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Kernel regression in the presence of size-bias. (English) Zbl 1113.62320

Summary: Kernel regression estimators of Nadaraya-Watson type for data sampled with size-bias were considered by I. A. Ahmad [Stat. Probab. Lett. 22, No. 2, 121–129 (1995; Zbl 0810.62050)]. We consider an alternative definition of the weight-functions which can be applied to a wider variety of practical situations. In these situations the estimators will have a different bias which we remedy by introducing a local linear estimator.

MSC:

62G08 Nonparametric regression and quantile regression

Citations:

Zbl 0810.62050
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References:

[1] DOI: 10.1016/0167-7152(94)00057-F · Zbl 0810.62050 · doi:10.1016/0167-7152(94)00057-F
[2] DOI: 10.2307/2289282 · doi:10.2307/2289282
[3] Cox D. R., New Developments in Survey Sampling pp 506– (1969)
[4] DOI: 10.2307/2290637 · Zbl 0850.62354 · doi:10.2307/2290637
[5] DOI: 10.1214/aos/1176349022 · Zbl 0773.62029 · doi:10.1214/aos/1176349022
[6] Feller W., Introduction to Probability Theory and Applications 2 (1966) · Zbl 0138.10207
[7] DOI: 10.1214/aos/1176350948 · Zbl 0668.62024 · doi:10.1214/aos/1176350948
[8] Härdle W., Smoothing Techniques with Implementation in S. (1990)
[9] DOI: 10.1093/biomet/78.3.511 · Zbl 1192.62107 · doi:10.1093/biomet/78.3.511
[10] DOI: 10.1137/1109020 · doi:10.1137/1109020
[11] Patil G. P., Applications of Statistics pp 383– (1977)
[12] Patil G. P., Encyclopedia of Statistical Sciences pp 565– (1988)
[13] DOI: 10.1214/aos/1176325632 · Zbl 0821.62020 · doi:10.1214/aos/1176325632
[14] DOI: 10.1214/aos/1176343886 · Zbl 0366.62051 · doi:10.1214/aos/1176343886
[15] DOI: 10.1214/aos/1176345802 · Zbl 0491.62034 · doi:10.1214/aos/1176345802
[16] DOI: 10.1214/aos/1176346585 · Zbl 0578.62047 · doi:10.1214/aos/1176346585
[17] Wand M. P., Kernel Smoothing (1995) · Zbl 0854.62043 · doi:10.1007/978-1-4899-4493-1
[18] Watson G. S., Sankhyā Ser. A 26 pp 359– (1985)
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