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Choice-based samples:A non-parametric approach

Authors
Journal
Journal of Econometrics
0304-4076
Publisher
Elsevier
Publication Date
Volume
32
Issue
1
Identifiers
DOI: 10.1016/0304-4076(86)90014-x
Disciplines
  • Mathematics

Abstract

Abstract In this paper we discuss a non-parametric approach to choice-based grouping. Specifically we derive the non-parametric maximum likelihood estimate for F( x, z), the joint distribution of ( x, z) = (choice, attributes), from choice-based samples. This estimate can be thought of as the bias-corrected empirical distribution of (choice, attributes) derived from our biased data. Having F at hand we investigate two alternative approaches for estimating the conditional probability P(choice∣attributes). The first is based on smoothing a non-parametric estimate derived from F( x, z). In the second, we fit a parametric family [ f θ ( x, z); θ∈Θ] to the bias-corrected empirical distribution function. The asymptotic behavior of this semi-parametric estimate, as well as numerical examples that demonstrate both methods, are given.

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