arXiv 26 Apr 2025 · Statistics — Methodology
arXiv:2504.19018 · PDF · DOI · OpenAlex · Extracted main text
This paper addresses the longstanding challenge of analyzing the mean squared error (MSE) of ridge-type estimators in nonlinear models, including duration, Poisson, and multinomial choice models, where theoretical results have been scarce. Using a finite-sample approximation technique from the econometrics literature, we derive new results showing that the generalized ridge maximum likelihood estimator (MLE) with a sufficiently small penalty achieves lower finite-sample MSE for both estimation and prediction than the conventional MLE, regardless of whether the hypotheses incorporated in the penalty are valid. A key theoretical contribution is to demonstrate that generalized ridge estimators generate a variance-bias trade-off in the first-order MSE of nonlinear likelihood-based models -- a feature absent for the conventional MLE -- which enables ridge-type estimators to attain smaller MSE when the penalty is properly selected. Extensive simulations and an empirical application to the estimation of marginal mean and quantile treatment effects further confirm the superior performance and practical relevance of the proposed method.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Rilstone, Paul and Srivastava, Virendra K and Ullah, Aman (1996) The second-order bias and mean squared error of nonlinear estimators | 1.000 | 6 | 3 | 100% |
| 2 | Le Cessie, S. and Van Houwelingen, J. C (1992) Ridge estimators in logistic regression | 0.843 | 3 | 3 | 100% |
| 3 | Andersen, Per Kragh and Bentzon, Michael Weis and Klein, John P (1996) Estimating the survival function in the proportional hazards regression model: a study of the small sample size properties | 0.644 | 2 | 2 | 100% |
| 4 | Blagus, Rok and Goeman, Jelle J (2020) Mean squared error of ridge estimators in logistic regression | 0.644 | 2 | 2 | 100% |
| 5 | Cattaneo, Matias D (2010) Efficient semiparametric estimation of multi-valued treatment effects under ignorability | 0.644 | 2 | 2 | 100% |
| 6 | de Jong, Valentijn MT and Eijkemans, Marinus JC and van Calster, Ben… (2019) Sample size considerations and predictive performance of multinomial logistic prediction models | 0.644 | 2 | 2 | 100% |
| 7 | Lambert, Diane (1992) Zero-inflated Poisson regression, with an application to defects in manufacturing | 0.644 | 2 | 2 | 100% |
| 8 | Newey, Whitney K and McFadden, Daniel (1994) Large sample estimation and hypothesis testing | 0.644 | 2 | 2 | 100% |
| 9 | Stein, Charles M (1981) Estimation of the mean of a multivariate normal distribution | 0.644 | 2 | 2 | 100% |
| 10 | Abadie, Alberto and Kasy, Maximilian (2019) Choosing among regularized estimators in empirical economics: The risk of machine learning | 0.405 | 1 | 1 | 100% |
Showing the top 10 of 27 scored citations.