×

zbMATH — the first resource for mathematics

Nonparametric additive model-assisted estimation for survey data. (English) Zbl 1216.62064
Summary: An additive model-assisted nonparametric method is investigated to estimate the finite population totals of massive survey data with the aid of auxiliary information. A class of estimators is proposed to improve the precision of the well known Horvitz-Thompson estimators by combining the spline and local polynomial smoothing methods. These estimators are calibrated, asymptotically design-unbiased, consistent, normal and robust in the sense of asymptotically attaining the Godambe-Joshi lower bound to the anticipated variance. A consistent model selection procedure is further developed to select the significant auxiliary variables. The proposed method is sufficiently fast to analyze large survey data of high dimension within seconds. The performance of the proposed method is assessed empirically via simulation studies.

MSC:
62G08 Nonparametric regression and quantile regression
62D05 Sampling theory, sample surveys
62H12 Estimation in multivariate analysis
62G05 Nonparametric estimation
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Breidt, F.J.; Claeskens, G.; Opsomer, J.D., Model-assisted estimation for complex surveys using penalised splines, Biometrika, 92, 831-846, (2005) · Zbl 1151.62306
[2] Breidt, F.J.; Opsomer, J.D., Local polynomial regression estimators in survey sampling, Ann. statist., 28, 1026-1053, (2000) · Zbl 1105.62302
[3] Breidt, F.J.; Opsomer, J.D.; Johnson, A.A.; Ranalli, M.G., Semiparametric model-assisted estimation for natural resource surveys, Surv. methodol., 33, 35-44, (2007)
[4] Chambers, R.L., Robust case-weighting for multipurpose establishment surveys, J. official statist., 12, 3-32, (1996)
[5] Chambers, R.L.; Dorfman, A.H.; Wang, S., Limited information likelihood analysis of survey data, J. R. stat. soc. ser. B, 60, 397-411, (1998) · Zbl 0918.62006
[6] Chambers, R.L.; Dorfman, A.H.; Wehrly, T.E., Bias robust estimation in finite populations using nonparametric calibration, J. amer. statist. assoc., 88, 268-277, (1993) · Zbl 0795.62007
[7] Deville, J.C.; Särndal, C.E., Calibration estimators in survey sampling, J. amer. statist. assoc., 87, 376-382, (1992) · Zbl 0760.62010
[8] Dorfman, A.H., Nonparametric regression for estimating totals in finite populations, (), 622-625
[9] Dorfman, A.H.; Hall, P., Estimators of the finite population distribution function using nonparametric regression, Ann. statist., 21, 1452-1475, (1993) · Zbl 0798.62017
[10] Fan, J.; Gijbels, I., Local polynomial modelling, its applications, (1996), Chapman, Hall London · Zbl 0873.62037
[11] Fan, Y.; Li, Q., A kernel-based method for estimating additive partially linear models, Statist. sinica, 13, 739-762, (2003) · Zbl 1028.62023
[12] Härdle, W., Applied nonparametric regression, (1990), Cambridge University Press Cambridge · Zbl 0714.62030
[13] Hastie, T.J.; Tibshirani, R.J., Generalized additive models, (1990), Chapman, Hall London · Zbl 0747.62061
[14] Huang, J.Z.; Yang, L., Identification of nonlinear additive autoregression models, J. R. stat. soc. ser. B, 66, 463-477, (2004) · Zbl 1062.62185
[15] Kim, J.K., Calibration estimation using empirical likelihood in survey sampling, Statist. sinica, 19, 145-158, (2009) · Zbl 1153.62006
[16] Linton, O.B.; Nielsen, J.P., A kernel method of estimating structured nonparametric regression based on marginal integration, Biometrika, 82, 93-101, (1995) · Zbl 0823.62036
[17] Mammen, E.; Linton, O.; Nielsen, J., The existence, asymptotic properties of a backfitting projection algorithm under weak conditions, Ann. statist., 27, 1443-1490, (1999) · Zbl 0986.62028
[18] Martins-Filho, C.; Yang, K., Finite sample performance of kernel-based regression methods for non-parametric additive models under common bandwidth selection criterion, J. nonparametr. stat., 19, 23-62, (2007) · Zbl 1116.62041
[19] Opsomer, J.D.; Breidt, F.J.; Moisen, G.G.; Kauermann, G., Model-assisted estimation of forest resources with generalized additive models (with discussion), J. amer. statist. assoc., 102, 400-416, (2007) · Zbl 1134.62389
[20] Särndal, C.E.; Lundström, S., Estimation in surveys with nonresponse, (2005), Wiley New York · Zbl 1079.62012
[21] Särndal, C.E.; Swensson, B.; Wretman, J., The weighted residual technique for estimating the variance of the general regression estimator of the finite population total, Biometrika, 76, 527-537, (1989) · Zbl 0677.62004
[22] Särndal, C.E.; Swensson, B.; Wretman, J., Model assisted survey sampling, (1992), Springer-Verlag New York · Zbl 0742.62008
[23] Schwarz, G.E., Estimating the dimension of a model, Ann. statist., 6, 461-464, (1978) · Zbl 0379.62005
[24] Sperlich, S.; Tjøstheim, D.; Yang, L., Nonparametric estimation and testing of interaction in additive models, Econom. theory, 18, 197-251, (2002) · Zbl 1109.62310
[25] Stone, C.J., Additive regression, other nonparametric models, Ann. statist., 13, 689-705, (1985) · Zbl 0605.62065
[26] Stone, C.J., The use of polynomial splines, their tensor products in multivariate function estimation, Ann. statist., 22, 118-184, (1994) · Zbl 0827.62038
[27] Wang, L., Single-index model-assisted estimation in survey sampling, J. nonparametr. stat., 21, 487-504, (2009) · Zbl 1161.62002
[28] Wang, S.; Dorfman, A.H., A new estimator for the finite population distribution function, Biometrika, 83, 639-652, (1997) · Zbl 0865.62008
[29] L. Wang, S. Wang, Nonparametric additive model-assisted estimation for survey data, http://arxiv.org/abs/1101.0831. · Zbl 1216.62064
[30] Wang, L.; Yang, L., Spline-backfitted kernel smoothing of nonlinear additive autoregression model, Ann. statist., 35, 2474-2503, (2007) · Zbl 1129.62038
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.