Multi-modality in the Likelihood Function of GARCH Model

2020 ◽  
Vol 23 (03) ◽  
pp. 2050018
Author(s):  
Farrukh Mahmood ◽  
Saud Ahmed Khan
Keyword(s):  
Maximum Likelihood ◽  
Real World ◽  
Likelihood Function ◽  
Estimation Method ◽  
Garch Model ◽  
Maximum Likelihood Estimates ◽  
Estimation Methods ◽  
Real World Application ◽  
Text Model

It is shown empirically that likelihood function of the GARCH is multi-modal. Hence, the maximum likelihood estimates at local and global maxima will be quantitatively different. Therefore, it is important to start an estimation method with consistent starting value that converge to global maxima. This study compares two estimation methods, BFGS and DE, on the basis of simulation and surface constructed by changing the value of GARCH [Formula: see text] model. DE is superior and consistent throughout the surface, and across distributions. PSX is used as real-world application and it has been found that the estimates obtained from DE are best and unbiased.

scholarly journals E-Bayesian Estimation Based on Burr-X Generalized Type-II Hybrid Censored Data

Symmetry ◽  
2019 ◽  
Vol 11 (5) ◽  
pp. 626
Author(s):  
Abdalla Rabie ◽  
Junping Li
Keyword(s):  
Maximum Likelihood ◽  
Bayesian Estimation ◽  
Real Life ◽  
Estimation Method ◽  
Reliability Function ◽  
Maximum Likelihood Estimates ◽  
Estimation Methods ◽  
Type Ii ◽  
Credible Intervals ◽  
Generalized Type

In this article, we are concerned with the E-Bayesian (the expectation of Bayesian estimate) method, the maximum likelihood and the Bayesian estimation methods of the shape parameter, and the reliability function of one-parameter Burr-X distribution. A hybrid generalized Type-II censored sample from one-parameter Burr-X distribution is considered. The Bayesian and E-Bayesian approaches are studied under squared error and LINEX loss functions by using the Markov chain Monte Carlo method. Confidence intervals for maximum likelihood estimates, as well as credible intervals for the E-Bayesian and Bayesian estimates, are constructed. Furthermore, an example of real-life data is presented for the sake of the illustration. Finally, the performance of the E-Bayesian estimation method is studied then compared with the performance of the Bayesian and maximum likelihood methods.

scholarly journals The Weibull Birnbaum-Saunders Distribution And Its Applications

2020 ◽  
Vol 9 (1) ◽  
pp. 61-81
Author(s):  
Lazhar BENKHELIFA
Keyword(s):  
Maximum Likelihood ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Real Data ◽  
Reliability Estimation ◽  
Maximum Likelihood Estimates ◽  
Model Parameters ◽  
Data Sets ◽  
Proposed Model ◽  
Modeling Data

A new lifetime model, with four positive parameters, called the Weibull Birnbaum-Saunders distribution is proposed. The proposed model extends the Birnbaum-Saunders distribution and provides great flexibility in modeling data in practice. Some mathematical properties of the new distribution are obtained including expansions for the cumulative and density functions, moments, generating function, mean deviations, order statistics and reliability. Estimation of the model parameters is carried out by the maximum likelihood estimation method. A simulation study is presented to show the performance of the maximum likelihood estimates of the model parameters. The flexibility of the new model is examined by applying it to two real data sets.

Maximum likelihood estimation in nonlinear structured fisheries models using survey and catch-at-age data

2011 ◽  
Vol 68 (10) ◽  
pp. 1717-1731 ◽  
Author(s):  
Christian N. Brinch ◽  
Anne Maria Eikeset ◽  
Nils Chr. Stenseth
Keyword(s):  
Maximum Likelihood ◽  
Gadus Morhua ◽  
Likelihood Function ◽  
Likelihood Estimation ◽  
Maximum Likelihood Estimates ◽  
Simulated Maximum Likelihood ◽  
True Parameter ◽  
Bayesian Techniques ◽  
Age Structured ◽  
Parameter Values

Age-structured population dynamics models play an important role in fisheries assessments. Such models have traditionally been estimated using crude likelihood approximations or more recently using Bayesian techniques. We contribute to this literature with three main messages. Firstly, we demonstrate how to estimate such models efficiently by simulated maximum likelihood using Laplace importance samplers for the likelihood function. Secondly, we demonstrate how simulated maximum likelihood estimates may be validated using different importance samplers known to approach the exact likelihood function in different regions of the parameter space. Thirdly, we show that our method works in practice by Monte Carlo simulations using parameter values as estimated from data on the Northeast Arctic cod ( Gadus morhua ) stock. The simulations suggest that we are able to recover the unknown true maximum likelihood estimates using moderate importance sample sizes and show that we are able to adequately recover the true parameter values.

AN ANALYSIS OF ACCELERATED PERFORMANCE DEGRADATION TESTS ASSUMING THE ARRHENIUS STRESS-RELATIONSHIP

2008 ◽  
Vol 25 (06) ◽  
pp. 847-864 ◽  
Author(s):  
TAE HYOUNG KANG ◽  
SANG WOOK CHUNG ◽  
WON YOUNG YUN
Keyword(s):  
Maximum Likelihood ◽  
Normal Distribution ◽  
Exposure Time ◽  
Failure Time ◽  
Likelihood Function ◽  
Likelihood Estimation ◽  
Location Parameter ◽  
Performance Degradation ◽  
Maximum Likelihood Estimates ◽  
Degradation Tests

An analytical model is developed for accelerated performance degradation tests. The performance degradations of products at a specified exposure time are assumed to follow a normal distribution. It is assumed that the relationship between the location parameter of normal distribution and the exposure time is a linear function of the exposure time that the slope coefficient of the linear relationship has an Arrhenius dependence on temperature, and that the scale parameter of the normal distribution is constant and independent of temperature or exposure time. The method of maximum likelihood estimation is used to estimate the parameters involved. The likelihood function for the accelerated performance degradation data is derived. The approximated variance-covariance matrix is also derived for calculating approximated confidence intervals of maximum likelihood estimates. Finally we use two real examples for estimating the failure-time distribution, technically defined as the time when performance degrades below a specified level.

The Estimated Probability of Dizygotic Twins: A Comparison of Two Methods

2009 ◽  
Vol 12 (1) ◽  
pp. 79-85 ◽  
Author(s):  
Jill Hardin ◽  
Steve Selvin ◽  
Suzan L. Carmichael ◽  
Gary M. Shaw
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Likelihood Estimation ◽  
Data Sources ◽  
Maximum Likelihood Estimates ◽  
Estimation Methods ◽  
Dizygotic Twin ◽  
Twin Data ◽  
Dizygotic Twins ◽  
The Relationship

AbstractThis study presents a general model of two binary variables and applies it to twin sex pairing data from 21 twin data sources to estimate the frequency of dizygotic twins. The purpose of this study is to clarify the relationship between maximum likelihood and Weinberg's differential rule zygosity estimation methods. We explore the accuracy of these zygosity estimation measures in relation to twin ascertainment methods and the probability of a male. Twin sex pairing data from 21 twin data sources representing 15 countries was collected for use in this study. Maximum likelihood estimation of the probability of dizygotic twins is applied to describe the variation in the frequency of dizygotic twin births. The differences between maximum likelihood and Weinberg's differential rule zygosity estimation methods are presented as a function of twin data ascertainment method and the probability of a male. Maximum likelihood estimation of the probability of dizygotic twins ranges from 0.083 (95% approximate CI: 0.082, 0.085) to 0.750 (95% approximate CI: 0.749, 0.752) for voluntary ascertainment data sources and from 0.374 (95% approximate CI: 0.373, 0.375) to 0.987 (95% approximate CI: 0.959, 1.016) for active ascertainment data sources. In 17 of the 21 twin data sources differences of 0.01 or less occur between maximum likelihood and Weinberg zygosity estimation methods. The Weinberg and maximum likelihood estimates are negligibly different in most applications. Using the above general maximum likelihood estimate, the probability of a dizygotic twin is subject to substantial variation that is largely a function of twin data ascertainment method.

scholarly journals Comparison between the maximum likelihood and the bayesian estimation methods for logistic regression model (case study: risk of low birth weight in Indonesia)

2021 ◽  
Vol 2106 (1) ◽  
pp. 012001
Author(s):  
P R Sihombing ◽  
S R Rohimah ◽  
A Kurnia
Keyword(s):  
Logistic Regression ◽  
Birth Weight ◽  
Maximum Likelihood ◽  
Low Birth Weight ◽  
Regression Model ◽  
Bayesian Estimation ◽  
Logistic Regression Model ◽  
Estimation Method ◽  
Estimation Methods ◽  
Model Case

Abstract This study aims to compare the efficacy of logistic regression model for identifying the risk factors of low-birth-weight babies in Indonesia using the maximum likelihood estimation (MLE)and the Bayesian estimation methods. The data used in this study is secondary data derived from the 2017 Indonesian Demographic Health Survey with a total sample of 16,344 newborn babies. Selection of the best logistic regression model was based on the smaller Bayesian Schwartz Information Criterion (BIC) value. The logistic regression model with the Bayesian estimation method has a smaller BIC value than the MLE method. Twin births, baby girl, maternal age at risk, birth spacing that is too close, iron deficiency, low education, low economy, inadequate drinking water sources have provided a higher risk of low-birth-weight incidence.

scholarly journals Estimating the Reliability Function of (2+1) Cascade Model

2019 ◽  
Vol 16 (2) ◽  
pp. 0395
Author(s):  
Khaleel Et al.
Keyword(s):  
Maximum Likelihood ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Reliability Function ◽  
Cascade Model ◽  
Least Square ◽  
Estimation Methods ◽  
Percentage Error ◽  
Estimate Reliability ◽  
Best Estimator

This paper discusses reliability R of the (2+1) Cascade model of inverse Weibull distribution. Reliability is to be found when strength-stress distributed is inverse Weibull random variables with unknown scale parameter and known shape parameter. Six estimation methods (Maximum likelihood, Moment, Least Square, Weighted Least Square, Regression and Percentile) are used to estimate reliability. There is a comparison between six different estimation methods by the simulation study by MATLAB 2016, using two statistical criteria Mean square error and Mean Absolute Percentage Error, where it is found that best estimator between the six estimators is Maximum likelihood estimation method.

scholarly journals Simple penalties on maximum likelihood estimates of genetic parameters to reduce sampling variation

2015 ◽  
Author(s):  
karin meyer
Keyword(s):  
Maximum Likelihood ◽  
Genetic Parameters ◽  
Likelihood Function ◽  
Maximum Likelihood Estimates ◽  
Data Sets ◽  
Simple Modification ◽  
Scale Free ◽  
Wide Range ◽  
Sampling Variation ◽  
The Difference

Multivariate estimates of genetic parameters are subject to substantial sampling variation, especially for smaller data sets and more than a few traits. A simple modification of standard, maximum likelihood procedures for multivariate analyses to estimate genetic covariances is described, which can improve estimates by substantially reducing their sampling variances. This is achieved maximizing the likelihood subject to a penalty. Borrowing from Bayesian principles, we propose a mild, default penalty -- derived assuming a Beta distribution of scale-free functions of the covariance components to be estimated -- rather than laboriously attempting to determine the stringency of penalization from the data. An extensive simulation study is presented demonstrating that such penalties can yield very worthwhile reductions in loss, i.e. the difference from population values, for a wide range of scenarios and without distorting estimates of phenotypic covariances. Moreover, mild default penalties tend not to increase loss in difficult cases and, on average, achieve reductions in loss of similar magnitude than computationally demanding schemes to optimize the degree of penalization. Pertinent details required for the adaptation of standard algorithms to locate the maximum of the likelihood function are outlined.

scholarly journals Determinants of banks’ cost efficiency: a case study of selected commercial banks, Ethiopia

2020 ◽  
Vol 8 (3) ◽  
pp. 231-244
Author(s):  
Astereye Enyew Ereta ◽  
Eshetu Yadecha Bedada ◽  
Tesfaye Ginbare Gutu
Keyword(s):  
Maximum Likelihood ◽  
Cost Efficiency ◽  
Commercial Banks ◽  
Likelihood Function ◽  
Estimation Method ◽  
Labor Cost ◽  
Single Stage ◽  
Capital Adequacy ◽  
Capital Adequacy Ratio ◽  
Cost Inefficiency

This study examines the determinants of cost efficiency commercial banks’ in Ethiopian using balanced panel data with a sample of 13 commercial banks over the period 2010-2017 by paying a translog stochastic cost frontier approach. The identification and selection of inputs and outputs variables was based on the intermediation approach. Accordingly, three input variables (cost of labor, cost of capital, and cost of fund) and two output variables (total loans and other earning assets) are used in the study. Furthermore, five banks specific and one macroeconomic variable are included to examine their effect on cost efficiency. So as to examine the effect of determinant variables which are associated with banks efficiency, a single stage maximum likelihood estimation method is applied to stochastic frontier cost function. The empirical estimations were accomplished by Appling a single stage maximum likelihood function assimilated into Stata software. The estimation is based on conditional mean model concepts. The finding shows that from bank specific factors, return on assets (ROA), and intermediation ratio have positive and significant for intermediation (IR) and insignificant for ROA with cost inefficiency. On the other hand, Bank size (lnTA), Credit risk (CR) and capital adequacy ratio (CAR) have a significant negative coefficient with cost inefficiency. GDP also has negative but insignificant with inefficiency. Therefore, banks are recommended to improve and sustain their efficiency by maintaining available proportion of capital adequacy ratio and attract high value, low interest-bearing demand deposits.

Maximum Likelihood Parameter Estimation of CNC System Reliability

2014 ◽  
Vol 487 ◽  
pp. 282-285
Author(s):  
Yan Gu ◽  
Yi Qiang Wang ◽  
Xiao Qin Zhou ◽  
Xiu Hua Yuan
Keyword(s):  
Genetic Algorithm ◽  
Parameter Estimation ◽  
Maximum Likelihood ◽  
System Reliability ◽  
Simulated Annealing Algorithm ◽  
Likelihood Function ◽  
Estimation Method ◽  
Distribution Model ◽  
Improved Genetic Algorithm ◽  
Cnc System

In order to increase calculation accuracy of CNC system reliability, this paper proposed a maximum likelihood parameter estimation method based on improved genetic algorithm. In the parameter estimation process for CNC system reliability distribution model, the maximum likelihood function value was gained by improving genetic algorithm through simulated annealing algorithm. Parameter estimation was carried out by setting Weibull distribution as an example. The result shows that the improved genetic algorithm can increase solution efficiency and convergence rate. Besides, it can effectively estimate parameters of reliability distribution model.

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