Linear programming-based estimators in simple linear regression

被引:6
作者
Preve, Daniel [1 ,2 ]
Medeiros, Marcelo C. [3 ]
机构
[1] Uppsala Univ, Dept Stat, S-75120 Uppsala, Sweden
[2] Singapore Management Univ, Sch Econ, S-75120 Uppsala, Sweden
[3] Pontifical Catholic Univ Rio de Janeiro, Rio De Janeiro, Brazil
关键词
Linear regression; Endogeneity; Linear programming estimator; Quasi-maximum likelihood estimator; Exact distribution; POSITIVE INNOVATIONS; AUTOREGRESSION;
D O I
10.1016/j.jeconom.2011.05.011
中图分类号
F [经济];
学科分类号
02 ;
摘要
In this paper we introduce a linear programming estimator (LPE) for the slope parameter in a constrained linear regression model with a single regressor. The LPE is interesting because it can be superconsistent in the presence of an endogenous regressor and, hence, preferable to the ordinary least squares estimator (LSE). Two different cases are considered as we investigate the statistical properties of the LPE. In the first case, the regressor is assumed to be fixed in repeated samples. In the second, the regressor is stochastic and potentially endogenous. For both cases the strong consistency and exact finite-sample distribution of the LPE is established. Conditions under which the LPE is consistent in the presence of serially correlated, heteroskedastic errors are also given. Finally, we describe how the LPE can be extended to the case with multiple regressors and conjecture that the extended estimator is consistent under conditions analogous to the ones given herein. Finite-sample properties of the LPE and extended LPE in comparison to the LSE and instrumental variable estimator (IVE) are investigated in a simulation study. One advantage of the LPE is that it does not require an instrument. (C) 2011 Elsevier B.V. All rights reserved.
引用
收藏
页码:128 / 136
页数:9
相关论文
共 8 条
[1]   On the distribution of the quotient of two chance variables [J].
Curtiss, JH .
ANNALS OF MATHEMATICAL STATISTICS, 1941, 12 :409-421
[2]   Nonlinear autoregression with positive innovations [J].
Datta, S ;
Mathew, G ;
McCormick, WP .
AUSTRALIAN & NEW ZEALAND JOURNAL OF STATISTICS, 1998, 40 (02) :229-239
[3]   Bootstrap inference for a first-order autoregression with positive innovations [J].
Datta, S ;
McCormick, WP .
JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION, 1995, 90 (432) :1289-1300
[4]   ESTIMATION FOR 1ST-ORDER AUTOREGRESSIVE PROCESSES WITH POSITIVE OR BOUNDED INNOVATIONS [J].
DAVIS, RA ;
MCCORMICK, WP .
STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 1989, 31 (02) :237-250
[5]   LIMIT DISTRIBUTIONS FOR LINEAR-PROGRAMMING TIME-SERIES ESTIMATORS [J].
FEIGIN, PD ;
RESNICK, SI .
STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 1994, 51 (01) :135-165
[6]  
FEIGIN PD, 1996, ANN APPL PROBAB, V12, P1157
[7]   Likelihood analysis of a first-order autoregressive model with exponential innovations [J].
Nielsen, B ;
Shephard, N .
JOURNAL OF TIME SERIES ANALYSIS, 2003, 24 (03) :337-344
[8]  
PREVE D, 2011, LINEAR PROGRAM UNPUB