Inference in the presence of influential units and nonresponse for functional and non-functional survey data

点击翻译按钮获取中文摘要

Nonresponse inevitably occurs in most, if not all, surveys. Essentially, survey statisticians distinguish unit nonresponse from item nonresponse. Unit nonresponse occurs when all the survey variables are missing or not enough usable information is available, whereas item nonresponse occurs when some but not all the survey variables have missing values. Weight adjustment procedures are generally used to treat unit nonresponse, whereas imputation is generally used to handle item nonresponse. The main objective when treating nonresponse is the reduction of the nonresponse bias, which occurs when respondents and nonrespondents are different with respect to the survey variables. In practice, surveys statisticians also face the problem of influential units. Influential units are correctly recorded and represent other population units similar in value. Their presence in the sample tends to make the classical estimators very unstable. Influential units occur when the distribution of the variables being collected is highly skewed or when some units have a large design weight. An estimator is said to be robust if it is not too sensitive to the presence of influential units. Robust estimators are biased but their mean square error is smaller than that of non-robust estimators. In some situations, the target parameter is not a mean real value but a mean function. For example, one may be interested in estimating the mean electricity consumption curve of a large number of consumers in a fixed time interval. We propose to study the problem of estimating the mean curve in the presence of missing data. We intend to establish the theoretical properties of estimators based on observed data and imputed data by means of nearest-neighbour imputation. Also, some units may be highly influential, which can make both the estimator of the mean curve and its variance very unstable. We plan to develop robust estimation procedures, study their theoretical properties and apply the proposed methods to real data. Robust small area estimation has received considerable attention in recent years. Most research has focussed on continuous characteristics of interest. Several robust versions of the empirical best linear unbiased predictor based on linear mixed models (LMM) have been proposed in the literature. In practice, many variables are categorical rather than continuous. As a result, methods based on LMMs are not suited. The objective is to propose a unified framework for robust small area estimation based on generalized LMMs so that robust predictors can be readily obtained for any type of variable. In practice, the target parameter may be a complex parameter; e.g., a quantile. Doubly robust procedures have been widely studied in the context of missing data. An estimation procedure is said to be doubly robust if it remains consistent if either the nonresponse model or the imputation model is correctly specified. So far, the literature has focussed on estimating a population mean. We plan to develop doubly protected estimation procedures for complex parameters and establish their theoretical properties. Finally, we propose to extend a recent concept called multiple robustness to finite population sampling. In practice, multiple nonresponse models and multiple imputation models may be fitted, each involving different subsets of covariates and possibly different link functions. An estimator is said to be multiply robust if it is consistent if any one of those multiple models, for either the propensity score or the characteristic of interest, is correctly specified. We also plan to develop multiply robust variance estimators that remain consistent for the true variance if any one of those multiple models is correct.