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Gijbels, I.; Goderniaux, A.-C.

Bootstrap test for change-points in nonparametric regression. (English) Zbl 1148.62304

J. Nonparametric Stat. 16, No. 3-4, 591-611 (2004).
Summary: The objective of this article is to test whether or not there is an abrupt change in the regression function itself or in its first derivative at certain (prespecified or not) locations. The test does not rely on asymptotics but approximates the sample distribution of the test statistic using a bootstrap procedure. The proposed testing method involves a data-driven choice of the smoothing parameters. The performance of the testing procedures is evaluated via a simulation study. Some comparison with an asymptotic test by Z. Hamrouni [Inférence statistique par lissage linéaire local pour une fonction de régression présentant des discontinuités. Doctoral thesis, Université de Joseph Fourier, Grenoble, France (1999)] and G. Grégoire and Z. Hamrouni [J. Nonparametric Stat. 14, No. 1-2, 87–112 (2002; Zbl 1016.62054)] and asymptotic tests by H.-G. Müller and U. Stadtmüller [Ann. Stat. 27, No. 1, 299–337 (1999; Zbl 0954.62052)] and Ch. Dubowik and U. Stadtmüller [Detecting jumps in nonparametric regression. In: Puri, M. L. (ed.), Asymptotics in Statistics and Probability, 171–184 (2000)] is provided. We also demonstrate the use of the testing procedures on some real data.

Cited in 20 Documents

MSC:

62G08 Nonparametric regression and quantile regression
62G10 Nonparametric hypothesis testing
62G09 Nonparametric statistical resampling methods

Keywords:

Bandwidth; Bootstrap; Cross-validation; Discontinuity Points; Derivative; Least-squares Fitting; Local Polynomial Approximation

Citations:

Zbl 1016.62054; Zbl 0954.62052
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Full Text: DOI

References:

[1] Antoniadis A, Journal of Nonparametric Statistics 14 pp 7– (2002) · Zbl 1017.62033 · doi:10.1080/10485250211396
[2] Bowman AW, Journal of Computational and Graphical Statistics 7 pp 489– (1998)
[3] Chu CK, Communications in Statistics, Part A-Theory and Methods 23 pp 3037– (1994) · Zbl 0823.62034 · doi:10.1080/03610929408831432
[4] Cline DBH, Journal of Statistical Research 29 pp 17– (1995)
[5] Cobb GW, Biometrika 62 pp 243– (1978) · Zbl 0394.62074 · doi:10.1093/biomet/65.2.243
[6] Dubowik Ch., Asymptotics in Statistics and Probability pp pp 171–184– (2000)
[7] Eubank RL, Change-point Problems 23 pp 130– (1994) · doi:10.1214/lnms/1215463119
[8] Fan J, Local Polynomial Modelling and its Applications, Chapman and Hall (1996) · Zbl 0873.62037
[9] Gijbels I, Technometrics 46 pp 76– (2004) · doi:10.1198/004017004000000130
[10] Gijbels I, Communications in Statistics, Part A – Theory and Methods 33 pp 851– (2004) · Zbl 1218.62031 · doi:10.1081/STA-120028730
[11] Gijbels I, The Annals of the Institute of Statistical Mathematics 51 pp 231– (1999) · Zbl 0934.62035 · doi:10.1023/A:1003802007064
[12] Gijbels I, Journal of Applied Probability (2003)
[13] Grégoire G, Journal of Multivariate Analysis 83 pp 56– (2002) · Zbl 1021.62026 · doi:10.1006/jmva.2001.2038
[14] Grégoire G, Journal of Nonparametric Statistics 14 pp 87– (2002) · Zbl 1016.62054 · doi:10.1080/10485250211386
[15] Hall P, Technometrics 34 pp 429– (1992) · doi:10.1080/00401706.1992.10484954
[16] Hamrouni Z, Doctoral thesis, Université de Joseph Fourier (1999)
[17] Härdle W, Applied Nonparametric Regression, Econometric Society Monograph Series Vol. 19 (1990) · Zbl 0714.62030
[18] Harezlak J, MSc thesis, Department of Statistics, University of British Columbia (1998)
[19] Harezlak J, Journal of Computational and Graphical Statistics 10 pp 713– (2001) · doi:10.1198/106186001317243412
[20] Horváth L, Technical report, University of Liverpool (1997)
[21] Horváth L, Statistics 36 pp 9– (2002) · Zbl 1010.62036 · doi:10.1080/02331880210930
[22] Jarrett RG, Biometrika 66 pp 191– (1979) · doi:10.1093/biomet/66.1.191
[23] Loader CR, The Annals of Statistics 24 pp 1667– (1996) · Zbl 0867.62033 · doi:10.1214/aos/1032298290
[24] McDonald JA, Technometrics 28 pp 195– (1986) · doi:10.1080/00401706.1986.10488127
[25] Müller H-G, The Annals of Statistics 20 pp 737– (1992) · Zbl 0783.62032 · doi:10.1214/aos/1176348654
[26] Müller H-G, Statistics & Probability Letters 34 pp 323– (1997) · Zbl 0874.62035 · doi:10.1016/S0167-7152(96)00197-6
[27] Müller H-G, The Annals of Statistics 27 pp 299– (1999) · Zbl 0954.62052 · doi:10.1214/aos/1018031113
[28] Müller H-G, Biometrika 74 (4) pp 743– (1987) · Zbl 0628.62034 · doi:10.1093/biomet/74.4.743
[29] Nadaraya EA, Theory of Probability and Applications 9 pp 141– (1964) · doi:10.1137/1109020
[30] Qiu P, Technometrics 40 pp 141– (1998)
[31] Raimondo M, The Annals of Statistics 26 pp 1379– (1998) · Zbl 0929.62039 · doi:10.1214/aos/1024691247
[32] Scott DW, Multivariate Density Estimation. Theory, Practice and Visualization, Wiley (1992) · doi:10.1002/9780470316849
[33] Silverman BW, Density Estimation for Statistics and Data Analysis, Chapman and Hall (1986) · doi:10.1007/978-1-4899-3324-9
[34] Speckman PL (1994) Detection of change-points in nonparametric regression (unpublished manuscript.)
[35] Speckman PL, Computing science and statistics 26 pp 257– (1995)
[36] Spokoiny VG, The Annals of Statistics 26 pp 1356– (1998) · Zbl 0934.62037 · doi:10.1214/aos/1024691246
[37] Wang Y, Biometrika 82 pp 385– (1995) · Zbl 0824.62031 · doi:10.1093/biomet/82.2.385
[38] Watson GS, Sankhyā 26 pp 359– (1964)
[39] Wu JS, The Annals of Statistics 21 pp 1545– (1993) · Zbl 0795.62043 · doi:10.1214/aos/1176349271
[40] Wu JS, Nonparametric Statistics 2 pp 341– (1993) · Zbl 1360.62144 · doi:10.1080/10485259308832563
[41] Wu JS, Statistica Sinica 3 pp 557– (1993)
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