What Actuaries Should Know About Nonparametric Regression With Missing Data

By Sam Efromovich

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To predict one variable, called the response, given another variable, called the predictor, nonparametric regression solves this problem without any assumption about the relationship between these two random variables. Traditional data, used in nonparametric regression, is a sample from the two variables; that is, it is a matrix with two complete columns. In practical applications some observations in that matrix may be missed, and what can be done in this case is the subject of this paper. Three possible scenarios are considered. First, if the probability of missing an observation depends on its value, then no consistent estimation is possible. Second, if all predictors are available and the probability of missing the response depends on value of the predictor, then a nonparametric regression, based on complete cases, is optimal. Third, if all responses are available and the probability of missing the predictor depends on value of the response, then a special estimation procedure, based on all available observations, is optimal. The results are illustrated via examples, and possible extensions are discussed.

Keywords: Adaptation, nonparametric estimation, prediction, regression, probability density


Efromovich, Sam, "What Actuaries Should Know About Nonparametric Regression With Missing Data," Variance 10:1, 2016, pp. 145-165.

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Variance (ISSN 1940-6452) is a peer-reviewed journal published by the Casualty Actuarial Society to disseminate work of interest to casualty actuaries worldwide. The focus of Variance is original practical and theoretical research in casualty actuarial science. Significant survey or similar articles are also considered for publication. Membership in the Casualty Actuarial Society is not a prerequisite for submitting papers to the journal and submissions by non-CAS members is encouraged.