zbMATH — the first resource for mathematics

Estimation of the number of jump of the jump regression functions. (English) Zbl 0825.62205
Summary: This paper suggests an estimator of the number of jumps of the jump regression functions. The estimator is based on the difference between right and left one-sided kernel smoothers. It is proved to be a.s. consistent. Some results about its rate of convergence are also provided.

62-XX Statistics
Full Text: DOI
[1] Chen X.R., Scientia Sinica 8 pp 1– (1988)
[2] DOI: 10.1007/BF00535491 · Zbl 0443.62029
[3] DOI: 10.1093/biomet/65.2.243 · Zbl 0394.62074
[4] Draper N.R., Applied Regression Analysis (1981) · Zbl 0548.62046
[5] DOI: 10.1080/00401706.1992.10484954
[6] DOI: 10.1017/CCOL0521382483
[7] DOI: 10.1080/00401706.1986.10488127
[8] Medvedev G., Detection of Changes in Random Processes (1986)
[9] DOI: 10.1214/aos/1176348654 · Zbl 0783.62032
[10] Qiu P., Systems Science and Mathematical Sciences 4 pp 1– (1991)
[11] Qiu P., Bulletin of Informatics and Cybernetics 24 pp 197– (1991)
[12] DOI: 10.1080/03610928708829477 · Zbl 0625.62030
[13] DOI: 10.1090/conm/059/870453
[14] Wu J.S., The Annals of statistics 59 (1992)
[15] DOI: 10.1080/15326348808807089 · Zbl 0666.62080
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.