scholarly journals Indirect Inference Estimation of Spatial Autoregressions

Econometrics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 34
Author(s):  
Yong Bao ◽  
Xiaotian Liu ◽  
Lihong Yang
Keyword(s):  
Monte Carlo ◽  
Least Squares ◽  
Asymptotic Distribution ◽  
Monte Carlo Study ◽  
Ordinary Least Squares ◽  
Indirect Inference ◽  
Finite Sample ◽  
Spatial Unit ◽  
Asymptotically Normal ◽  
Distribution Result

The ordinary least squares (OLS) estimator for spatial autoregressions may be consistent as pointed out by Lee (2002), provided that each spatial unit is influenced aggregately by a significant portion of the total units. This paper presents a unified asymptotic distribution result of the properly recentered OLS estimator and proposes a new estimator that is based on the indirect inference (II) procedure. The resulting estimator can always be used regardless of the degree of aggregate influence on each spatial unit from other units and is consistent and asymptotically normal. The new estimator does not rely on distributional assumptions and is robust to unknown heteroscedasticity. Its good finite-sample performance, in comparison with existing estimators that are also robust to heteroscedasticity, is demonstrated by a Monte Carlo study.

scholarly journals Profile Inferences on Restricted Additive Partially Linear EV Models

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Xiuli Wang
Keyword(s):  
Least Squares ◽  
Asymptotic Distribution ◽  
The Other ◽  
Finite Sample ◽  
Test Statistic ◽  
Two Stage ◽  
Chi Square ◽  
Partially Linear ◽  
Profile Least Squares ◽  
Restricted Estimator

We consider the testing problem for the parameter and restricted estimator for the nonparametric component in the additive partially linear errors-in-variables (EV) models under additional restricted condition. We propose a profile Lagrange multiplier test statistic based on modified profile least-squares method and two-stage restricted estimator for the nonparametric component. We derive two important results. One is that, without requiring the undersmoothing of the nonparametric components, the proposed test statistic is proved asymptotically to be a standard chi-square distribution under the null hypothesis and a noncentral chi-square distribution under the alternative hypothesis. These results are the same as the results derived by Wei and Wang (2012) for their adjusted test statistic. But our method does not need an adjustment and is easier to implement especially for the unknown covariance of measurement error. The other is that asymptotic distribution of proposed two-stage restricted estimator of the nonparametric component is asymptotically normal and has an oracle property in the sense that, though the other component is unknown, the estimator performs well as if it was known. Some simulation studies are carried out to illustrate relevant performances with a finite sample. The asymptotic distribution of the restricted corrected-profile least-squares estimator, which has not been considered by Wei and Wang (2012), is also investigated.

scholarly journals Quantile Regression with Clustered Data

2016 ◽  
Vol 5 (1) ◽  
pp. 1-15 ◽  
Author(s):  
Paulo M.D.C. Parente ◽  
João M.C. Santos Silva
Keyword(s):  
Quantile Regression ◽  
Covariance Matrix ◽  
Asymptotic Distribution ◽  
Simulation Study ◽  
Consistent Estimator ◽  
Regression Estimator ◽  
Finite Sample ◽  
Specification Test ◽  
Asymptotically Normal ◽  
Cluster Correlation

AbstractWe study the properties of the quantile regression estimator when data are sampled from independent and identically distributed clusters, and show that the estimator is consistent and asymptotically normal even when there is intra-cluster correlation. A consistent estimator of the covariance matrix of the asymptotic distribution is provided, and we propose a specification test capable of detecting the presence of intra-cluster correlation. A small simulation study illustrates the finite sample performance of the test and of the covariance matrix estimator.

Least absolute deviation estimates in autoregression with infinite variance

1979 ◽  
Vol 16 (1) ◽  
pp. 104-116 ◽  
Author(s):  
S. Gross ◽  
W. L. Steiger
Keyword(s):  
Monte Carlo ◽  
Convergence Rate ◽  
Least Squares ◽  
Finite Order ◽  
Monte Carlo Study ◽  
Least Squares Estimator ◽  
Infinite Variance ◽  
Least Absolute Deviation ◽  
Absolute Deviation ◽  
Strongly Consistent

We consider an L1 analogue of the least squares estimator for the parameters of stationary, finite-order autoregressions. This estimator, the least absolute deviation (LAD), is shown to be strongly consistent via a result that may have independent interest. The striking feature is that the conditions are so mild as to include processes with infinite variance, notably the stationary, finite autoregressions driven by stable increments in Lα, α > 1. Finally, sampling properties of LAD are compared to those of least squares. Together with a known convergence rate result for least squares, the Monte Carlo study provides evidence for a conjecture on the convergence rate of LAD.

Lasso-based simulation for high-dimensional multi-period portfolio optimization

2019 ◽  
Vol 31 (3) ◽  
pp. 257-280
Author(s):  
Zhongyu Li ◽  
Ka Ho Tsang ◽  
Hoi Ying Wong
Keyword(s):  
Least Squares ◽  
Portfolio Optimization ◽  
Optimization Problems ◽  
Estimation Error ◽  
Sample Path ◽  
Ordinary Least Squares ◽  
Monte Carlo Algorithm ◽  
High Dimensional ◽  
Finite Sample ◽  
Sample Paths

Abstract This paper proposes a regression-based simulation algorithm for multi-period mean-variance portfolio optimization problems with constraints under a high-dimensional setting. For a high-dimensional portfolio, the least squares Monte Carlo algorithm for portfolio optimization can perform less satisfactorily with finite sample paths due to the estimation error from the ordinary least squares (OLS) in the regression steps. Our algorithm, which resolves this problem e, that demonstrates significant improvements in numerical performance for the case of finite sample path and high dimensionality. Specifically, we replace the OLS by the least absolute shrinkage and selection operator (lasso). Our major contribution is the proof of the asymptotic convergence of the novel lasso-based simulation in a recursive regression setting. Numerical experiments suggest that our algorithm achieves good stability in both low- and higher-dimensional cases.

LM TESTS IN THE PRESENCE OF NON-NORMAL ERROR DISTRIBUTIONS

2000 ◽  
Vol 16 (2) ◽  
pp. 249-261 ◽  
Author(s):  
Marilena Furno
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Study ◽  
Ordinary Least Squares ◽  
Conditional Heteroskedasticity ◽  
Absolute Deviation ◽  
Absolute Value ◽  
Lm Tests ◽  
Normal Error ◽  
Error Distributions ◽  
Squared Residuals

The paper considers different versions of the Lagrange multiplier (LM) tests for autocorrelation and/or for conditional heteroskedasticity. These versions differ in terms of the residuals, and of the functions of the residuals, used to build the tests. In particular, we compare ordinary least squares versus least absolute deviation (LAD) residuals, and we compare squared residuals versus their absolute value. We show that the LM tests based on LAD residuals are asymptotically distributed as a χ2 and that these tests are robust to nonnormality. The Monte Carlo study provides evidence in favor of the LAD residuals, and of the absolute value of the LAD residuals, to build the LM tests here discussed.

scholarly journals INFERENCE ON NONSTATIONARY TIME SERIES WITH MOVING MEAN

2014 ◽  
Vol 32 (2) ◽  
pp. 431-457 ◽  
Author(s):  
Jiti Gao ◽  
Peter M. Robinson
Keyword(s):  
Time Series ◽  
Monte Carlo ◽  
Monte Carlo Study ◽  
Semiparametric Model ◽  
Nonstationary Time Series ◽  
Finite Sample ◽  
Trend Function ◽  
Deterministic Trend ◽  
Short Memory ◽  
Memory Parameter

A semiparametric model is proposed in which a parametric filtering of a nonstationary time series, incorporating fractionally differencing with short memory correction, removes correlation but leaves a nonparametric deterministic trend. Estimates of the memory parameter and other dependence parameters are proposed, and shown to be consistent and asymptotically normally distributed with parametric rate. Tests with standard asymptotics for I(1) and other hypotheses are thereby justified. Estimation of the trend function is also considered. We include a Monte Carlo study of finite-sample performance.

Sign in / Sign up

Export Citation Format

Share Document