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Gaussian Transforms Modeling and the Estimation of Distributional Regression Functions

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  • Richard Spady
  • Sami Stouli

Abstract

We propose flexible Gaussian representations for conditional cumulative distribution functions and give a concave likelihood criterion for their estimation. Optimal representations satisfy the monotonicity property of conditional cumulative distribution functions, including in finite samples and under general misspecification. We use these representations to provide a unified framework for the flexible Maximum Likelihood estimation of conditional density, cumulative distribution, and quantile functions at parametric rate. Our formulation yields substantial simplifications and finite sample improvements over related methods. An empirical application to the gender wage gap in the United States illustrates our framework.

Suggested Citation

  • Richard Spady & Sami Stouli, 2020. "Gaussian Transforms Modeling and the Estimation of Distributional Regression Functions," Papers 2011.06416, arXiv.org, revised Apr 2025.
    • Handle: RePEc:arx:papers:2011.06416
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    1. Whitney K. Newey & Sami Stouli, 2018. "Identification of Treatment Effects under Limited Exogenous Variation," Papers 1811.09837, arXiv.org, revised Jan 2025.

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