scholarly journals Comparing Parameter Estimation of Random Coefficient Autoregressive Model by Frequentist Method

Mathematics ◽  
2020 ◽  
Vol 8 (1) ◽  
pp. 62 ◽  
Author(s):  
Autcha Araveeporn
Keyword(s):  
Maximum Likelihood ◽  
Least Squares ◽  
Mean Square Error ◽  
Maximum Likelihood Method ◽  
Least Squares Method ◽  
Likelihood Function ◽  
Likelihood Method ◽  
Mean Square ◽  
Average Mean Square Error ◽  
Frequentist Method

This paper compares the frequentist method that consisted of the least-squares method and the maximum likelihood method for estimating an unknown parameter on the Random Coefficient Autoregressive (RCA) model. The frequentist methods depend on the likelihood function that draws a conclusion from observed data by emphasizing the frequency or proportion of the data namely least squares and maximum likelihood methods. The method of least squares is often used to estimate the parameter of the frequentist method. The minimum of the sum of squared residuals is found by setting the gradient to zero. The maximum likelihood method carries out the observed data to estimate the parameter of a probability distribution by maximizing a likelihood function under the statistical model, while this estimator is obtained by a differential parameter of the likelihood function. The efficiency of two methods is considered by average mean square error for simulation data, and mean square error for actual data. For simulation data, the data are generated at only the first-order models of the RCA model. The results have shown that the least-squares method performs better than the maximum likelihood. The average mean square error of the least-squares method shows the minimum values in all cases that indicated their performance. Finally, these methods are applied to the actual data. The series of monthly averages of the Stock Exchange of Thailand (SET) index and daily volume of the exchange rate of Baht/Dollar are considered to estimate and forecast based on the RCA model. The result shows that the least-squares method outperforms the maximum likelihood method.

scholarly journals Best estimation for the Reliability of 2-parameter Weibull Distribution

2009 ◽  
Vol 6 (4) ◽  
pp. 705-710
Author(s):  
Baghdad Science Journal
Keyword(s):  
Maximum Likelihood ◽  
Weibull Distribution ◽  
Mean Square Error ◽  
Maximum Likelihood Method ◽  
Likelihood Method ◽  
Statistical Criterion ◽  
Mean Square ◽  
Simulation Process ◽  
The Mean ◽  
Two Parameter

This Research Tries To Investigate The Problem Of Estimating The Reliability Of Two Parameter Weibull Distribution,By Using Maximum Likelihood Method, And White Method. The Comparison Is done Through Simulation Process Depending On Three Choices Of Models (?=0.8 , ß=0.9) , (?=1.2 , ß=1.5) and (?=2.5 , ß=2). And Sample Size n=10 , 70, 150 We Use the Statistical Criterion Based On the Mean Square Error (MSE) For Comparison Amongst The Methods.

scholarly journals Data bank: nine numerical methods for determining the parameters of weibull for wind energy generation tested by five statistical tools

2021 ◽  
Vol 12 (2) ◽  
pp. 1114
Author(s):  
Ahmed Samir Badawi ◽  
Siti Hajar Yusoff ◽  
Alhareth Mohammed Zyoud ◽  
Sheroz Khan ◽  
Aisha Hashim ◽  
...  
Keyword(s):  
Maximum Likelihood ◽  
Numerical Methods ◽  
Root Mean Square Error ◽  
Mean Square Error ◽  
Root Mean Square ◽  
Prediction Accuracy ◽  
Maximum Likelihood Method ◽  
Likelihood Method ◽  
Mean Square ◽  
Modified Maximum Likelihood

This study aims to determine the potential of wind energy in the mediterranean coastal plain of Palestine. The parameters of the Weibull distribution were calculated on basis of wind speed data. Accordingly, two approaches were employed: analysis of a set of actual time series data and theoretical Weibull probability function. In this analysis, the parameters Weibull shape factor ‘<em>k</em>’ and the Weibull scale factor ‘<em>c</em>’ were adopted. These suitability values were calculated using the following popular methods: method of moments (MM), standard deviation method (STDM), empirical method (EM), maximum likelihood method (MLM), modified maximum likelihood method (MMLM), second modified maximum likelihood method (SMMLM), graphical method (GM), least mean square method (LSM) and energy pattern factor method (EPF). The performance of these numerical methods was tested by root mean square error (RMSE), index of agreement (IA), Chi-square test (X<sup>2</sup>), mean absolute percentage error (MAPE) and relative root mean square error (RRMSE) to estimate the percentage of error. Among the prediction techniques. The EPF exhibited the greatest accuracy performance followed by MM and MLM, whereas the SMMLM exhibited the worst performance. The RMSE achieved the best prediction accuracy, whereas the RRMSE attained the worst prediction accuracy.

scholarly journals On the Estimation of Parameter of Weighted Sums of Exponential Distribution

2014 ◽  
Vol 2014 ◽  
pp. 1-3
Author(s):  
N. Abbasi ◽  
A. Namju ◽  
N. Safari
Keyword(s):  
Maximum Likelihood ◽  
Exponential Distribution ◽  
Mean Square Error ◽  
Moment Method ◽  
Maximum Likelihood Method ◽  
Random Variable ◽  
Likelihood Method ◽  
Weighted Sums ◽  
Mean Square ◽  
The Mean

The random variable Zn,α=Y1+2αY2+⋯+nαYn, with α∈ℝ and Y1,Y2,…  being independent exponentially distributed random variables with mean one, is considered. Van Leeuwaarden and Temme (2011) attempted to determine good approximation of the distribution of Zn,α. The main problem is estimating the parameter α that has the main state in applicable research. In this paper we show that estimating the parameter α by using the relation between α and mode is available. The mean square error values are obtained for estimating α by mode, moment method, and maximum likelihood method.

scholarly journals Validation and Comparison of Different Statistical Models for the Prediction of Water Main Pipe Breaks in a Municipal Network in Québec, Canada

2016 ◽  
Vol 29 (1) ◽  
pp. 11-24 ◽  
Author(s):  
Sophie Duchesne ◽  
Babacar Toumbou ◽  
Jean-Pierre Villeneuve
Keyword(s):  
Maximum Likelihood ◽  
Least Squares ◽  
Maximum Likelihood Method ◽  
Least Squares Method ◽  
Likelihood Method ◽  
Water Main ◽  
Pipe Replacement ◽  
The Impact ◽  
Over Time ◽  
Observation Period

In this study, three models for the simulation of the number of breaks in a water main network are presented and compared: linear regression, the Weibull-Exponential-Exponential (WEE), and the Weibull-Exponential-Exponential-Exponential (WEEE) models. These models were calibrated using a database of recorded breaks in a real water main network of a municipality in the province of Québec, for the observation period 1976 to 1996, with the least squares and the maximum likelihood methods. The ability of these models to predict breaks over time was then evaluated by comparing the predicted number of breaks for the years 1997 to 2007 with the observed breaks in the network over the same time period. Results show that if the period of observation is short (around 20 years), calibration of the WEE and WEEE models with the maximum likelihood method leads to estimates that are closer to the observations than when these models are calibrated with the least squares method. When the observation period is longer (around 30 years), the predictions obtained with the models calibrated using the maximum likelihood or the least squares methods are similar. However, the use of the maximum likelihood method for calibration is only possible when data for the occurrence of each break for each pipe of the network are available (a pipe being a homogeneous network segment between two adjacent street junctions). If this is not the case, a trend line will be sufficient to predict the number of breaks over time, though this type of curve does not allow to account for pipe replacement scenarios. If the only information available is the total number of breaks on the network each year, then the impact of replacement scenarios could be simulated with the WEE and WEEE models calibrated using the least squares method.

scholarly journals "Evaluation of Some Methods for Estimating the Weibull Distribution Parameters"

2017 ◽  
Vol 4 (2) ◽  
pp. 8-14
Author(s):  
J. A. Labban ◽  
H. H. Depheal
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Weibull Distribution ◽  
Least Squares ◽  
Mean Square Error ◽  
Random Sample ◽  
Likelihood Estimation ◽  
Mean Square ◽  
Distribution Parameters

"This paper some of different methods to estimate the parameters of the 2-Paramaters Weibull distribution such as (Maximum likelihood Estimation, Moments, Least Squares, Term Omission). Mean square error will be considered to compare methods fits in case to select the best one. There by simulation will be implemented to generate different random sample of the 2-parameters Weibull distribution, those contain (n=10, 50, 100, 200) iteration each 1000 times."

scholarly journals Analysis of Risk using Value at Risk (VaR) After Crisis in 2008 Study in Stocks of Bank Mandiri, Bank BRI and Bank BNI in 2009-2011

2013 ◽  
Vol 5 (8) ◽  
pp. 394-400 ◽  
Author(s):  
Hasna Fadhila ◽  
Nora Amelda Rizal
Keyword(s):  
At Risk ◽  
Maximum Likelihood ◽  
Value At Risk ◽  
Maximum Likelihood Method ◽  
Historical Data ◽  
Likelihood Function ◽  
Likelihood Method ◽  
Normal Curve ◽  
Historical Simulation ◽  
Time Value

Value at Risk (VaR) is a tool to predict the greater loss less than the certain confidence level over a period of time. Value at Risk Historical Simulation produce reliable value of VaR because of the historical data and measure the skewness of the observe data. So, Value at Risk well used by investors to determine the risk to be faced on their investment. To calculate VAR it is better to use maximum likelihood, which has been considered for estimating from historical data and also available for estimating nonlinear model. It is also a mathematic function that can approximate return. From the maximum likelihood function with normal distribution, we can draw the normal curve at one tail test. This research conducted to calculate Value at Risk using maximum likelihood. The normal curve will be compared with data return at each bank (Bank Mandiri, Bank BRI and Bank BNI). Empirical results demonstrated that Bank BNI in 2009, Bank BRI in 2010 and Bank BNI in 2011, had less value of VaR by historical simulation in each year. It is concluded that by using maximum likelihood method in the estimation of VaR, has certain appropriates compared with the normal curve.

Monopulse Estimation of Unknown Polarization for Conformal Phased Array with Arbitrarily Oriented Dipoles

2021 ◽  
Author(s):  
Yuhao Deng ◽  
Julan Xie ◽  
Zishu He ◽  
Jun Li
Keyword(s):  
Least Squares ◽  
Phased Array ◽  
Least Squares Method ◽  
Likelihood Function ◽  
Hessian Matrix ◽  
Mean Square ◽  
Similar Technique ◽  
Dipole Orientation ◽  
Initial Direction ◽  
The Difference

Abstract In this paper, a novel monopulse estimator is proposed to surmount obstacles caused by unknown polarized pattern and the difference among each dipole orientation. Polarized pattern often alters the phased array response and we could hardly recover it if we known nothing about polarized parameters. The sum and difference beamforming of conformal phased array is affected due to the difference among each dipole orientation. Therefore the conventional monopulse estimator is dumped in this circumstance. The method proposed in this paper is a remarkable estimator based on maximum likelihood methodology. In this method, polarized parameters are considered as a part of desired signal and the least-squares solution of desired signal is obtained. With the desired signal solution, the likelihood function with respect to direction is derived at first. Then from the above, Jacobian and Hessian matrix of likelihood function is deduced. The boresight is considered as the initial direction value and the estimator of desired signal direction is obtained by Newton's formula. Finally, the polarized parameters are estimated by least-squares method using the direction estimator. The root-mean-square error (RMSE) of angle estimation is acceptable when prior polarized information is completely unknown. Polarized parameters are estimated by similar technique after we find out azimuth and elevation. Our research fills a gap of monopulse estimation with arbitrary polarization and diverse dipole arrangement.

scholarly journals Restricted maximum-likelihood method for learning latent variance components in gene expression data with known and unknown confounders

2020 ◽  
Author(s):  
Muhammad Ammar Malik ◽  
Tom Michoel
Keyword(s):  
Gene Expression ◽  
Maximum Likelihood ◽  
Latent Variables ◽  
Variance Components ◽  
Maximum Likelihood Method ◽  
Likelihood Function ◽  
Restricted Maximum Likelihood ◽  
Likelihood Method ◽  
Confounding Factors ◽  
Gradient Based

AbstractLinear mixed modelling is a popular approach for detecting and correcting spurious sample correlations due to hidden confounders in genome-wide gene expression data. In applications where some confounding factors are known, estimating simultaneously the contribution of known and latent variance components in linear mixed models is a challenge that has so far relied on numerical gradient-based optimizers to maximize the likelihood function. This is unsatisfactory because the resulting solution is poorly characterized and the efficiency of the method may be suboptimal. Here we prove analytically that maximumlikelihood latent variables can always be chosen orthogonal to the known confounding factors, in other words, that maximum-likelihood latent variables explain sample covariances not already explained by known factors. Based on this result we propose a restricted maximum-likelihood method which estimates the latent variables by maximizing the likelihood on the restricted subspace orthogonal to the known confounding factors, and show that this reduces to probabilistic PCA on that subspace. The method then estimates the variance-covariance parameters by maximizing the remaining terms in the likelihood function given the latent variables, using a newly derived analytic solution for this problem. Compared to gradient-based optimizers, our method attains equal or higher likelihood values, can be computed using standard matrix operations, results in latent factors that don’t overlap with any known factors, and has a runtime reduced by several orders of magnitude. We anticipate that the restricted maximum-likelihood method will facilitate the application of linear mixed modelling strategies for learning latent variance components to much larger gene expression datasets than currently possible.

scholarly journals Analysis of selected mathematical models of high-cycle S-N characteristics

2017 ◽  
Vol 3 (20) ◽  
pp. 227-240
Author(s):  
Przemysław Strzelecki ◽  
Janusz Sempruch ◽  
Tomasz Tomaszewski
Keyword(s):  
Fatigue Life ◽  
Maximum Likelihood ◽  
Maximum Likelihood Method ◽  
Least Squares Method ◽  
Construction Materials ◽  
The Other ◽  
Likelihood Method ◽  
Staircase Method ◽  
Aisi 1045 ◽  
Fatigue Characteristics

The paper presents two approaches of determining S-N fatigue characteristics. The first is a commonly used and well-documented approach based on the least squares method and staircase method for limited fatigue life and fatigue limit, accordingly. The other approach employs the maximum likelihood method. The analysis of the parameters obtained through both approaches exhibited minor differences. The analysis was performed for four steel construction materials, i.e. C45+C, 45, SUS630 and AISI 1045. It should be noted that the quantity of samples required in the second approach is significantly smaller than with the first approach, which translates into lower duration and costs of tests.

Curve Fitting of Heterodyne Data

1985 ◽  
Vol 39 (3) ◽  
pp. 480-484 ◽  
Author(s):  
B. R. Reddy
Keyword(s):  
Experimental Data ◽  
Maximum Likelihood ◽  
Least Squares ◽  
Curve Fitting ◽  
Maximum Likelihood Method ◽  
Heterodyne Detection ◽  
Likelihood Method ◽  
Fitting Procedure ◽  
Least Squares Curve Fitting

The least-squares curve fitting procedure of experimental data is described for heterodyne detection. Two independent methods, the Maximum Likelihood method of Fisher and SIMPLEX, have been tried. The relative merits and limitations are discussed in detail.

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