Data driven smooth tests for composite hypotheses

Annals of Statistics

Volumn 25, Issue 3, 1997, Pages 1222-1250

  Inglot, Tadeusz ^a   Kallenberg, Wilbert C M ^b   Ledwina, Teresa ^a  

^a WROCLAW UNIVERSITY OF TECHNOLOGY   (Poland)

^b UNIVERSITY OF TWENTE   (Netherlands)

Author keywords

Data driven procedure; Goodness of fit; Neyman's test; Schwarz's BIC criterion; Smooth test

Indexed keywords

EID: 0031490137     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/aos/1069362746     Document Type: Article

References (58)

1. ANGUS, J. E. (1982). Goodness-of-fit tests for exponentiality based on a loss-of-memory type functional equation. J. Statist. Plann. Inference 6 241-251.
2. ASCHER, S. (1990). A survey of tests for exponentiality. Comm. Statist. Theory Methods 19 1811-1825.
3. BARRON, A. R. and SHEU, C. (1991). Approximation of density functions by sequences of exponential families. Ann. Statist. 19 1347-1369.
4. BARTON, D. E. (1985). Neyman's and other smooth goodness-of-fit tests. In Encyclopedia of Statistical Sciences 6 230-232. Wiley, New York.
5. BICKEL, P. J. and DOKSUM, K. A. (1977). Mathematical Statistics, Basic Ideas and Selected Topics. Holden-Day, San Francisco.
6. BICKEL, P. J. and RITOV, Y. (1992). Testing for goodness of fit: a new approach. In Nonparametric Statistics and Related Topics (A. K. Md. E. Saleh, ed.) 51-57. North-Holland, Amsterdam.
7. BOGDAN, M. (1995). Data driven versions of Pearson's chi-square test for uniformity. J. Statist. Comput. Simulation 52 217-237.
8. BOGDAN, M. and LEDWINA, T. (1996). Testing uniformity via log-spline modeling. Statistics 28 131-157.
9. BOULERICE, B. and DUCHARME, G. R. (1995). A note on smooth tests of goodness of fit for location-scale families. Biometrika 82 437-438.
10. BURKE, M. D. and GOMBAY, E. (1988). On goodness-of-fit and the bootstrap. Statist. Probab. Lett. 6 287-293.
11. COX, D. R. and HINKLEY, D. V. (1974). Theoretical Statistics. Chapman and Hall, London.
12. D'AGOSTINO, R. B. and STEPHENS, M. A. (1986). Goodness-of-Fit Techniques. Dekker, New York.
13. DURBIN, J. (1973). Distribution Theory for Tests Based on the Sample Distribution Function. SIAM, Philadelphia.
14. EUBANK, R. L., HART, J. D. and LARICCIA, V. N. (1993). Testing goodness of fit via nonparametric function estimation techniques. Comm. Statist. Theory Methods 22 3327-3354.
15. EUBANK, R. L., HART, J. D., SIMPSON, D. G. and STEFANSKI, L. A. (1995). Testing for additivity in nonparametric regression. Ann. Statist. 23 1896-1920.
16. EUBANK, R. L. and LARICCIA, V. N. (1992). Asymptotic comparison of Cramér-von Mises and nonparametric function estimation techniques for testing goodness-of-fit. Ann. Statist. 20 2071-2086.
17. FAN, J. (1996). Test of significance based on wavelet thresholding and Neyman's truncation. J. Amer. Statist. Assoc. 91 674-688.
18. GAN, F. F. and KOEHLER, K. J. (1990). Goodness-of-fit tests based on P-P probability plots. Technometrics 32 289-303.
19. HAJEK, J. (1972). Local asymptotic minimax and admissibility in estimation. Proc. Sixth Berkeley Symp. Math. Statist. Probab. 1 175-194. Univ. California Press, Berkeley.
20. HALL, W. J. and MATHIASON, D. J. (1990). On large-sample estimation and testing in parametric models. Internat. Statist. Rev. 58 77-97.
21. INGLOT, T., KALLENBERG, W. C. M. and LEDWINA, T. (1992). Strong moderate deviation theorems. Ann. Probab. 20 987-1003.
22. INGLOT, T., KALLENBERG, W. C. M. and LEDWINA, T. (1994). Power approximations to and power comparison of certain goodness-of-fit tests. Scand. J. Statist. 21 131-145.
23. INGLOT, T. and LEDWINA, T. (1996). Asymptotic optimality of data driven Neyman's tests. Ann. Statist. 24 1982-2019.
24. JANSSEN, A. (1995). Principal component decomposition of non-parametric tests. Probab. Theory Related Fields 101 193-209.
25. JAVITZ, H. S. (1975). Generalized smooth tests of goodness of fit, independence, and equality of distributions. Ph.D. dissertation, Univ. California, Berkeley.
26. JUREČKOVÁ, J., KALLENBERG, W. C. M. and VERAVERBEKE, N. (1988). Moderate and Cramér-type large deviation theorems for M-estimators. Statist. Probab. Lett. 6 191-199.
27. KAIGH, W. D. (1992). EDF and EQF orthogonal component decompositions and tests of uniformity. J. Nonparametr. Statist. 1 313-334.
28. KALLENBEKG, W. C. M. (1983). On moderate deviation theory in estimation. Ann. Statist. 11 498-514.
29. KALLENBERG, W. C. M. and LEDWINA, T. (1995a). Consistency and Monte Carlo simulation of a data driven version of smooth goodness-of-fit tests. Ann. Statist. 23 1594-1608.
30. KALLENBERG, W. C. M. and LEDWINA, T. (1995b). On data driven Neyman's tests. Probab. Math. Statist. 15 409-426.
31. KALLENBERG, W. C. M. and LEDWINA, T. (1995c). Data driven smooth tests for composite hypotheses: comparison of powers. Unpublished manuscript.
32. KALLENBERG, W. C. M. and LEDWINA, T. (1997). Data driven smooth tests when the hypothesis is composite. J. Amer. Statist. Assoc. To appear.
33. KHAMALADZE, E. V. (1981). Martingale approach to the theory of goodness of fit tests. Theory Probab. Appl. 26 240-257.
34. KHAMALADZE, E. V. (1982). Some applications of the theory of martingales to statistics. Russian Math. Surveys 37 215-237.
35. KHAMALADZE, E. V. (1993). Goodness of fit problem and scanning innovation martingales. Ann. Statist. 21 798-829.
36. KIM, J. (1992). Testing goodness-of-fit via order selection criteria. Ph.D. dissertation, Texas A&M Univ.
37. LE CAM, L. (1956). On the asymptotic theory of estimation and testing hypotheses. Proc. Third Berkeley Symp. Math. Statist. Probab. 1 129-156. Univ. California Press, Berkeley.
38. LEDWINA, T. (1994). Data-driven version of Neyman's smooth test of fit. J. Amer. Statist. Assoc. 89 1000-1005.
39. LOCKE, C. and SPURRIER, J. D. (1978). On tests of uniformity. Comm. Statist. Theory Methods 7 241-258.
40. MASSART, P. (1990). The tight constant in the Dvoretzky-Kiefer-Wolfowitz inequality. Ann Probab. 18 1269-1283.
41. MILBRODT, H. and STRASSER, H. (1990). On the asymptotic power of the two-sided Kolmogorov-Smirnov test. J. Statist. Plann. Inference 26 1-23.
42. MILLER, F. L. and QUESENBERRY, C. P. (1979). Power studies of tests for uniformity II. Comm. Statist. Simulation Comput. 8 271-290.
43. NEUHAUS, G. (1976). Asymptotic power properties of the Cramér-von Mises test under contiguous alternatives. J. Multivariate Anal. 6 95-110.
44. NEUHAUS, G. (1979). Asymptotic theory of goodness of fit when parameters are present: a survey. Math. Operationsforsch. Statist. Ser. Statist. 10 479-494.
45. NEYMAN, J. (1937). "Smooth test" for goodness of fit. Skand. Aktuarietidskr. 20 149-199.
46. PETROV, V. V. (1975). Sums of Independent Random Variables. Springer, New York.
47. PROHOROV, A. V. (1973). On sums of random vectors. Theory Probab. Appl. 18 186-188.
48. QUESENBERRY, C. P. and MILLER, F. L. (1977). Power studies of some tests for uniformity. J. Statist. Comput. Simulation 5 169-191.
49. RAYNER, J. C. W. and BEST, D. J. (1986). Neyman-type smooth tests for location-scale families. Biometrika 73 437-446.
50. RAYNER, J. C. W. and BEST, D. J. (1989). Smooth Tests of Goodness of Fit. Oxford Univ. Press, New York.
51. RAYNER, J. C. W. and BEST, D. J. (1990). Smooth tests of goodness of fit: an overview. Internat. Statist. Rev. 58 9-17.
52. RUBIN, H. and SETHURAMAN, J. (1965). Probabilities of moderate deviations. Sankhyā Ser. A 27 325-346.
53. SANSONE, G. (1959). Orthogonal Functions. Interscience, New York.
54. SEN, P. K. and SINGER, J. M. (1993). Large Sample Methods in Statistics. Chapman and Hall, New York.
55. SCHWARZ, G. (1978). Estimating the dimension of a model. Ann. Statist. 6 461-464.
56. SHORACK, G. R. and WELLNER, J. A. (1986). Empirical Processes with Applications to Statistics. Wiley, New York.
57. STONE, C. J. (1990). Large sample inference for log-spline models. Ann. Statist. 18 717-741.
58. THOMAS, D. R. and PIERCE, D. A. (1979). Neyman's smooth goodness-of-fit test when the hypothesis is composite. J. Amer. Statist. Assoc. 74 441-445.