×

Nonparametric inference of jump regression surface. (English) Zbl 0996.62037

Summary: Estimators for jump location curve and jump size function of a two-dimensional jump regression function (jump regression surface) are proposed. The estimators are obtained by fitting kernel weighted least squares regression based on the observations in the four quadrants of a neighborhood of a given point. The proposed procedure can be used in the case of jump in the regression surface and/or in its slope (jump in the partial derivatives). The limiting distributions and the asymptotic properties of the estimators are investigated. The procedure is illustrated through a simulation study.

MSC:

62G08 Nonparametric regression and quantile regression
62G20 Asymptotic properties of nonparametric inference
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] DOI: 10.1093/biomet/56.3.495 · Zbl 0183.48505 · doi:10.1093/biomet/56.3.495
[2] DOI: 10.2307/2284220 · Zbl 0226.62068 · doi:10.2307/2284220
[3] Shaban S. A., International Statistical Review 48 pp 83– (1980)
[4] Bhattacharya P.K., Change-point problems. IMS Lecture Notes 23 (1994)
[5] DOI: 10.2307/1269075 · Zbl 0626.65010 · doi:10.2307/1269075
[6] DOI: 10.2307/1268942 · doi:10.2307/1268942
[7] DOI: 10.1080/15326348808807089 · Zbl 0666.62080 · doi:10.1080/15326348808807089
[8] DOI: 10.1214/aos/1176348654 · Zbl 0783.62032 · doi:10.1214/aos/1176348654
[9] DOI: 10.1214/aos/1176349271 · Zbl 0795.62043 · doi:10.1214/aos/1176349271
[10] DOI: 10.1214/aos/1032298290 · Zbl 0867.62033 · doi:10.1214/aos/1032298290
[11] DOI: 10.1080/03610929708832067 · Zbl 0955.62571 · doi:10.1080/03610929708832067
[12] DOI: 10.1080/03610929908832393 · Zbl 0935.62047 · doi:10.1080/03610929908832393
[13] Korostelev A. P., Minimax Tfteory of Image Reconstruction,Lecture Notes in Statistics 82 (1993) · Zbl 0833.62039 · doi:10.1007/978-1-4612-2712-0
[14] Tsybakov A. B., Change-Point Problems.IMS Lecture Notes and Monographs Series pp 317– (1994)
[15] Rudemo M., Change-Point Problems. IMS LectureNotes and Monographs Series (1994)
[16] Rudemo M., Scandinavian Journal of Statistics 21 pp 41– (1994)
[17] DOI: 10.1006/jmva.1994.1042 · Zbl 0798.62053 · doi:10.1006/jmva.1994.1042
[18] Qiu P., Sankhya, Series A 59 pp 268– (1997)
[19] DOI: 10.2307/2669613 · Zbl 0906.62035 · doi:10.2307/2669613
[20] DOI: 10.1214/aos/1176325632 · Zbl 0821.62020 · doi:10.1214/aos/1176325632
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.