×

zbMATH — the first resource for mathematics

Kernel regression estimators for nonparametric model calibration in survey sampling. (English) Zbl 1216.62055
Summary: This paper introduces new kernel regression estimators with strictly non-negative smoothing weights that are iteratively adjusted. One estimator shares the “optimal” asymptotic bias and variance of the local linear regressor. Other estimators have zero sum of residuals, a desirable property in many applications. In a survey sampling context these estimators can easily be adjusted so that they are internally bias calibrated, which is a property with intuitive appeal. We demonstrate in simulations that one of the estimators with zero sum residuals has bias and variance properties that are very close to “optimal”. In addition, we propose a potentially useful refinement to the usual orders of asymptotic approximations for bias and variance of kernel regression smoothers. The smoothers are illustrated using two examples from fisheries applications, one of which involves data from a stratified random bottom-trawl survey.
MSC:
62G08 Nonparametric regression and quantile regression
62D05 Sampling theory, sample surveys
65C60 Computational problems in statistics (MSC2010)
62G20 Asymptotic properties of nonparametric inference
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Breidt F. J., Ann. Statist. 28 pp 1026– (2000) · Zbl 1105.62302 · doi:10.1214/aos/1015956706
[2] Breidt F. J., Biometrika 92 pp 831– (2005) · Zbl 1151.62306 · doi:10.1093/biomet/92.4.831
[3] Chambers R. L., J. Amer. Statist. Assoc. 88 pp 268– (1993) · Zbl 0795.62007 · doi:10.2307/2290722
[4] Chen J., Biometrics 60 pp 116– (2004) · Zbl 1130.62390 · doi:10.1111/j.0006-341X.2004.00162.x
[5] Chu C.-K., Statist. Sci. 6 pp 404– (1991) · Zbl 0955.62561 · doi:10.1214/ss/1177011586
[6] Cochran W. G., Sampling Techniques., 3. ed. (1997)
[7] A Harvest Strategy Compliant with the Precautionary Approach (2006)
[8] Di Marzioa M., J. Statist. Plann. Inference 138 pp 2483– (2007) · Zbl 1182.62091 · doi:10.1016/j.jspi.2007.10.005
[9] Doubleday W. G., NAFO Sci. Coun. Studies 2 pp 7– (1981)
[10] Dwyer K. S., An assessment of American plaice in NAFO Div. 3LNO (2007)
[11] Eubank R. L., Nonparametric Regression and Spline Smoothing., 2. ed. (1999) · Zbl 0936.62044
[12] Fan J., J. Amer. Statist. Assoc. 87 pp 998– (1992)
[13] Fan J., Ann. Statist. 21 pp 196– (1993) · Zbl 0773.62029 · doi:10.1214/aos/1176349022
[14] Firth D., J. Roy. Statist. Soc. Ser. B 60 pp 3– (1998) · Zbl 0910.62009 · doi:10.1111/1467-9868.00105
[15] Fuller W. A., Surv. Method 28 pp 5– (2002)
[16] Gasser T., Smoothing Techniques for Curve Estimation pp 23– (1979) · doi:10.1007/BFb0098489
[17] Gunderson D. R., Surveys of Fisheries Resources (1993)
[18] Hall P., Ann. Statist. 25 pp 756– (1997) · Zbl 0874.62037 · doi:10.1214/aos/1031833672
[19] Hall P., J. Amer. Statist. Assoc. 92 pp 466– (1997)
[20] Härdle W., Applied Nonparametric Regression (1990) · Zbl 0714.62030 · doi:10.1017/CCOL0521382483
[21] Hart J. D., J. Amer. Statist. Assoc. 87 pp 1018– (1992)
[22] Hastie T., Statist. Sci. 8 pp 120– (1993) · doi:10.1214/ss/1177011002
[23] Jones M. C., J. Amer. Statist. Assoc. 89 pp 825– (1994)
[24] Jones M. C., Biometrika 82 pp 327– (1995) · Zbl 0823.62033 · doi:10.1093/biomet/82.2.327
[25] Leung D. H.-Y., Ann. Statist. 33 pp 2291– (2005) · Zbl 1086.62055 · doi:10.1214/009053605000000499
[26] Mack Y. P., Sankhyā Ser. A 51 pp 59– (1989)
[27] Mammen E., Biometrika 84 pp 765– (1997) · Zbl 1090.62530 · doi:10.1093/biomet/84.4.765
[28] Montanari G. E., J. Amer. Statist. Assoc. 100 pp 1429– (2005) · Zbl 1117.62403 · doi:10.1198/016214505000000141
[29] Müller H.-G., J. Multivariate Anal. 46 pp 237– (1993) · Zbl 0778.62035 · doi:10.1006/jmva.1993.1059
[30] Müller H.-G., Statist. Probab. Lett. 36 pp 161– (1997) · Zbl 0893.62026 · doi:10.1016/S0167-7152(97)00059-X
[31] Nadaraya E. A., Theory Probab. Appl. 9 pp 141– (1964) · doi:10.1137/1109020
[32] Opsomer J. D., J. Nonparametr. Stat. 17 pp 593– (2005) · Zbl 1065.62071 · doi:10.1080/10485250500054642
[33] Opsomer J. D., J. Amer. Statist. Assoc. 102 pp 400– (2007) · Zbl 1134.62389 · doi:10.1198/016214506000001491
[34] Park B. U., Statist. Probab. Lett. 32 pp 279– (1997) · Zbl 0886.62045 · doi:10.1016/S0167-7152(96)00085-5
[35] Park B. U., Scand. J. Statist. 24 pp 145– (1997) · Zbl 0881.62048 · doi:10.1111/1467-9469.00055
[36] Quinn T. J., Quantitative Fish Dynamics (1999)
[37] Rodríguez J. G., A probabilistic nonparametric estimator (2005)
[38] Särndal C., Model Assisted Survey Sampling (1992) · Zbl 0742.62008 · doi:10.1007/978-1-4612-4378-6
[39] Seifert B., J. Amer. Statist. Assoc. 91 pp 267– (1996) · doi:10.1080/01621459.1996.10476685
[40] Shelton P. A., Limits to overfishing: Reference points in the context of the Canadian perspective on the precautionary approach (2002)
[41] Silverman B. W., Density Estimation for Statistics and Data Analysis (1986) · Zbl 0617.62042 · doi:10.1007/978-1-4899-3324-9
[42] Smith S. J., Can. J. Fish. Aquat. Sci. 47 pp 894– (1990) · doi:10.1139/f90-103
[43] Watson G. S., Sankhyā Ser. A 26 pp 359– (1964)
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.