scholarly journals Asymptotic Theory for Regressions with Smoothly Changing Parameters

2013 ◽  
Vol 5 (2) ◽  
pp. 133-162 ◽  
Author(s):  
Eric Hillebrand ◽  
Marcelo C. Medeiros ◽  
Junyue Xu
Keyword(s):  
Maximum Likelihood ◽  
Asymptotic Theory ◽  
Asymptotic Properties ◽  
Smooth Transition ◽  
Finite Sample ◽  
Likelihood Estimator ◽  
Output Data ◽  
Asymptotically Normal ◽  
Finite Sample Properties ◽  
Quasi Maximum Likelihood

Abstract: We derive asymptotic properties of the quasi-maximum likelihood estimator of smooth transition regressions when time is the transition variable. The consistency of the estimator and its asymptotic distribution are examined. It is shown that the estimator converges at the usual -rate and has an asymptotically normal distribution. Finite sample properties of the estimator are explored in simulations. We illustrate with an application to US inflation and output data.

Asymmetric Laplace Regression: Maximum Likelihood, Maximum Entropy and Quantile Regression

2016 ◽  
Vol 5 (1) ◽  
Author(s):  
Anil K. Bera ◽  
Antonio F. Galvao ◽  
Gabriel V. Montes-Rojas ◽  
Sung Y. Park
Keyword(s):  
Maximum Likelihood ◽  
Quantile Regression ◽  
Maximum Entropy ◽  
Asymptotic Properties ◽  
Likelihood Estimation ◽  
Finite Sample ◽  
Score Functions ◽  
Finite Sample Properties ◽  
Quasi Maximum Likelihood ◽  
Joint Consideration

AbstractThis paper studies the connections among the asymmetric Laplace probability density (ALPD), maximum likelihood, maximum entropy and quantile regression. We show that the maximum likelihood problem is equivalent to the solution of a maximum entropy problem where we impose moment constraints given by the joint consideration of the mean and median. The ALPD score functions lead to joint estimating equations that delivers estimates for the slope parameters together with a representative quantile. Asymptotic properties of the estimator are derived under the framework of the quasi maximum likelihood estimation. With a limited simulation experiment we evaluate the finite sample properties of our estimator. Finally, we illustrate the use of the estimator with an application to the US wage data to evaluate the effect of training on wages.

ASYMPTOTIC THEORY FOR EMPIRICAL SIMILARITY MODELS

2009 ◽  
Vol 26 (4) ◽  
pp. 1032-1059 ◽  
Author(s):  
Offer Lieberman
Keyword(s):  
Stochastic Process ◽  
Maximum Likelihood ◽  
Maximum Likelihood Estimator ◽  
Asymptotic Theory ◽  
Econometric Models ◽  
Similarity Function ◽  
Random Disturbance ◽  
Likelihood Estimator ◽  
Disturbance Term ◽  
Quasi Maximum Likelihood

We consider the stochastic process $Y_t = \sum\nolimits_{i < t} {s_w } (x_t ,x_i)Y_i /\sum\nolimits_{i < t} {s_w } (x_t ,x_i) + \varepsilon _t$, t = 2, …, n, where sw(xt, xi) is a similarity function between the tth and the ith observations and {εt} is a random disturbance term. This process was originally axiomatized by Gilboa, Lieberman, and Schmeidler (2006, Review of Economics and Statistics 88, 433–444) as a way by which agents, or even nature, reason. In the present paper, consistency and the asymptotic distribution of the quasi-maximum likelihood estimator of the parameters of the model are established. Connections to other models and techniques are drawn. In its general form, the model does not fall within any class of nonstationary econometric models for which asymptotic theory is available. For this reason, the developments in this paper are new and nonstandard.

Bias in Conditional and Unconditional Fixed Effects Logit Estimation

2001 ◽  
Vol 9 (4) ◽  
pp. 379-384 ◽  
Author(s):  
Ethan Katz
Keyword(s):  
Maximum Likelihood ◽  
Fixed Effects ◽  
Panel Data Analysis ◽  
Asymptotic Properties ◽  
Logit Models ◽  
Finite Sample ◽  
Monte Carlo Experiments ◽  
Logit Estimation ◽  
Finite Sample Properties ◽  
Conditional Maximum

Fixed-effects logit models can be useful in panel data analysis, when N units have been observed for T time periods. There are two main estimators for such models: unconditional maximum likelihood and conditional maximum likelihood. Judged on asymptotic properties, the conditional estimator is superior. However, the unconditional estimator holds several practical advantages, and therefore I sought to determine whether its use could be justified on the basis of finite-sample properties. In a series of Monte Carlo experiments for T < 20, I found a negligible amount of bias in both estimators when T ≥ 16, suggesting that a researcher can safely use either estimator under such conditions. When T < 16, the conditional estimator continued to have a very small amount of bias, but the unconditional estimator developed more bias as T decreased.

scholarly journals MODELING MULTIPLE REGIMES IN FINANCIAL VOLATILITY WITH A FLEXIBLE COEFFICIENT GARCH(1,1) MODEL

2009 ◽  
Vol 25 (1) ◽  
pp. 117-161 ◽  
Author(s):  
Marcelo C. Medeiros ◽  
Alvaro Veiga
Keyword(s):  
Asymptotic Properties ◽  
Monte Carlo Experiment ◽  
Type Model ◽  
Finite Sample ◽  
Financial Volatility ◽  
Proposed Model ◽  
Multiple Regimes ◽  
Finite Sample Properties ◽  
Quasi Maximum Likelihood ◽  
Errors Estimation

In this paper a flexible multiple regime GARCH(1,1)-type model is developed to describe the sign and size asymmetries and intermittent dynamics in financial volatility. The results of the paper are important to other nonlinear GARCH models. The proposed model nests some of the previous specifications found in the literature and has the following advantages. First, contrary to most of the previous models, more than two limiting regimes are possible, and the number of regimes is determined by a simple sequence of tests that circumvents identification problems that are usually found in nonlinear time series models. The second advantage is that the novel stationarity restriction on the parameters is relatively weak, thereby allowing for rich dynamics. It is shown that the model may have explosive regimes but can still be strictly stationary and ergodic. A simulation experiment shows that the proposed model can generate series with high kurtosis and low first-order autocorrelation of the squared observations and exhibit the so-called Taylor effect, even with Gaussian errors. Estimation of the parameters is addressed, and the asymptotic properties of the quasi-maximum likelihood estimator are derived under weak conditions. A Monte-Carlo experiment is designed to evaluate the finite-sample properties of the sequence of tests. Empirical examples are also considered.

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