msvymean: Robust M-estimation of the mean for complex samples In rhte: Robust Horvitz-Thompson Estimation

Description

msvymean computes robust Horvitz-Thompson estimates of the mean or robust weighted mean estimates for complex samples based on using M-estimation.

Usage

 1 2 msvymean(y, design, k, type = "rht", na.rm = FALSE, control = rht.control(...), ...)

Arguments

 y a formula object (only one variable) design a survey.design object k robustness tuning constant type either "rht" for robust Horvitz-Thompson estimator (default), or "rwm" for robust weighted mean estimator na.rm should cases with missing values be dropped? (default FALSE) control control object; see rht.control ... (additional specifications which are delivered to rht.control)

Details

msvymean performs (inverse probability-) weighted M-estimation (Huber psi-function or asymmetric Huber psi-function; asymmetric=TRUE). The msvymean methods supports the following two methods (depending on the underlying sampling design)

• robust Horvitz-Thompson estimator (type="rht"),

• robust weighted mean estimator (type="rwm").

If y is positively correlated with the inclusion probabilities, a "rht" type estimator should be used, and "rwm" otherwise. The initial value is a weighted median or a ratio of weighted medians. You may set steps equal to one in order to get a one-step estimator. Variance estimates are computed as first-order linearization using the design-based-estimation facilities in the survey package.

msvymean allows also the estimation for domains. Use the command subset and a design subset expression instead of the original survey.design object in msvymean (see examples for more details).

Users may set exact=TRUE to compute an "exact" linearization-variance estimate, which takes into account that the MAD has been used as preliminary scale estimate. However, the estimates may become very unstable.

Value

Object of class "svystat.rob".

The following (S3) methods are defined for objects of the class "svystat.rob":

• print method,

• summary method,

• coef method,

• vcov method,

• residuals method,

• robweights method.

Author(s)

Beat Hulliger and Tobias Schoch

References

Hulliger, B. (1995): Outlier robust Horvitz-Thompson estimators, Survey Methodology 21 (1), pp. 79-87.

Hulliger, B. (1999): Simple and robust estimators for sampling, Proceedings of the Survey Research Methods Section, American Statistical Association, 1999, pp. 54-63.

Hulliger, B. and T. Schoch (2011): Elementary robust estimators. In: Robust methodology for Laeken indicators: AMELI Deliverable D4.2, ed. by B. Hulliger, A. Alfons, P. Filzmoser, A. Meraner, T. Schoch and M. Templ. AMELI Project.