Outliers and influential observations can have an important effect on work with estimation and inference from establishment survey data. Practical development and implementation of methods to identify and account for outliers and influential observations in complex survey data

Outliers and influential observations can have an important effect on work with estimation and inference from establishment survey data. Practical development and implementation of methods to identify and account for outliers and influential observations in complex survey data require an agency to balance several factors, including: (i) the mathematical statistics properties of detection methods and prospective estimators; (ii) a range of objective functions that include traditional measures like variance and mean squared error, as well as other functions tuned to reduction of risks associated with very rare extreme observations and estimates; (iii) information available on the underlying populations of interest; (iv) cost structures; and (v) important constraints on production systems and modification thereof. This in turn has three practical implications for research on outlier methods for establishment surveys. First, the predominant outlier literature in mathematical statistics has focused primarily on area (i). Consequently, it is important to expand our mathematical structure and objective functions to account for factors (ii)-(v). Second, methods that may appear to be inefficient or inadmissible under evaluation criteria in the traditional literature may warrant serious consideration under the more complex structure defined by (i)-(v). Third, the structure defined by (i)-(v) presents an opportunity to enrich and deepen the current mathematical statistics literature on outliers. In keeping with previous requests from FESAC, this paper focuses primarily on research that is at various stages of development, rather than on finalized research results.