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Selection-bias-adjusted inference for the bivariate normal distribution under soft-threshold sampling

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  • Joseph B. Lang

    (University of Iowa)

Abstract

The problem of estimating parameters and predicting outcomes of a bivariate Normal distribution is more challenging when, owing to data-dependent selection (or missingness or dropout), the available data are not a representative sample of bivariate realizations. This problem is addressed using an observation model that is induced by a combination of a multivariate Normal “science” model and a realistic “soft-threshold selection” model with unknown truncation point. This observation model, which is expressed using an intuitive selection subset notation, is a generalization of existing “hard-threshold” models. It affords simple-to-compute selection-bias-adjusted estimates of both the regression (conditional mean) parameters and the bivariate correlation. In addition, a simple bootstrap approach for computing both confidence and prediction intervals in the soft-threshold selection setting is described. Simulation results are promising. To motivate this research, two illustrative examples describe a setting where selection bias is an issue of concern.

Suggested Citation

  • Joseph B. Lang, 2025. "Selection-bias-adjusted inference for the bivariate normal distribution under soft-threshold sampling," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 77(4), pages 597-625, August.
    • Handle: RePEc:spr:aistmt:v:77:y:2025:i:4:d:10.1007_s10463-025-00925-0
    DOI: 10.1007/s10463-025-00925-0
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