for the Behrens-Fisher Problem, " Selected Translations in Mathematical Statistics and Probability, 6, 207-217.
40. Linnik, Y. V. (1968): Statistical Problems With Nuisance Parameters. New York: American Mathematical Society.
41. Mickey, M. R., and M. B. Brown (1966): "Bounds on the Distribution Functions of the Behrens-Fisher Statistic, " The Annals of Mathematical Statistics, 37, 639-642. 10.1214/aoms/1177699457
42. Mikusheva, A. (2007): "Uniform Inference in Autoregressive Models, " Econometrica, 75, 1411-1452. 10.1111/j.1468-0262.2007.00798.x
43. Moon, H. R., and F. Schorfheide (2009): "Estimation With Overidentifying Inequality Moment Conditions, " Journal of Econometrics, 153, 136-154. 10.1016/j.jeconom.2009.05.003
44. Moreira, H., and M. J. Moreira (2013): "Contributions to the Theory of Optimal Tests, " Working Paper, FGV/EPGE.
45. Moreira, M. J. (2003): "A Conditional Likelihood Ratio Test for Structural Models, " Econometrica, 71, 1027-1048. 10.1111/1468-0262.00438
46. Müller, U. K. (2011): "Efficient Tests Under a Weak Convergence Assumption, " Econometrica, 79, 395-435. 10.3982/ECTA7793
47. Müller, U. K. (2014): "HAC Corrections for Strongly Autocorrelated Time Series, " Journal of Business & Economic Statistics, 32, 311-322. 10.1080/07350015.2014.931238
48. Müller, U. K., and M. W. Watson (2013a): "Measuring Uncertainty About Long-Run Predictions, " Working Paper, Princeton University.
49. Müller, U. K., and M. W. Watson (2013b): "Low-Frequency Robust Cointegration Testing, " Journal of Econometrics, 174, 66-81. 10.1016/j.jeconom.2012.09.006
50. Phillips, P. C. B. (1987): "Towards a Unified Asymptotic Theory for Autoregression, " Biometrika, 74, 535-547. 10.1093/biomet/74.3.535
51. Phillips, P. C. B. (2014): "On Confidence Intervals for Autoregressive Roots and Predictive Regression, " Econometrica, 82, 1177-1195. 10.3982/ECTA11094
52. Salaevskii, O. V. (1963): "On the Non-Existence of Regularly Varying Tests for the Behrens-Fisher Problem, " Soviet Mathematics-Doklady, 4, 1043-1045.
53. Sriananthakumar, S., and M. L. King (2006): "A New Approximate Point Optimal Test of a Composite Null Hypothesis, " Journal of Econometrics, 130, 101-122. 10.1016/j.jeconom.2004.08.020
54. Stock, J. H., and M. W. Watson (1996): "Confidence Sets in Regressions With Highly Serially Correlated Regressors, " Working Paper, Harvard University.
55. Stoye, J. (2009): "More on Confidence Intervals for Partially Identified Parameters, " Econometrica, 77, 1299-1315. 10.3982/ECTA7347
56. Tsui, K.-W., and S. Weerahandi (1989): "Generalized p-Values in Significance Testing of Hypotheses in the Presence of Nuisance Parameters, " Journal of the American Statistical Association, 84, 602-607.
57. van der Vaart, A. W. (1998): Asymptotic Statistics. Cambridge, U.K.: Cambridge University Press. 10.1017/CBO9780511802256
58. van der Vaart, A. W. (2002): "The Statistical Work of Lucien Le Cam, " The Annals of Statistics, 30, 631-682. 10.1214/aos/1028674836
59. Wald, A. (1943): "Tests of Statistical Hypotheses Concerning Several Parameters When the Number of Observations Is Large, " Transactions of the American Mathematical Society, 54, 426-482. 10.1090/S0002-9947-1943-0012401-3
60. Wang, Y. Y. (1971): "Probabilities of the Type I Errors of the Welch Tests for the Behrens-Fisher Problem, " Journal of the American Statistical Association, 66, 605-608. 10.1080/01621459.1971.10482315
61. Welch, B. L. (1947): "The Generalization of 'Student's' Problem When Several Different Population Variances Are Involved, " Biometrika, 34, 28-35. 10.1093/biomet/34.1-2.28
62. Woutersen, T. (2006): "A Simple Way to Calculate Confidence Intervals for Partially Identified Parameters, " Unpublished Manuscript, Johns Hopkins University.