• Journal of applied mathematics & informatics
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• v.27 no.1_2
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• pp.315-326
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• 2009

The unknown parameters in regression models are usually estimated by using various existing methods. There are several existing methods, such as the least squares method, which is the most common one, the least absolute deviation method, the regression quantile method, and the asymmetric least squares method. For the nonlinear time series regression models, which do not satisfy the general conditions, we will compare them in two ways: 1) a theoretical comparison in the asymptotic sense and 2) an empirical comparison using Monte Carlo simulation for a small sample size.

• Earthquakes and Structures
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• v.12 no.5
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• pp.569-581
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• 2017

The Monte Carlo Simulation (MCS) based seismic fragility analysis (SFA) approach allows defining more realistic relationship between failure probability and seismic intensity. However, the approach requires simulating large number of nonlinear dynamic analyses of structure for reliable estimate of fragility. It makes the approach computationally challenging. The response surface method (RSM) based metamodeling approach which replaces computationally involve complex mechanical model of a structure is found to be a viable alternative in this regard. An adaptive moving least squares method (MLSM) based RSM in the MCS framework is explored in the present study for efficient SFA of existing structures. In doing so, the repetition of seismic intensity for complete generation of fragility curve is avoided by including this as one of the predictors in the response estimate model. The proposed procedure is elucidated by considering a non-linear SDOF system and an existing reinforced concrete frame considered to be located in the Guwahati City of the Northeast region of India. The fragility results are obtained by the usual least squares based and the proposed MLSM based RSM and compared with that of obtained by the direct MCS technique to study the effectiveness of the proposed approach.

• Wind and Structures
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• v.27 no.3
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• pp.199-211
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• 2018

This paper deals with wind fragility and risk analysis of high rise buildings subjected to stochastic wind load. Conventionally, such problems are dealt in full Monte Carlo Simulation framework, which requires extensive computational time. Thus, to make the procedure computationally efficient, application of metamodelling technique in fragility analysis is explored in the present study. Since, accuracy by the conventional Least Squares Method (LSM) based metamodelling is often challenged, an efficient Moving Least Squares Method based adaptive metamodelling technique is proposed for wind fragility analysis. In doing so, artificial time history of wind load is generated by three wind field models: i.e., a simple one based on alongwind component of wind speed; a more detailed one considering coherence and wind directionality effect, and a third one considering nonstationary effect of mean wind. The results show that the proposed approach is more accurate than the conventional LSM based metamodelling approach when compared to full simulation approach as reference. At the same time, the proposed approach drastically reduces computational time in comparison to the full simulation approach. The results by the three wind field models are compared. The importance of non-linear structural analysis in fragility evaluation has been also demonstrated.

• Environmental and Resource Economics Review
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• v.24 no.4
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• pp.607-627
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• 2015

As observed and experienced in EU ETS, allowance price volatility is one of major concerns in decision making process for $CO_2$ abatement investment. The problem of linearly non-separable profits functions could emerge when one power company holds several power plants with different technology specifications. Under this circumstance, conventional analytical solution for investment option is no longer available, thereby calling for the development of numerical analysis. This paper attempts to develop a Monte-Carlo least squares model to analyze investment options for power companies under emission trading scheme regulations. Stochastic allowance price is considered, and simulation is performed to verify model performance.

• Journal of the Korean Statistical Society
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• v.31 no.1
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• pp.77-91
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• 2002

This paper considers a functional regression model with truncated errors in explanatory variables. We show that the ordinary least squares (OLS) estimators produce bias in regression parameter estimates under misspecified models with ignored errors in the explanatory variable measurements, and then propose methods for analyzing the functional model. Fully parametric frequentist approaches for analyzing the model are intractable and thus Bayesian methods are pursued using a Markov chain Monte Carlo (MCMC) sampling based approach. Necessary theories involved in modeling and computation are provided. Finally, a simulation study is given to illustrate and examine the proposed methods.

• Journal of the Korea Society for Simulation
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• v.10 no.3
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• pp.31-46
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• 2001

Repeated measurements on units under different conditions are common in biological and biomedical studies. In a number of growth and pharmacokinetic studies, the relationship between the response and the covariates is assumed to be nonlinear in some unknown parameters and the form remains the same for all units. Nonlinear random coefficient models are used to analyze such repeated measurement data. Extended least squares methods are proposed in the literature for estimating the parameters of the model. However, neither objective function has closed form expression in practice. This paper proposes Monte Carlo methods to estimate the objective functions and the corresponding estimators. A simulation study that compare various methods is included.

• Communications for Statistical Applications and Methods
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• v.28 no.1
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• pp.81-88
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• 2021

k-least quantile of squares (k-LQS) estimates are a generalization of least median of squares (LMS) estimates. They have not been used as much as LMS because their breakdown points become small as k increases. But if the size of outliers is assumed to be fixed LQS estimates yield a good fit to the majority of data and residuals calculated from LQS estimates can be a reliable tool to detect outliers. We propose to use LQS estimates for separating a clean set from the data in the context of outlyingness of the cases. Three procedures are suggested for the identification of outliers using LQS estimates. Examples are provided to illustrate the methods. A Monte Carlo study show that proposed methods are effective.

• Journal of Electrical Engineering and Technology
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• v.8 no.6
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• pp.1269-1275
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• 2013

Recently, many studies have suggested that an electric vehicle (EV) is one of the means for increasing the reliability of power systems in new energy environments. EVs can make a contribution to improving reliability by providing frequency regulation in power systems in which the Vehicle-to-Grid (V2G) technology has been implemented and, if economically viable, can be helpful in increasing power system reliability. This paper presents a stochastic method for optimal coordination of charging and frequency regulation decisions for an EV aggregator using the Least Square Monte-Carlo (LSMC) with modeling of electricity price uncertainty. The LSMC can be used to assess the value of options based on electricity price uncertainty in order to simultaneously optimize the scheduling of EV charging and regulation service for the EV aggregator. The results of a numerical example show that the proposed method can significantly improve the expected profits of an EV aggregator.

• Korean Management Science Review
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• v.19 no.1
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• pp.117-128
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• 2002

In this Paper we investigate the performance of the five efficiency estimation methods which include the stochastic frontier model estimated by maximum likelihood (SFML), the stochastic frontier model estimated by corrected ordinary least squares (SFCOLS), the data envelopment analysis (DIA) model, the combined estimation of SFML and DEA (SFML + DEA), and the combined estimation of SFCOLS arid DIA (SFCOLS+ DEA) using Monte Carlo analysis. The results include: 1) SFML provides most accurate efficiency estimates for the sample sloe 150 or over,2) SFML+DEAor SFCOLS + DIA Perform better for the cases with sample sloe 25, 50, and low random errors, 3) SFCOLS performs better for the close with sample sloe 25, 50, and very high random errors.

• International Journal of Aeronautical and Space Sciences
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• v.14 no.1
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• pp.85-90
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• 2013

This paper presents a study on terrain referenced navigation (TRN). The extended Kalman filter (EKF) is adopted as a filter method. A Jacobian matrix of measurement equations in the EKF consists of terrain slope terms, and accurate slope estimation is essential to keep filter stability. Two slope estimation methods are proposed in this study. Both methods are based on the least-squares approach. One is planar regression searching the best plane, in the least-squares sense, representing the terrain map over the region, determined by position error covariance. It is shown that the method could provide a more accurate solution than the previously developed linear regression approach, which uses lines rather than a plane in the least-squares measure. The other proposed method is weighted planar regression. Additional weights formed by Gaussian pdf are multiplied in the planar regression, to reflect the actual pdf of the position estimate of EKF. Monte Carlo simulations are conducted, to compare the performance between the previous and two proposed methods, by analyzing the filter properties of divergence probability and convergence speed. It is expected that one of the slope estimation methods could be implemented, after determining which of the filter properties is more significant at each mission.