• The Korean Journal of Applied Statistics
• /
• v.34 no.5
• /
• pp.761-772
• /
• 2021

Simulation results for the comparison of estimators of interest are usually reported in tables or plots. However, if the simulations are conducted under various conditions for many estimators, the comparison can be difficult to be made with tables or plots. Furthermore, for algorithms that take a long time to run, the number of iterations of the simulation is costly to to be increased. The analysis of simulation results using regression models allows us to compare the estimators more systematically and effectively. Since variances in performance measures may vary depending on the simulation conditions and estimators, the heteroscedasticity of the error term should be allowed in the regression model. And multiple comparisons should be made because multiple estimators should be compared simultaneously. We introduce background theories of heteroscedasticity and multiple comparisons in the context of analyzing simulation results. We also present a concrete example.

• Journal of Animal Science and Technology
• /
• v.64 no.1
• /
• pp.135-142
• /
• 2022

It is impossible to know the amount of pork primal cut by pig carcass grade which is determined only by carcass weight and backfat thickness in the Korean Pig Carcass System. The aim of this study was to investigate the correlation between the pig carcass grade and the amount of pork primal cut estimated with AutoFom III. A total of 419,321 Landrace, Yorkshire, and Duroc (LYD) pigs were graded with the Korean Pig Carcass Grade System. Amounts of belly, neck, loin, tenderloin, spare ribs, shoulder, and ham were estimated with AutoFom III. Regression equations for seven primal cuts according to each grade were derived. There were significant differences among the three carcass grades due to heteroscedasticity variance (p < 0.0001). Three regression equations were derived from AutoFom III estimation of primal cuts according to carcass grades. The coefficient of determination of the regression equation was 0.941 for grade 1⁺, 0.982 for grade 1, and 0.993 for grade 2. Regression equations obtained from this study are suitable for AutoFom III software, a useful tool for the analysis of each pig carcass grade in the Korean Pig Carcass Grade System. The high reliability of predicting the amount of primal cut with AutoFom III is advantageous for the management of slaughterhouses to optimize their product sorting in Korea.

• The Korean Journal of Applied Statistics
• /
• v.36 no.4
• /
• pp.295-307
• /
• 2023

The heterogeneous autoregressive (HAR) model is a simple linear model that is commonly used to explain long memory in the realized volatility. However, as realized volatility has more complicated features such as conditional heteroscedasticity, leverage effect, and volatility clustering, it is necessary to extend the simple HAR model. Therefore, to better incorporate the stylized facts, we propose a threshold HAR model with GARCH errors, namely the THAR-GARCH model. That is, the THAR-GARCH model is a nonlinear model whose coefficients vary according to a threshold value, and the conditional heteroscedasticity is explained through the GARCH errors. Model parameters are estimated using an iterative weighted least squares estimation method. Our simulation study supports the consistency of the iterative estimation method. In addition, we show that the proposed THAR-GARCH model has better forecasting power by applying to the realized volatility of major 21 stock indices around the world.

• Journal of the Korean Data and Information Science Society
• /
• v.21 no.1
• /
• pp.155-162
• /
• 2010

In this paper we propose a doubly penalized kernel method which estimates both the mean function and the variance function simultaneously by kernel machines for heteroscedastic autoregressive data. We also present the model selection method which employs the cross validation techniques for choosing the hyper-parameters which aect the performance of proposed method. Simulated examples are provided to indicate the usefulness of proposed method for the estimation of mean and variance functions.

• Journal of the Korean Data and Information Science Society
• /
• v.28 no.5
• /
• pp.1191-1204
• /
• 2017

Weighted least squares (WLS) estimation is often easily used for the data with heteroscedastic errors because it is intuitive and computationally inexpensive. However, WLS estimator is less robust to a few outliers and sometimes it may be inefficient. In order to overcome robustness problems, Box-Cox transformation, Huber's M estimation, bisquare estimation, and Yohai's MM estimation have been proposed. Also, more efficient estimations than WLS have been suggested such as Bayesian methods (Cepeda and Achcar, 2009) and semiparametric methods (Kim and Ma, 2012) in heteroscedastic error models. Recently, Çelik (2015) proposed the weight methods applicable to the heteroscedasticity patterns including butterfly-distributed residuals and megaphone-shaped residuals. In this paper, we review heteroscedastic regression estimators related to robust or efficient estimation and describe their properties. Also, we analyze cost data of U.S. Electricity Producers in 1955 using the methods discussed in the paper.

• Journal of the Korean Statistical Society
• /
• v.34 no.2
• /
• pp.161-172
• /
• 2005

In this paper a nonparametric method is proposed for detecting conditionally heteroscedastic errors in a nonparametric time series regression model where the observation points are equally spaced on [0,1]. It turns out that the first-order sample autocorrelation of the squared residuals from the kernel regression estimates provides essential information. Illustrative simulation study is presented for diverse errors such as ARCH(1), GARCH(1,1) and threshold-ARCH(1) models.

• Communications for Statistical Applications and Methods
• /
• v.13 no.3
• /
• pp.491-501
• /
• 2006

We consider a multiple change point model with autoregressive conditional heteroscedasticity (ARCH). The model assumes that all or the part of the parameters in the ARCH equation change over time. The occurrence of the change points is modelled as the discrete time Markov process with unknown transition probabilities. The model is estimated by Markov chain Monte Carlo methods based on the approach of Chib (1998). Simulation is performed using a variant of perfect sampling algorithm to achieve the accuracy and efficiency. We apply the proposed model to the simulated data for verifying the usefulness of the model.

• Journal of applied mathematics & informatics
• /
• v.9 no.2
• /
• pp.771-785
• /
• 2002

Many industries like energy, utilities, ice cream and leisure sports are closely related to the weather. In order to hedge weather related risks, they invest their assets with portfolios like option, coupons, future, and other weather derivatives. Among weather related derivatives, CDD and HDD index options are mainly transacted between companies. In this paper, the autocorrelation system of temperature will be checked for several cities in Korea and the parameter estimation will be carried based on the maximum likelihood estimation. Since the log likelihood increase as the number of parameters increases, we adopt the Schwarz information criterion .

• Journal of the Korean Data and Information Science Society
• /
• v.20 no.5
• /
• pp.925-931
• /
• 2009

In this paper we propose a variance function estimation method for replicated data based on averages of squared residuals obtained from estimated mean function by the least squares support vector machine. Newton-Raphson method is used to obtain associated parameter vector for the variance function estimation. Furthermore, the cross validation functions are introduced to select the hyper-parameters which affect the performance of the proposed estimation method. Experimental results are then presented which illustrate the performance of the proposed procedure.

• Communications for Statistical Applications and Methods
• /
• v.16 no.2
• /
• pp.383-388
• /
• 2009

In this paper we propose a variance function estimation method based on kernel trick for replicated data or data consisted of sample variances. Newton-Raphson method is used to obtain associated parameter vector. Furthermore, the generalized approximate cross validation function is introduced to select the hyper-parameters which affect the performance of the proposed variance function estimation method. Experimental results are then presented which illustrate the performance of the proposed procedure.