Finite sample properties of maximum likelihood and quasi-maximum likelihood estimators of egarch models

1996 ◽  
Vol 15 (1) ◽  
pp. 51-68 ◽  
Author(s):  
Partha Deb
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimators ◽  
Finite Sample ◽  
Finite Sample Properties ◽  
Quasi Maximum Likelihood

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.

AN EMPIRICAL STUDY OF TWO CLASSES OF ESTIMATORS FOR PROCESS VARIATION TRANSMISSION

1999 ◽  
Vol 06 (03) ◽  
pp. 289-300 ◽  
Author(s):  
DANIEL Y. T. FONG
Keyword(s):  
Maximum Likelihood ◽  
Final Stage ◽  
Maximum Likelihood Estimators ◽  
Quality Characteristic ◽  
Manufacturing Processes ◽  
Finite Sample ◽  
Interval Estimates ◽  
Moderate Number ◽  
Finite Sample Properties ◽  
Remedial Actions

Manufacturing processes often consist of a number of sequential stages. Of interest is to control the variation in one or more quality characteristics of a production unit at the final stage. By understanding how variation is transmitted and added across the stages, remedial actions in reducing variation at the final stage can be properly planned. With one quality characteristic measured at each stage, a set of naive estimators is previously proposed and shown to perform indistinguishably well with maximum likelihood estimators. Thus naive estimators are more convenient than maximum likelihood estimators as the former exist in closed form while the latter do not. This article considers situations when more than one quality characteristic is measured throughout the stages. Methods of analyzing variation transmission are briefly reviewed and the finite sample properties of naive and maximum likelihood estimators for multivariate measurements are further examined. A broad conclusion is that for moderate number of production units, naive estimators have smaller bias and variability. Furthermore, "proper" naive estimates provide more accurate interval estimates at a given confidence level. Finally, a set of piston-machining data is used for illustration.

Finite-Sample Theory and Bias Correction of Maximum Likelihood Estimators in the EGARCH Model

2018 ◽  
Vol 11 (1) ◽  
Author(s):  
Antonis Demos ◽  
Dimitra Kyriakopoulou
Keyword(s):  
Monte Carlo ◽  
Maximum Likelihood ◽  
Bias Correction ◽  
Maximum Likelihood Estimators ◽  
Finite Sample ◽  
Egarch Model ◽  
Quasi Maximum Likelihood ◽  
Measure Of Performance ◽  
Analytical Expressions ◽  
Better Than

AbstractWe derive the analytical expressions of bias approximations for maximum likelihood (ML) and quasi-maximum likelihood (QML) estimators of the EGARCH (1,1) parameters that enable us to correct after the bias of all estimators. The bias-correction mechanism is constructed under the specification of two methods that are analytically described. We also evaluate the residual bootstrapped estimator as a measure of performance. Monte Carlo simulations indicate that, for given sets of parameters values, the bias corrections work satisfactory for all parameters. The proposed full-step estimator performs better than the classical one and is also faster than the bootstrap. The results can be also used to formulate the approximate Edgeworth distribution of the estimators.

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.

Estimation of Dynamic Term Structure Models

2012 ◽  
Vol 02 (02) ◽  
pp. 1250008 ◽  
Author(s):  
Gregory R. Duffee ◽  
Richard H. Stanton
Keyword(s):  
Maximum Likelihood ◽  
Term Structure ◽  
Empirical Work ◽  
Interest Rate Risk ◽  
Small Sample ◽  
Accurate Estimation ◽  
Parameter Estimates ◽  
Finite Sample ◽  
Term Structure Models ◽  
Finite Sample Properties

We study the finite-sample properties of some of the standard techniques used to estimate modern term structure models. For sample sizes and models similar to those used in most empirical work, we reach three surprising conclusions. First, while maximum likelihood works well for simple models, it produces strongly biased parameter estimates when the model includes a flexible specification of the dynamics of interest rate risk. Second, despite having the same asymptotic efficiency as maximum likelihood, the small-sample performance of Efficient Method of Moments (a commonly used method for estimating complicated models) is unacceptable even in the simplest term structure settings. Third, the linearized Kalman filter is a tractable and reasonably accurate estimation technique, which we recommend in settings where maximum likelihood is impractical.

Finite Sample Properties of Several Predictors From an Autoregressive Model

1987 ◽  
Vol 3 (3) ◽  
pp. 359-370 ◽  
Author(s):  
Koichi Maekawa
Keyword(s):  
Maximum Likelihood ◽  
Sample Size ◽  
Asymptotic Expansions ◽  
Autoregressive Model ◽  
Mean Squared Error ◽  
The Other ◽  
Finite Sample ◽  
Squared Error ◽  
Distributional Properties ◽  
Finite Sample Properties

We compare the distributional properties of the four predictors commonly used in practice. They are based on the maximum likelihood, two types of the least squared, and the Yule-Walker estimators. The asymptotic expansions of the distribution, bias, and mean-squared error for the four predictors are derived up to O(T−1), where T is the sample size. Examining the formulas of the asymptotic expansions, we find that except for the Yule-Walker type predictor, the other three predictors have the same distributional properties up to O(T−1).

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