Dealing with nonresponse in complex surveys

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In complex and large scale surveys, the presence of missing values in the collected data sets is often inevitable. Nonresponse generally introduces a bias and an increase in the variance of the estimator. Hence, the treatment of nonresponse is necessary to produce reliable analysis. The estimators and the estimation of their precision then need to be adapted to account for the treatment. This research program concerns the development of methods and tools to deal with nonresponse in complex surveys and large data sets. In a first part of the research program, the estimation methods of the variance of estimated parameters will be investigated. Theoretical properties of variance estimators will be established. Also, the estimation methods that have been recently developed will be overviewed and compared. There is a need to unravel the recent developments in variance estimation to facilitate the work of practitioners. In a second part of the research program, new imputation methods will be developed to deal with multivariate nonresponse, when several variables of a data set are subject to missing values. A donor imputation method will be developed and the use of modern statistical learning techniques in imputation methods will be investigated. In survey sampling, few treatments have been developed for multivariate nonresponse. As it becomes easier to collect large scale data, the progresses in the treatment of multivariate nonresponse are important to produce reliable studies. In a last part of the research program, nonresponse notions will be used to deal with non-representative samples. The accessibility to different sources of data brings new challenges in survey sampling. Coverage errors resulting from the different sources of information will be investigated. Methods to reduce the coverage biases will be proposed. It will be possible to use these methods in important applications such as in forest inventories.