Non response weighting adjustment using response probability estimated via kernel regression methods

It is well known that unit nonresponse is a common problem in sample surveys. It has the potential to bias significantly the results of the survey and to prevent valid inference. Weighing adjustment is a method usually applied to compensate for unit nonresponse. According to the theory for two-phase sampling, for which the set of respondents is treated as a second phase sampling from the original sample, weighting adjustment operates by increasing the sampling weights of the respondents in the sample, multiplying them by the inverse of the response probabilities. Since the true response probabilities are usually unknown, estimated response probabilities are used to correct for nonresponse bias. Typically, response probabilities are estimated by fitting parametric models relating response occurrences and auxiliary variables. An alternative solution is the estimation of them by nonparametric methods which require only that the response probabilities be related to the auxiliary variables by a smooth but unspecified function. This possibility was first proposed by Giommi (1984) then considered by Niyonsenga (1994, 1997) and recently further investigated by Da Silva and Opsomer (2006, 2008) who derived some new important theoretical properties of the non-parametrically weighting adjusted estimators. The aim of this paper is to investigate, via simulation experiments, the small-sample properties of kernel regression estimation of the response probabilities when auxiliary information consists in multiple covariates that are both categorical and continuous.