The empirical saddlepoint estimator

Empirical saddlepoint approximation; Kullback-Leibler divergence criterion; method of moments; variance penalization; weak instruments; Statistics and Probability; Statistics, Probability and Uncertainty

Abstract :

[en] We define a moment-based estimator that maximizes the empirical saddlepoint (ESP) approximation of the distribution of solutions to empirical moment conditions. We call it the ESP estimator. We prove its existence, consistency and asymptotic normality, and we propose novel test statistics. We also show that the ESP estimator corresponds to the MM (method of moments) estimator shrunk toward parameter values with lower implied estimated variance, so it reduces the documented instability of existing moment-based estimators. In the case of just-identified moment conditions, which is the case we focus on, the ESP estimator is different from the MM estimator, unlike the more recent alternatives, such as the empirical-likelihood-type estimators.

Disciplines :

Mathematics

Author, co-author :

HOLCBLAT, Benjamin ; University of Luxembourg > Faculty of Law, Economics and Finance (FDEF) > Department of Finance (DF)

Sowell, Fallaw; Carnegie Mellon University, Tepper School of Business, Pittsburgh, United States

External co-authors :

yes

Language :

English

Title :

The empirical saddlepoint estimator

Publication date :

2022

Journal title :

Electronic Journal of Statistics

eISSN :

1935-7524

Publisher :

Institute of Mathematical Statistics

Volume :

Issue :

Pages :

3672 - 3694

Peer reviewed :

Peer Reviewed verified by ORBi

Funding text :

Parts of the present paper have previously circulated under the title “The Empirical Saddlepoint Likelihood Estimator Applied to Two-Step GMM” [78]. Some proofs of the present paper also borrow technical results from [40]. Helpful comments were provided by Patrick Gagliardini (discussant), Philipp Ketz (discus-sant), Eric Renault, Enrique Sentana, Aman Ullah and seminar/conference par-ticipants at Carnegie Mellon University, CFE-CMStatistics 2017, Swiss Finance Institute (EPFL and the University of Lausanne), 10th French Econometrics Conference (Paris School of Economics), at the Econometric Society European Winter Meeting 2018 (University of Naples Federico II), the University of Lux-embourg, and Collegio Carlo Alberto (University of Torino, 2nd LTI conference).

Data Set :

10.1214/21-EJS1976

Available on ORBilu :

since 22 December 2023

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