Semiparametric efficiency bounds for seemingly unrelated conditional moment restrictions

Computing all roots of the likelihood equations of seemingly unrelated regressions

Seemingly unrelated regressions are statistical regression models based on the Gaussian distribution. They are popular in econometrics but also arise in graphical modeling of multivariate dependencies. In maximum likelihood estimation, the parameters of the model are estimated by maximizing the likelihood function, which maps the parameters to the likelihood of observing the given data. By transforming this optimization problem into a polynomial optimization problem, it was recently shown that the likelihood function of a simple bivariate seemingly unrelated regressions model may have several …

Robust Inference for Seemingly Unrelated Regression Models

Seemingly unrelated regression models generalize linear regression models by considering multiple regression equations that are linked by contemporaneously correlated disturbances. Robust inference for seemingly unrelated regression models is considered. MM-estimators are introduced to obtain estimators that have both a high breakdown point and a high normal efficiency. A fast and robust bootstrap procedure is developed to obtain robust inference for these estimators. Confidence intervals for the model parameters as well as hypothesis tests for linear restrictions of the regression coefficient…

Using mixtures in seemingly unrelated linear regression models with non-normal errors

Seemingly unrelated linear regression models are introduced in which the distribution of the errors is a finite mixture of Gaussian components. Identifiability conditions are provided. The score vector and the Hessian matrix are derived. Parameter estimation is performed using the maximum likelihood method and an Expectation-Maximisation algorithm is developed. The usefulness of the proposed methods and a numerical evaluation of their properties are illustrated through the analysis of a real dataset.

Average Density Estimators: Efficiency and Bootstrap Consistency

This paper highlights a tension between semiparametric efficiency and bootstrap consistency in the context of a canonical semiparametric estimation problem, namely the problem of estimating the average density. It is shown that although simple plug-in estimators suffer from bias problems preventing them from achieving semiparametric efficiency under minimal smoothness conditions, the nonparametric bootstrap automatically corrects for this bias and that, as a result, these seemingly inferior estimators achieve bootstrap consistency under minimal smoothness conditions. In contrast, several "debi…

Seemingly unrelated and fixed-effect panel regressions: collinearity and singular dispersion

The paper discusses identification conditions, representations and relations of generalized least squares estimators of regression parameters in multivariate linear regression models such as seemingly unrelated and fixed effect panel models. Results are presented on identification for unrestricted dispersion structure and general heteroskedasticity and cross-equation dependence, considering explicit and implicit restrictions, singularity of the dispersion and multicollinearity in the design matrix.

对称定位问题：效率与鲁棒性的协奏曲

The Symmetric Location Problem: a Song of Efficiency and Robustness

本文通过半参数统计框架解决对称定位问题，在存在无限维 nuisance 参数时实现有限维参数的估计，兼顾统计效率与分布自由鲁棒性。