scholarly journals INFERENCE AFTER MODEL AVERAGING IN LINEAR REGRESSION MODELS

2018 ◽  
Vol 35 (4) ◽  
pp. 816-841 ◽  
Author(s):  
Xinyu Zhang ◽  
Chu-An Liu
Keyword(s):  
Asymptotic Behavior ◽  
Least Squares ◽  
Regression Models ◽  
Model Averaging ◽  
Asymptotic Distributions ◽  
Linear Regression Models ◽  
Nominal Level ◽  
Coverage Probabilities ◽  
Simulation Based ◽  
Mallows Model

This article considers the problem of inference for nested least squares averaging estimators. We study the asymptotic behavior of the Mallows model averaging estimator (MMA; Hansen, 2007) and the jackknife model averaging estimator (JMA; Hansen and Racine, 2012) under the standard asymptotics with fixed parameters setup. We find that both MMA and JMA estimators asymptotically assign zero weight to the under-fitted models, and MMA and JMA weights of just-fitted and over-fitted models are asymptotically random. Building on the asymptotic behavior of model weights, we derive the asymptotic distributions of MMA and JMA estimators and propose a simulation-based confidence interval for the least squares averaging estimator. Monte Carlo simulations show that the coverage probabilities of proposed confidence intervals achieve the nominal level.

Estimation in Dynamic Linear Regression Models with Infinite Variance Errors

1993 ◽  
Vol 9 (4) ◽  
pp. 570-588 ◽  
Author(s):  
Keith Knight
Keyword(s):  
Asymptotic Behavior ◽  
Linear Regression ◽  
Regression Model ◽  
Linear Regression Model ◽  
Regression Models ◽  
Infinite Variance ◽  
Linear Regression Models ◽  
Asymptotically Normal ◽  
Second Moments ◽  
True Values

This paper considers the asymptotic behavior of M-estimates in a dynamic linear regression model where the errors have infinite second moments but the exogenous regressors satisfy the standard assumptions. It is shown that under certain conditions, the estimates of the parameters corresponding to the exogenous regressors are asymptotically normal and converge to the true values at the standard n−½ rate.

Sequential Model Averaging for High Dimensional Linear Regression Models

2017 ◽  
Author(s):  
Wei Lan ◽  
Yingying Ma ◽  
Junlong Zhao ◽  
Hansheng Wang ◽  
Chih-Ling Tsai
Keyword(s):  
Linear Regression ◽  
Regression Models ◽  
Model Averaging ◽  
High Dimensional ◽  
Linear Regression Models ◽  
Sequential Model

On Consistency of Estimators in Simple Linear Regression Models

2002 ◽  
Vol 53 (3-4) ◽  
pp. 261-264 ◽  
Author(s):  
Anindya Roy ◽  
Thomas I. Seidman
Keyword(s):  
Linear Regression ◽  
Least Squares ◽  
Regression Models ◽  
Sufficient Condition ◽  
Simple Linear Regression ◽  
Linear Regression Models ◽  
Least Squares Estimators

We derive a property of real sequences which can be used to provide a natural sufficient condition for the consistency of the least squares estimators of slope and intercept for a simple linear regression models.

scholarly journals Bayesian Model Averaging and Weighted-Average Least Squares: Equivariance, Stability, and Numerical Issues

2011 ◽  
Vol 11 (4) ◽  
pp. 518-544 ◽  
Author(s):  
Giuseppe De Luca ◽  
Jan R. Magnus
Keyword(s):  
Least Squares ◽  
Bayesian Model ◽  
Bayesian Model Averaging ◽  
Model Averaging ◽  
Weighted Average ◽  
Simulated Data ◽  
Linear Regression Models ◽  
Explanatory Variables ◽  
Memory Problems ◽  
Regression Parameters

In this article, we describe the estimation of linear regression models with uncertainty about the choice of the explanatory variables. We introduce the Stata commands bma and wals, which implement, respectively, the exact Bayesian model-averaging estimator and the weighted-average least-squares estimator developed by Magnus, Powell, and Prüfer (2010, Journal of Econometrics 154: 139–153). Unlike standard pretest estimators that are based on some preliminary diagnostic test, these model-averaging estimators provide a coherent way of making inference on the regression parameters of interest by taking into account the uncertainty due to both the estimation and the model selection steps. Special emphasis is given to several practical issues that users are likely to face in applied work: equivariance to certain transformations of the explanatory variables, stability, accuracy, computing speed, and out-of-memory problems. Performances of our bma and wals commands are illustrated using simulated data and empirical applications from the literature on model-averaging estimation.

scholarly journals QML Estimators in Linear Regression Models with Functional Coefficient Autoregressive Processes

2010 ◽  
Vol 2010 ◽  
pp. 1-30 ◽  
Author(s):  
Hongchang Hu
Keyword(s):  
Maximum Likelihood ◽  
Linear Regression ◽  
Regression Models ◽  
Asymptotic Properties ◽  
Asymptotic Distributions ◽  
Autoregressive Processes ◽  
Linear Regression Models ◽  
Unknown Parameters ◽  
Quasi Maximum Likelihood ◽  
Functional Coefficient

This paper studies a linear regression model, whose errors are functional coefficient autoregressive processes. Firstly, the quasi-maximum likelihood (QML) estimators of some unknown parameters are given. Secondly, under general conditions, the asymptotic properties (existence, consistency, and asymptotic distributions) of the QML estimators are investigated. These results extend those of Maller (2003), White (1959), Brockwell and Davis (1987), and so on. Lastly, the validity and feasibility of the method are illuminated by a simulation example and a real example.

Sign in / Sign up

Export Citation Format

Share Document