New imputation methods for missing data using quantiles

The problem of missing values commonly arises in data sets, and imputation is usually employed to compensate for non-response. We propose a novel imputation method based on quantiles, which can be implemented with or without the presence of auxiliary information. The proposed method is extended to unequal sampling designs and non-uniform response mechanisms. Iterative algorithms to compute the proposed imputation methods are presented. Monte Carlo simulations are conducted to assess the performance of the proposed imputation methods with respect to alternative imputation methods. Simulation results indicate that the proposed methods perform competitively in terms of relative bias and relative root mean square error.

[1]  M. Healy,et al.  Missing Values in Experiments Analysed on Automatic Computers , 1956 .

[2]  Rolf-Dieter Reiss.  Sampling from Finite Populations , 1993 .

[3]  R. Chambers,et al.  Estimating distribution functions from survey data , 1986 .

[4]  J. Rao,et al.  On estimating distribution functions and quantiles from survey data using auxiliary information , 1990 .

[5]  Chris J. Skinner,et al.  Estimating distribution functions with auxiliary information using poststratification , 1995 .

[6]  New York Dover,et al.  ON THE CONVERGENCE PROPERTIES OF THE EM ALGORITHM , 1983 .

[7]  Donald B. Rubin,et al.  Multiple imputations in sample surveys , 1978 .

[8]  G. Kalton,et al.  The treatment of missing survey data , 1986 .

[9]  G. Kalton,et al.  Handling missing data in survey research , 1996, Statistical methods in medical research.

[10]  J. Rao.  On Variance Estimation with Imputed Survey Data , 1996 .

[11]  M. Rueda,et al.  Estimation of the distribution function with calibration methods , 2007 .

[12]  T. Valdés,et al.  Global dynamics of a system governing an algorithm for regression with censored and non-censored data under general errors , 2004 .

[13]  J. Shao,et al.  Jackknife variance estimation with survey data under hot deck imputation , 1992 .

[14]  Donald B. Rubin,et al.  On Variance Estimation With Imputed Survey Data: Comment , 1996 .

[15]  J. Rao,et al.  Adjusted jackknife for imputation under unequal probability sampling without replacement , 2006 .

[16]  D. Rubin.  Multiple Imputation After 18+ Years , 1996 .

[17]  Sarjinder Singh,et al.  Advanced Sampling Theory with Applications : How Michael ' selected' Amy Volume I , 2003 .

[18]  D. Rubin,et al.  Statistical Analysis with Missing Data. , 1989 .

[19]  M. Ageel.  A novel means of estimating quantiles for 2-parameter Weibull distribution under the right random censoring model , 2002 .

[20]  Richard Valliant,et al.  Poststratification and Conditional Variance Estimation , 1993 .

[21]  J. Shao,et al.  Nearest Neighbor Imputation for Survey Data , 2000 .

[22]  Russ B. Altman,et al.  Missing value estimation methods for DNA microarrays , 2001, Bioinform..

[23]  Ki-Yeol Kim,et al.  Reuse of imputed data in microarray analysis increases imputation efficiency , 2004, BMC Bioinformatics.

[24]  Carl-Erik Särndal,et al.  Model Assisted Survey Sampling , 1997 .

[25]  W J Krzanowski,et al.  Missing value imputation in multivariate data using the singular value decomposition of a matrix , 1988 .