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非线性指数族回归模型的极大似然与拟似然AI 解读

Linear and nonlinear exponential family and quasi-likelihood regression models form a class of models with a structure that invites using one algorithmic framework to compute parameter estimates and regression diagnostics. This framework extends our work on nonlinear least squares; it includes iteratively reweighted least squares but also encompasses secant updates for part of the Hessian matrix of the likelihood or quasi-likelihood function along with tests for when to use…

Janson is to be commended for elements of his study. His insistence on using a priori knowledge of the system that he is modeling and his critical examination of the data are two demonstrably worthwhile steps that, although well known to many, are all too often ignored by many others. This article thus provides important reminders, and applause is in order. Unfortunately, there are also substantive grounds for criticism. First, the author does not fully discover important…

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使用加权工具变量的联立方程模型稳健估计AI 解读

IN THIS PAPER we present a weighted-instrumental-variables estimator that is resistant2 to heavy-tailed errors, aberrant data in either the endogenous or exogenous variables, and certain other model failures. The estimator is analogous to the weighted-least-squares approach to robustness proposed by Krasker and Welsch [21] for ordinary regression. We will discuss the theory that motivated this estimator, derive some of its properties, describe our computational algorithm,…

高效的有界影响回归估计AI 解读

The least squares estimator for β in the classical linear regression model is strongly efficient under certain conditions. However, in the presence of heavy-tailed errors and/or anomalous data, the least squares efficiency can be markedly reduced. In this article we propose an estimator that limits the influence of any small subset of the data and show that it satisfies a first-order condition for strong efficiency subject to the constraint. We then show that the estimator…

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This paper considers the effect of aggregation on the variance of parameter estimates for a linear regression model with random coefficients and an additive error term. Aggregate and microvariances are compared and measures of relative efficiency are introduced. Necessary conditions for efficient aggregation procedures are obtained from the Theil aggregation weights and from measures of synchronization related to the work of Grunfeld and Griliches.