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Volumn 29, Issue 1, 2001, Pages 153-193

Generalized likelihood ratio statistics and wilks phenomenon

Author keywords

Asymptotic null distribution; Gaussian white noise models; Generalized likelihood; Nonparametric test; Optimal rates; Power function; Wilks thoerem

Indexed keywords


EID: 0035633948     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/aos/996986505     Document Type: Article
Times cited : (518)

References (49)
  • 2
    • 0000357414 scopus 로고
    • On the use of nonparametric regression for checking linear relationships
    • AZZALINI, A. and BOWMAN, A. N. (1993). On the use of nonparametric regression for checking linear relationships. J. Roy. Statist. Soc. Ser. B 55 549-557.
    • (1993) J. Roy. Statist. Soc. Ser. B , vol.55 , pp. 549-557
    • Azzalini, A.1    Bowman, A.N.2
  • 3
    • 0002701230 scopus 로고
    • On the use of nonparametric regression for model checking
    • AZZALINI, A., BOWMAN, A. N. and Härdle, W. (1989). On the use of nonparametric regression for model checking. Biometrika 76 1-11.
    • (1989) Biometrika , vol.76 , pp. 1-11
    • Azzalini, A.1    Bowman, A.N.2    Härdle, W.3
  • 4
    • 0001824125 scopus 로고
    • Testing for goodness of fit: A new approach
    • (A. K. Md. E. Saleh, ed.) North-Holland, New York
    • 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, New York.
    • (1992) Nonparametric Statistics and Related Topics , pp. 51-57
    • Bickel, P.J.1    Ritov, Y.2
  • 5
    • 0000797991 scopus 로고
    • On some global measures of the deviation of density function estimates
    • BICKEL, P. J. and ROSENBLATT, M. (1973). On some global measures of the deviation of density function estimates. Ann. Statist. 1 1071-1095.
    • (1973) Ann. Statist. , vol.1 , pp. 1071-1095
    • Bickel, P.J.1    Rosenblatt, M.2
  • 6
    • 0030335402 scopus 로고    scopus 로고
    • Asymptotic equivalence of nonparametric regression and white noise
    • BROWN, L. D. and LOW, M. G. (1996). Asymptotic equivalence of nonparametric regression and white noise. Ann. Statist. 24 2384-2398.
    • (1996) Ann. Statist. , vol.24 , pp. 2384-2398
    • Brown, L.D.1    Low, M.G.2
  • 7
    • 2242444502 scopus 로고    scopus 로고
    • Efficient estimation and inferences for varying-coefficient models
    • To appear
    • CAI, Z., FAN, J. and LI, R. (2000). Efficient estimation and inferences for varying-coefficient models. J. Amer. Statist. Assoc. To appear.
    • (2000) J. Amer. Statist. Assoc.
    • Cai, Z.1    Fan, J.2    Li, R.3
  • 9
    • 0001315746 scopus 로고
    • Empirical likelihood estimation for finite populations and the effective usage of auxiliary information
    • CHEN, J. H. and QIN, J. (1993). Empirical likelihood estimation for finite populations and the effective usage of auxiliary information. Biometrika 80 107-116.
    • (1993) Biometrika , vol.80 , pp. 107-116
    • Chen, J.H.1    Qin, J.2
  • 10
    • 84947318637 scopus 로고
    • Locally-weighted regression: An approach to regression analysis by local fitting
    • CLEVELAND, W. S. and DEVLIN, S. J. (1988). Locally-weighted regression: an approach to regression analysis by local fitting. J. Amer. Statist. Assoc. 83 597-610.
    • (1988) J. Amer. Statist. Assoc. , vol.83 , pp. 597-610
    • Cleveland, W.S.1    Devlin, S.J.2
  • 11
    • 85053520810 scopus 로고
    • Local regression models
    • (J. M. Chambers and T. J. Hastie, eds.) Wadsworth and Brooks Cole, Pacific Grove, CA
    • CLEVELAND, W. S., GROSSE, E. and SHYU, W. M. (1992). Local regression models. In Statistical Models in S (J. M. Chambers and T. J. Hastie, eds.) 309-376. Wadsworth and Brooks Cole, Pacific Grove, CA.
    • (1992) Statistical Models in S , pp. 309-376
    • Cleveland, W.S.1    Grosse, E.2    Shyu, W.M.3
  • 12
    • 34250109475 scopus 로고
    • A central limit theorem for generalized quadratic forms
    • DE JONG, P. (1987). A central limit theorem for generalized quadratic forms. Probab. Theory Related Fields 75 261-277.
    • (1987) Probab. Theory Related Fields , vol.75 , pp. 261-277
    • De Jong, P.1
  • 13
    • 21144482103 scopus 로고
    • Testing goodness-of-fit in regression via order selection criteria
    • EUBANK, R. L. and HART, J. D. (1992). Testing goodness-of-fit in regression via order selection criteria. Ann. Statist. 20 1412-1425.
    • (1992) Ann. Statist. , vol.20 , pp. 1412-1425
    • Eubank, R.L.1    Hart, J.D.2
  • 14
    • 21144481988 scopus 로고
    • Asymptotic comparison of Cramér-von Mises and nonparametric function estimation techniques for testing goodness-of-fit
    • EUBANK, R. L. and LARICCIA, V. M. (1992). Asymptotic comparison of Cramér-von Mises and nonparametric function estimation techniques for testing goodness-of-fit. Ann. Statist. 20 2071-2086.
    • (1992) Ann. Statist. , vol.20 , pp. 2071-2086
    • Eubank, R.L.1    Lariccia, V.M.2
  • 15
    • 3042869574 scopus 로고
    • Local linear regression smoothers and their minimax efficiency
    • FAN, J. (1993). Local linear regression smoothers and their minimax efficiency. Ann. Statist. 21 196-216.
    • (1993) Ann. Statist. , vol.21 , pp. 196-216
    • Fan, J.1
  • 16
    • 0030549054 scopus 로고    scopus 로고
    • Test of significance based on wavelet thresholding and Neyman's truncation
    • FAN, J. (1996). Test of significance based on wavelet thresholding and Neyman's truncation. J. Amer. Statist. Assoc. 91 674-688.
    • (1996) J. Amer. Statist. Assoc. , vol.91 , pp. 674-688
    • Fan, J.1
  • 18
    • 1542746314 scopus 로고    scopus 로고
    • Goodness-of-fit test for parametric regression models
    • Dept. Statistics, Univ. California, Los Angeles
    • FAN, J. and HUANG, L. (1998). Goodness-of-fit test for parametric regression models. Technical Report, Dept. Statistics, Univ. California, Los Angeles.
    • (1998) Technical Report
    • Fan, J.1    Huang, L.2
  • 20
    • 0012768874 scopus 로고
    • Empirical likelihood confidence bands in density estimation
    • HALL, P. and OWEN, A. B. (1993). Empirical likelihood confidence bands in density estimation. J. Comput. Graph. Statist. 2 273-289.
    • (1993) J. Comput. Graph. Statist. , vol.2 , pp. 273-289
    • Hall, P.1    Owen, A.B.2
  • 21
    • 21344496537 scopus 로고
    • Comparing nonparametric versus parametric regression fits
    • HÄRDLE, W. and MAMMEN, E. (1993). Comparing nonparametric versus parametric regression fits. Ann. Statist. 21 1926-1947.
    • (1993) Ann. Statist. , vol.21 , pp. 1926-1947
    • Härdle, W.1    Mammen, E.2
  • 25
    • 0001033261 scopus 로고
    • Robust regression: Asymptotics, conjectures and Monte Carlo
    • HUBER, P. J. (1973). Robust regression: asymptotics, conjectures and Monte Carlo. Ann. Statist. 1 799-821.
    • (1973) Ann. Statist. , vol.1 , pp. 799-821
    • Huber, P.J.1
  • 26
    • 0007224094 scopus 로고
    • Power approximations to and power comparison of smooth goodness-of-fit tests
    • INGLOT, T., KALLENBERG, W. C. M. and LEDWINA, T. (1994). Power approximations to and power comparison of smooth goodness-of-fit tests. Scand. J. Statist. 21 131-145.
    • (1994) Scand. J. Statist. , vol.21 , pp. 131-145
    • Inglot, T.1    Kallenberg, W.C.M.2    Ledwina, T.3
  • 27
    • 0030363428 scopus 로고    scopus 로고
    • Asymptotic optimality of data-driven Neyman's tests for uniformity
    • INGLOT, T. and LEDWINA, T. (1996). Asymptotic optimality of data-driven Neyman's tests for uniformity. Ann. Statist. 24 1982-2019.
    • (1996) Ann. Statist. , vol.24 , pp. 1982-2019
    • Inglot, T.1    Ledwina, T.2
  • 28
    • 0003058689 scopus 로고
    • Asymptotic minimax hypothesis testing for nonparametric alternatives I-III
    • INGSTER, YU. I. (1993). Asymptotic minimax hypothesis testing for nonparametric alternatives I-III. Math. Methods Statist. 2 85-114; 3 171-189; 4 249-268.
    • (1993) Math. Methods Statist. , vol.2 , pp. 85-114
    • Ingster, Yu.I.1
  • 29
    • 0000484198 scopus 로고    scopus 로고
    • INGSTER, YU. I. (1993). Asymptotic minimax hypothesis testing for nonparametric alternatives I-III. Math. Methods Statist. 2 85-114; 3 171-189; 4 249-268.
    • Math. Methods Statist. , vol.3 , pp. 171-189
  • 30
    • 0001047522 scopus 로고    scopus 로고
    • INGSTER, YU. I. (1993). Asymptotic minimax hypothesis testing for nonparametric alternatives I-III. Math. Methods Statist. 2 85-114; 3 171-189; 4 249-268.
    • Math. Methods Statist. , vol.4 , pp. 249-268
  • 31
    • 21744458278 scopus 로고    scopus 로고
    • Data-driven smooth tests when the hypothesis is composite
    • KALLENBERG, W. C. M. and LEDWINA, T. (1997). Data-driven smooth tests when the hypothesis is composite. J. Amer. Statist. Assoc. 92 1094-1104.
    • (1997) J. Amer. Statist. Assoc. , vol.92 , pp. 1094-1104
    • Kallenberg, W.C.M.1    Ledwina, T.2
  • 33
    • 0002546986 scopus 로고    scopus 로고
    • Smoothing-based lack-of-fit tests: Variations on a theme
    • KUCHIBHATLA, M. and HART, J. D. (1996). Smoothing-based lack-of-fit tests: variations on a theme. J. Nonparameter. Statist. 7 1-22.
    • (1996) J. Nonparameter. Statist. , vol.7 , pp. 1-22
    • Kuchibhatla, M.1    Hart, J.D.2
  • 34
    • 0000365255 scopus 로고    scopus 로고
    • Minimax nonparametric hypothesis testing: The case of an inhomogeneous alternative
    • LEPSKI, O. V. and SPOKOINY, V. G. (1999). Minimax nonparametric hypothesis testing: the case of an inhomogeneous alternative. Bernoulli 5 333-358.
    • (1999) Bernoulli , vol.5 , pp. 333-358
    • Lepski, O.V.1    Spokoiny, V.G.2
  • 35
    • 0030493542 scopus 로고    scopus 로고
    • Nonparametric likelihood ratio confidence bands for quantile functions from incomplete survival data
    • LI, G., HOLLANDER, M., MCKEAGUE, I. W. and YANG, J (1996). Nonparametric likelihood ratio confidence bands for quantile functions from incomplete survival data. Ann. Statist. 24 628-640.
    • (1996) Ann. Statist. , vol.24 , pp. 628-640
    • Li, G.1    Hollander, M.2    McKeague, I.W.3    Yang, J.4
  • 36
    • 0002792513 scopus 로고
    • Testing for a time dependent coefficient in Cox's regression model
    • MURPHY, S. A. (1993). Testing for a time dependent coefficient in Cox's regression model. Scand. J. Statist. 20 35-50.
    • (1993) Scand. J. Statist. , vol.20 , pp. 35-50
    • Murphy, S.A.1
  • 37
    • 84945593245 scopus 로고
    • Smooth test for goodness of fit
    • NEYMAN, J. (1937). Smooth test for goodness of fit. Skand. Aktuar. J. 20 149-199.
    • (1937) Skand. Aktuar. J. , vol.20 , pp. 149-199
    • Neyman, J.1
  • 38
    • 0030328670 scopus 로고    scopus 로고
    • Asymptotic equivalence of density estimation and Gaussian white noise
    • NUSSBAUM, M. (1996). Asymptotic equivalence of density estimation and Gaussian white noise. Ann. Statist. 24 2399-2430.
    • (1996) Ann. Statist. , vol.24 , pp. 2399-2430
    • Nussbaum, M.1
  • 39
    • 0000060427 scopus 로고
    • Empirical likelihood ratio confidence intervals for a single functional
    • OWEN, A. B. (1988). Empirical likelihood ratio confidence intervals for a single functional. Biometrika 75 237-249.
    • (1988) Biometrika , vol.75 , pp. 237-249
    • Owen, A.B.1
  • 40
    • 0002552463 scopus 로고
    • Empirical likelihood ratio confidence regions
    • OWEN, A. B. (1990). Empirical likelihood ratio confidence regions. Ann. Statist. 18 90-120.
    • (1990) Ann. Statist. , vol.18 , pp. 90-120
    • Owen, A.B.1
  • 41
    • 0000791208 scopus 로고
    • Asymptotic behavior of likelihood methods for exponential families when the number of parameters tends to infinity
    • PORTNOY, S. (1988). Asymptotic behavior of likelihood methods for exponential families when the number of parameters tends to infinity. Ann. Statist. 16 356-366.
    • (1988) Ann. Statist. , vol.16 , pp. 356-366
    • Portnoy, S.1
  • 44
    • 1542742691 scopus 로고    scopus 로고
    • Random sieve likelihood and general regression models
    • SHEN, X., SHI, J. and WONG, W. H. (1999). Random sieve likelihood and general regression models. J. Amer. Statist. Assoc. 94 835-846.
    • (1999) J. Amer. Statist. Assoc. , vol.94 , pp. 835-846
    • Shen, X.1    Shi, J.2    Wong, W.H.3
  • 45
    • 21144469737 scopus 로고
    • Generalized profile likelihood and conditional parametric models
    • SEVERINI, T. A. and WONG, W. H. (1992). Generalized profile likelihood and conditional parametric models. Ann. Statist. 20 1768-1802.
    • (1992) Ann. Statist. , vol.20 , pp. 1768-1802
    • Severini, T.A.1    Wong, W.H.2
  • 46
    • 0000997747 scopus 로고
    • Spline smoothing: The equivalent variable kernel method
    • SILVERMAN, B. W. (1984). Spline smoothing: the equivalent variable kernel method. Ann. Statist. 12 898-916.
    • (1984) Ann. Statist. , vol.12 , pp. 898-916
    • Silverman, B.W.1
  • 47
    • 0030342998 scopus 로고    scopus 로고
    • Adaptive hypothesis testing using wavelets
    • SPOKOINY, V. G. (1996). Adaptive hypothesis testing using wavelets. Ann. Statist. 24 2477-2498.
    • (1996) Ann. Statist. , vol.24 , pp. 2477-2498
    • Spokoiny, V.G.1
  • 48
    • 0001972601 scopus 로고
    • The large-sample distribution of the likelihood ratio for testing composite hypotheses
    • WILKS, S. S. (1938). The large-sample distribution of the likelihood ratio for testing composite hypotheses. Ann. Math. Statist. 9 60-62.
    • (1938) Ann. Math. Statist. , vol.9 , pp. 60-62
    • Wilks, S.S.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.