• Title, Summary, Keyword: maximum-likelihood estimation

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Maximum Likelihood Estimation for the Laplacian Autoregressive Time Series Model

  • Son, Young-Sook;Cho, Sin-Sup
    • Journal of the Korean Statistical Society
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    • v.25 no.3
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    • pp.359-368
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    • 1996
  • The maximum likelihood estimation is discussed for the NLAR model with Laplacian marginals. Since the explicit form of the estimates cannot be obtained due to the complicated nature of the likelihood function we utilize the automatic computer optimization subroutine using a direct search complex algorithm. The conditional least square estimates are used as initial estimates in maximum likelihood procedures. The results of a simulation study for the maximum likelihood estimates of the NLAR(1) and the NLAR(2) models are presented.

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An Approximation of the Cumulant Generating Functions of Diffusion Models and the Pseudo-likelihood Estimation Method (확산모형에 대한 누율생성함수의 근사와 가우도 추정법)

  • Lee, Yoon-Dong;Lee, Eun-Kyung
    • Journal of the Korean Operations Research and Management Science Society
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    • v.38 no.1
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    • pp.201-216
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    • 2013
  • Diffusion is a basic mathematical tool for modern financial engineering. The theory of the estimation methods for diffusion models is an important topic of the financial engineering. Many researches have been tried to apply the likelihood estimation method for estimating diffusion models. However, the likelihood estimation method for diffusion is complicated and needs much amount of computing. In this paper we develop the estimation methods which are simple enough to be compared to the Euler approximation method, and efficient enough statistically to be compared to the likelihood estimation method. We devise pseudo-likelihood and propose the maximum pseudo-likelihood estimation methods. The pseudo-likelihoods are obtained by approximating the transition density with normal distributions. The means and the variances of the distributions are obtained from the delta expansion suggested by Lee, Song and Lee (2012). We compare the newly suggested estimators with other existing estimators by simulation study. From the simulation study we find the maximum pseudo-likelihood estimator has very similar properties with the maximum likelihood estimator. Also the maximum pseudo-likelihood estimator is easy to apply to general diffusion models, and can be obtained by simple numerical steps.

Comparison of parameter estimation methods for normal inverse Gaussian distribution

  • Yoon, Jeongyoen;Kim, Jiyeon;Song, Seongjoo
    • Communications for Statistical Applications and Methods
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    • v.27 no.1
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    • pp.97-108
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    • 2020
  • This paper compares several methods for estimating parameters of normal inverse Gaussian distribution. Ordinary maximum likelihood estimation and the method of moment estimation often do not work properly due to restrictions on parameters. We examine the performance of adjusted estimation methods along with the ordinary maximum likelihood estimation and the method of moment estimation by simulation and real data application. We also see the effect of the initial value in estimation methods. The simulation results show that the ordinary maximum likelihood estimator is significantly affected by the initial value; in addition, the adjusted estimators have smaller root mean square error than ordinary estimators as well as less impact on the initial value. With real datasets, we obtain similar results to what we see in simulation studies. Based on the results of simulation and real data application, we suggest using adjusted maximum likelihood estimates with adjusted method of moment estimates as initial values to estimate the parameters of normal inverse Gaussian distribution.

Notes on the Comparative Study of the Reliability Estimation for Standby System with Exponential Lifetime Distribution

  • Kim, Hee-Jae
    • Journal of the Korean Data and Information Science Society
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    • v.14 no.4
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    • pp.1055-1065
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    • 2003
  • We shall propose maximum likelihood, Bayesian and generalized maximum likelihood estimation for the reliability of the two-unit hot standby system with exponential lifetime distribution that switch is perfect. Each estimation will be compared numerically in terms of various mission times, parameter values and asymptotic relative efficiency through Monte Carlo simulation.

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Notes on the Comparative Study of the Reliability Estimation for Standby System with Rayleigh Lifetime Distribution

  • Kim, Hee-Jae
    • Journal of the Korean Data and Information Science Society
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    • v.15 no.1
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    • pp.239-250
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    • 2004
  • We shall propose maximum likelihood, Bayesian and generalized maximum likelihood estimation for the reliability of the two-unit hot standby system with Rayleigh lifetime distribution that switch is perfect. Each estimation will be compared numerically in terms of various mission times, parameter values and asymptotic relative efficiency through Monte Carlo simulation.

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A Doubly Winsorized Poisson Auto-model

  • Jaehyung Lee
    • Communications for Statistical Applications and Methods
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    • v.5 no.2
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    • pp.559-570
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    • 1998
  • This paper introduces doubly Winsorized Poisson auto-model by truncating the support of a Poisson random variable both from above and below, and shows that this model has a same form of negpotential function as regular Poisson auto-model and one-way Winsorized Poisson auto-model. Strategies for maximum likelihood estimation of parameters are discussed. In addition to exact maximum likelihood estimation, Monte Carlo maximum likelihood estimation may be applied to this model.

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Estimation for the generalized exponential distribution under progressive type I interval censoring (일반화 지수분포를 따르는 제 1종 구간 중도절단표본에서 모수 추정)

  • Cho, Youngseukm;Lee, Changsoo;Shin, Hyejung
    • Journal of the Korean Data and Information Science Society
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    • v.24 no.6
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    • pp.1309-1317
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    • 2013
  • There are various parameter estimation methods for the generalized exponential distribution under progressive type I interval censoring. Chen and Lio (2010) studied the parameter estimation method by the maximum likelihood estimation method, mid-point approximation method, expectation maximization algorithm and methods of moments. Among those, mid-point approximation method has the smallest mean square error in the generalized exponential distribution under progressive type I interval censoring. However, this method is difficult to derive closed form of solution for the parameter estimation using by maximum likelihood estimation method. In this paper, we propose two type of approximate maximum likelihood estimate to solve that problem. The simulation results show the obtained estimators have good performance in the sense of the mean square error. And proposed method derive closed form of solution for the parameter estimation from the generalized exponential distribution under progressive type I interval censoring.

Maximum Likelihood SNR Estimation for QAM Signals Over Slow Flat Fading Rayleigh Channel

  • Ishtiaq, Nida;Sheikh, Shahzad A.
    • KSII Transactions on Internet and Information Systems (TIIS)
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    • v.10 no.11
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    • pp.5365-5380
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    • 2016
  • Estimation of signal-to-noise ratio (SNR) is an important problem in wireless communication systems. It has been studied for various constellation types and channels using different estimation techniques. Maximum likelihood estimation is a technique which provides efficient and in most cases unbiased estimators. In this paper, we have applied maximum likelihood estimation for systems employing square or cross QAM signals which are undergoing slow flat Rayleigh fading. The problem has been considered under various scenarios like data-aided (DA), non-data-aided (NDA) and partially data-aided (PDA) and the performance of each type of estimator has been evaluated and compared. It has been observed that the performance of DA estimator is best due to usage of pilot symbols, with the drawback of greater bandwidth consumption. However, this can be catered for by using partially data-aided estimators whose performance is better than NDA systems with some extra bandwidth requirement.

Parameter Estimation for an Infinite Dimensional Stochastic Differential Equation

  • Kim, Yoon-Tae
    • Journal of the Korean Statistical Society
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    • v.25 no.2
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    • pp.161-173
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    • 1996
  • When we deal with a Hilbert space-valued Stochastic Differential Equation (SDE) (or Stochastic Partial Differential Equation (SPDE)), depending on some unknown parameters, the solution usually has a Fourier series expansion. In this situation we consider the maximum likelihood method for the statistical estimation problem and derive the asymptotic properties (consistency and normality) of the Maximum Likelihood Estimator (MLE).

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Simplified Maximum Likelihood Estimation of the Frequencies of Multiple Sinusoids (간략화된 최우도 방법을 사용한 다중 정현파의 주파수 추정)

  • Ahn, Tae-Chon;Oh, Sung-Kwun
    • The Journal of the Acoustical Society of Korea
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    • v.13 no.4
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    • pp.20-31
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    • 1994
  • The maximum likelihood(ML) estimation has excellent accuracy for frequency estimation of multiple sinusoids, but the maximum likelihood function requires much loss owing to the high nonlinearity. This paper presents a simplified maximum likelihood estimation, in order to improve the nonlinearity of the maximum likelihood estimation for frequencies of sinusoids in signals. This method is applied to the frequency estimation of sinusoidal signals corrupted by white or colored measurement noise. Monte-carlo simulations are conducted for the comparison of ML method with the best MFBLP method, in terms of sampled mean, root mean square and relative bias. The power spectral density and the position of frequency in unit circle are appeared in figures.

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