The study focuses on the
imputation for the longitudinal survey data which often has nonignorable
nonrespondents. Local linear regression is used to impute the missing values
and then the estimation of the time-dependent finite populations means. The asymptotic
properties (unbiasedness and consistency) of the proposed estimator are
investigated. Comparisons between different parametric and nonparametric
estimators are performed based on the bootstrap standard deviation, mean square
error and percentage relative bias. A simulation study is carried out to
determine the best performing estimator of the time-dependent finite population
means. The simulation results show that local linear regression estimator
yields good properties.
References
[1]
Dorfman, A.H. (1992) Nonparametric Regression for Estimating Totals in Finite Population. Proceeding Section of Survey Methodology. American Statistical Association Alexandria, VA, 622-625.
[2]
Xu, J., Shao, J., Palta, M. and Wang. L. (2008) Imputation for Nonmonotone Last-Value-Dependent Nonrespondents in Longitudinal Surveys. Survey Methodology, 34, 153-162.
[3]
Nadaraya, E.A. (1964) On Estimating Regression. Theory of Probability and Its Applications, 9, 141-142.
[4]
Watson, G.S. (1964) Smooth Regression Analysis. Sankhy: The Indian Journal of Statistics, 26, 359-372.
[5]
Hastie, T.J. and Loader, C. (1993) Local Regression: Automatic Kernel Carpentry (with Discussion). Statistical Science, 8, 120-143.
Cai, Z. (2001) Weighted Nadaraya-Watson Regression Estimation. Statistics & Probability Letters, 51, 307-318.
[8]
Fan, J. and Gijbels, I. (1996) Local Polynomial Modelling and Its Applications. Chapman and Hall, London.
[9]
Stone, C.J. (1977) Consistent Nonparametric Regression. The Annals of Statistics, 3, 595-620.
[10]
Rubin, D.B. (1987) Multiple Imputation for Nonresponse in Surveys. John Wiley & Sons, Inc., New York. https://doi.org/10.1002/9780470316696
[11]
Paik, M.C. (1997) The Generalized Estimating Equation Approach When Data Are Not Missing Completely at Random. Journal of American Statistical Association, 92, 1320-1329.
[12]
Cheng, P.E. (1994) Nonparametric Estimation of Mean Functionals with Data Missing at Random. Journal of the American Statistical Association, 89, 81-87.
[13]
Shao, J., Klein, M. and Xu, J. (2012) Imputation for Nonmonotone Nonresponse in the Survey of Industrial Research and Development. Survey Methodology, 38, 143-155.
[14]
Masry, E. (1996) Multivariate Local Polynomial Regression for Time Series. Uniform Strong Consistence and Rates. Journal of Time Series Analysis, 17, 571-599.
