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Volumn 41, Issue 2, 2013, Pages 838-869

Minimax adaptive tests for the functional linear model

Author keywords

Adaptive testing; Eigenfunction; Ellipsoid; Functional linear regression; Goodness of fit; Minimax hypothesis testing; Minimax separation rate; Multiple testing; Principal component analysis

Indexed keywords


EID: 84879170216     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/13-AOS1093     Document Type: Article
Times cited : (54)

References (36)
  • 1
  • 2
    • 24344470806 scopus 로고    scopus 로고
    • Non-asymptotic minimax rates of testing in signal detection
    • MR1935648
    • BARAUD, Y. (2002). Non-asymptotic minimax rates of testing in signal detection. Bernoulli 8 577-606. MR1935648.
    • (2002) Bernoulli , vol.8 , pp. 577-606
    • Baraud, Y.1
  • 3
    • 21144438312 scopus 로고    scopus 로고
    • Adaptive tests of linear hypotheses by model selection
    • MR1962505
    • BARAUD, Y., HUET, S. and LAURENT, B. (2003). Adaptive tests of linear hypotheses by model selection. Ann. Statist. 31 225-251. MR1962505.
    • (2003) Ann. Statist. , vol.31 , pp. 225-251
    • Baraud, Y.1    Huet, S.2    Laurent, B.3
  • 4
    • 33847349358 scopus 로고    scopus 로고
    • Prediction in functional linear regression
    • MR2291496
    • CAI, T. T. and HALL, P. (2006). Prediction in functional linear regression. Ann. Statist. 34 2159-2179. MR2291496.
    • (2006) Ann. Statist. , vol.34 , pp. 2159-2179
    • Cai, T.T.1    Hall, P.2
  • 5
    • 0038784362 scopus 로고    scopus 로고
    • Testing hypotheses in the functional linear model
    • MR1965105
    • CARDOT, H., FERRATY, F., MAS, A. and SARDA, P. (2003). Testing hypotheses in the functional linear model. Scand. J. Stat. 30 241-255. MR1965105.
    • (2003) Scand. J. Stat. , vol.30 , pp. 241-255
    • Cardot, H.1    Ferraty, F.2    Mas, A.3    Sarda, P.4
  • 6
    • 0041459525 scopus 로고    scopus 로고
    • Spline estimators for the functional linear model
    • MR1997162
    • CARDOT, H., FERRATY, F. and SARDA, P. (2003). Spline estimators for the functional linear model. Statist. Sinica 13 571-591. MR1997162.
    • (2003) Statist. Sinica , vol.13 , pp. 571-591
    • Cardot, H.1    Ferraty, F.2    Sarda, P.3
  • 7
    • 1642405059 scopus 로고    scopus 로고
    • Testing for no effect in functional linear regression models, some computational approaches
    • MR2044864
    • CARDOT, H., GOIA, A. and SARDA, P. (2004). Testing for no effect in functional linear regression models, some computational approaches. Comm. Statist. Simulation Comput. 33 179-199. MR2044864.
    • (2004) Comm. Statist. Simulation Comput. , vol.33 , pp. 179-199
    • Cardot, H.1    Goia, A.2    Sarda, P.3
  • 8
    • 70449532455 scopus 로고    scopus 로고
    • Thresholding projection estimators in functional linear models
    • MR2564349
    • CARDOT, H. and JOHANNES, J. (2010). Thresholding projection estimators in functional linear models. J. Multivariate Anal. 101 395-408. MR2564349.
    • (2010) J. Multivariate Anal. , vol.101 , pp. 395-408
    • Cardot, H.1    Johannes, J.2
  • 9
    • 34248349998 scopus 로고    scopus 로고
    • Clt in functional linear regression models
    • MR2299711
    • CARDOT, H., MAS, A. and SARDA, P. (2007). CLT in functional linear regression models. Probab. Theory Related Fields 138 325-361. MR2299711.
    • (2007) Probab. Theory Related Fields , vol.138 , pp. 325-361
    • Cardot, H.1    Mas, A.2    Sarda, P.3
  • 11
    • 84859508035 scopus 로고    scopus 로고
    • Adaptive estimation in circular functional linear models
    • MR2682854
    • COMTE, F. and JOHANNES, J. (2010). Adaptive estimation in circular functional linear models. Math. Methods Statist. 19 42-63. MR2682854.
    • (2010) Math. Methods Statist. , vol.19 , pp. 42-63
    • Comte, F.1    Johannes, J.2
  • 12
    • 84879133076 scopus 로고    scopus 로고
    • Adaptive functional linear regression
    • COMTE, F. and JOHANNES, J. (2012). Adaptive functional linear regression. Ann. Statist. 40 2765-2797.
    • (2012) Ann. Statist. , vol.40 , pp. 2765-2797
    • Comte, F.1    Johannes, J.2
  • 13
    • 65349171811 scopus 로고    scopus 로고
    • Smoothing splines estimators for functional linear regression
    • MR2488344
    • CRAMBES, C., KNEIP, A. and SARDA, P. (2009). Smoothing splines estimators for functional linear regression. Ann. Statist. 37 35-72. MR2488344.
    • (2009) Ann. Statist. , vol.37 , pp. 35-72
    • Crambes, C.1    Kneip, A.2    Sarda, P.3
  • 14
  • 15
    • 0000957849 scopus 로고
    • Asymptotic theory for the principal component analysis of a vector random function: Some applications to statistical inference
    • MR0650934
    • DAUXOIS, J., POUSSE, A. and ROMAIN, Y. (1982). Asymptotic theory for the principal component analysis of a vector random function: Some applications to statistical inference. J. Multivariate Anal. 12 136-154. MR0650934.
    • (1982) J. Multivariate Anal. , vol.12 , pp. 136-154
    • Dauxois, J.1    Pousse, A.2    Romain, Y.3
  • 16
    • 23744475601 scopus 로고    scopus 로고
    • Higher criticism for detecting sparse heterogeneous mixtures
    • MR2065195
    • DONOHO, D. and JIN, J. (2004). Higher criticism for detecting sparse heterogeneous mixtures. Ann. Statist. 32 962-994. MR2065195.
    • (2004) Ann. Statist. , vol.32 , pp. 962-994
    • Donoho, D.1    Jin, J.2
  • 21
    • 35348874516 scopus 로고    scopus 로고
    • Methodology and convergence rates for functional linear regression
    • MR2332269
    • HALL, P. and HOROWITZ, J. L. (2007). Methodology and convergence rates for functional linear regression. Ann. Statist. 35 70-91. MR2332269.
    • (2007) Ann. Statist. , vol.35 , pp. 70-91
    • Hall, P.1    Horowitz, J.L.2
  • 22
    • 33645039219 scopus 로고    scopus 로고
    • On properties of functional principal components analysis
    • MR2212577
    • HALL, P. and HOSSEINI-NASAB, M. (2006). On properties of functional principal components analysis. J. R. Stat. Soc. Ser. B Stat. Methodol. 68 109-126. MR2212577.
    • (2006) J. R. Stat. Soc. Ser. B Stat. Methodol. , vol.68 , pp. 109-126
    • Hall, P.1    Hosseini-nasab, M.2
  • 23
    • 57549119141 scopus 로고    scopus 로고
    • Theory for high-order bounds in functional principal components analysis
    • MR2461880
    • HALL, P. and HOSSEINI-NASAB, M. (2009). Theory for high-order bounds in functional principal components analysis. Math. Proc. Cambridge Philos. Soc. 146 225-256. MR2461880.
    • (2009) Math. Proc. Cambridge Philos. Soc. , vol.146 , pp. 225-256
    • Hall, P.1    Hosseini-nasab, M.2
  • 24
    • 33747183021 scopus 로고    scopus 로고
    • Assessing extrema of empirical principal component functions
    • MR2278366
    • HALL, P. and VIAL, C. (2006). Assessing extrema of empirical principal component functions. Ann. Statist. 34 1518-1544. MR2278366.
    • (2006) Ann. Statist. , vol.34 , pp. 1518-1544
    • Hall, P.1    Vial, C.2
  • 26
    • 0003058689 scopus 로고
    • Asymptotically minimax hypothesis testing for nonparametric alternatives, I
    • MR1257978
    • INGSTER, Y. I. (1993). Asymptotically minimax hypothesis testing for nonparametric alternatives. I. Math. Methods Statist. 2 85-114. MR1257978.
    • (1993) Math. Methods Statist. , vol.2 , pp. 85-114
    • Ingster, Y.I.1
  • 27
    • 0000484198 scopus 로고
    • Asymptotically minimax hypothesis testing for nonparametric alternatives, II
    • MR1257983
    • INGSTER, Y. I. (1993). Asymptotically minimax hypothesis testing for nonparametric alternatives. II. Math. Methods Statist. 2 171-189. MR1257983.
    • (1993) Math. Methods Statist. , vol.2 , pp. 171-189
    • Ingster, Y.I.1
  • 28
    • 0001047522 scopus 로고
    • Asymptotically minimax hypothesis testing for nonparametric alternatives, III
    • MR1259685
    • INGSTER, Y. I. (1993). Asymptotically minimax hypothesis testing for nonparametric alternatives. III. Math. Methods Statist. 2 249-268. MR1259685.
    • (1993) Math. Methods Statist. , vol.2 , pp. 249-268
    • Ingster, Y.I.1
  • 29
    • 33749479351 scopus 로고    scopus 로고
    • Perturbation approach applied to the asymptotic study of random operators
    • (Sandjberg, 2002), Progress in Probability 55, Birkhäuser, Basel, MR2033885
    • MAS, A. and MENNETEAU, L. (2003). Perturbation approach applied to the asymptotic study of random operators. In High Dimensional Probability, III (Sandjberg, 2002). Progress in Probability 55 127-134. Birkhäuser, Basel. MR2033885.
    • (2003) High Dimensional Probability , vol.3 , pp. 127-134
    • Mas, A.1    Menneteau, L.2
  • 30
    • 79957976204 scopus 로고    scopus 로고
    • Asymptotic equivalence of functional linear regression and a white noise inverse problem
    • MR2850209
    • MEISTER, A. (2011). Asymptotic equivalence of functional linear regression and a white noise inverse problem. Ann. Statist. 39 1471-1495. MR2850209.
    • (2011) Ann. Statist. , vol.39 , pp. 1471-1495
    • Meister, A.1
  • 31
    • 84907095419 scopus 로고    scopus 로고
    • R: A language and environment for statistical computing
    • R DEVELOPMENT CORE TEAM ., Vienna, Austria. ISBN 3-900051-07-0. Available at
    • R DEVELOPMENT CORE TEAM (2009). R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria. ISBN 3-900051-07-0. Available at http://www.R-project.org.
    • (2009) R Foundation for Statistical Computing
  • 32
    • 0004116414 scopus 로고
    • 3rd ed. McGraw-Hill, New York, MR0924157
    • RUDIN, W. (1987). Real and Complex Analysis, 3rd ed. McGraw-Hill, New York. MR0924157.
    • (1987) Real and Complex Analysis
    • Rudin, W.1
  • 33
    • 0030342998 scopus 로고    scopus 로고
    • Adaptive hypothesis testing using wavelets
    • MR1425962
    • SPOKOINY, V. G. (1996). Adaptive hypothesis testing using wavelets. Ann. Statist. 24 2477- 2498. MR1425962.
    • (1996) Ann. Statist. , vol.24 , pp. 2477-2498
    • Spokoiny, V.G.1
  • 34
    • 84857090762 scopus 로고    scopus 로고
    • Minimax risks for sparse regressions: Ultra-high dimensional phenomenons
    • MR2879672
    • VERZELEN, N. (2012). Minimax risks for sparse regressions: Ultra-high dimensional phenomenons. Electron. J. Stat. 6 38-90. MR2879672.
    • (2012) Electron. J. Stat. , vol.6 , pp. 38-90
    • Verzelen, N.1
  • 35
    • 77649319133 scopus 로고    scopus 로고
    • Goodness-of-fit tests for high-dimensional gaussian linear models
    • MR2604699
    • VERZELEN, N. and VILLERS, F. (2010). Goodness-of-fit tests for high-dimensional Gaussian linear models. Ann. Statist. 38 704-752. MR2604699.
    • (2010) Ann. Statist. , vol.38 , pp. 704-752
    • Verzelen, N.1    Villers, F.2
  • 36
    • 78650085539 scopus 로고    scopus 로고
    • A reproducing kernel hilbert space approach to functional linear regression
    • MR2766857
    • YUAN, M. and CAI, T. T. (2010). A reproducing kernel Hilbert space approach to functional linear regression. Ann. Statist. 38 3412-3444. MR2766857.
    • (2010) Ann. Statist. , vol.38 , pp. 3412-3444
    • Yuan, M.1    Cai, T.T.2


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