scholarly journals Impact of Algorithm Selection on Modeling Ozone Pollution: A Perspective on Box and Tiao (1975)

Forests ◽  
2020 ◽  
Vol 11 (12) ◽  
pp. 1311
Author(s):  
Mihaela Paun ◽  
Nevine Gunaime ◽  
Bogdan M. Strimbu
Keyword(s):  
Maximum Likelihood ◽  
Los Angeles ◽  
Mean Square Error ◽  
Arima Model ◽  
Autoregressive Process ◽  
Least Square ◽  
Mean Square ◽  
Ozone Pollution ◽  
Complex Models ◽  
The Mean

Estimation using a suboptimal method can lead to imprecise models, with cascading effects in complex models, such as climate change or pollution. The goal of this study is to compare the solutions supplied by different algorithms used to model ozone pollution. Using Box and Tiao (1975) study, we have predicted ozone concentration in Los Angeles with an ARIMA and an autoregressive process. We have solved the ARIMA process with three algorithms (i.e., maximum likelihood, like Box and Tiao, conditional least square and unconditional least square) and the autoregressive process with four algorithms (i.e., Yule–Walker, iterative Yule–Walker, maximum likelihood, and unconditional least square). Our study shows that Box and Tiao chose the appropriate algorithm according to the AIC but not according to the mean square error. Furthermore, Yule–Walker, which is the default algorithm in many software, has the least reliable results, suggesting that the method of solving complex models could alter the findings. Finally, the model selection depends on the technical details and on the applicability of the model, as the ARIMA model is suitable from the AIC perspective but an autoregressive model could be preferred from the mean square error viewpoint. Our study shows that time series analysis should consider not only the model shape but also the model estimation, to ensure valid results.

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.

On Some Asymptotic Results for Multivariate Autoregressive Models with Estimated Parameters

1986 ◽  
Vol 35 (3-4) ◽  
pp. 123-132 ◽  
Author(s):  
A. K. Basu ◽  
S. Sen Roy
Keyword(s):  
Mean Square Error ◽  
Autoregressive Process ◽  
Mean Square ◽  
Asymptotic Equivalence ◽  
Asymptotic Results ◽  
Stable Case ◽  
Estimated Parameters ◽  
Multivariate Autoregressive Models ◽  
The Mean ◽  
Dependent Error

In this paper the asymptotic equivalence of the estimated predictor and the optimal predictor of k-dimensional pth order autoregressive process in the stable case with dependent error variables bas been shown. An expression for the mean square error of the estimated predictor has also been derived.

scholarly journals Econometric Estimation of Production Function with Applications

2019 ◽  
pp. 57-61 ◽  
Author(s):  
Awoingo Adonijah Maxwell ◽  
Isaac Didi Essi
Keyword(s):  
Monte Carlo ◽  
Mean Square Error ◽  
Production Function ◽  
Least Square ◽  
Production Model ◽  
Mean Square ◽  
Unknown Parameters ◽  
Data Generating Process ◽  
The Mean ◽  
Input Variables

This study focuses on Monte Carlo Methods in parameter estimation of production function. The ordinary least square (OLS) method is used to estimate the unknown parameters. The Monte Carlo simulation methods are used for the data generating process. The Cobb-Douglas production model with multiplicative error term is fitted to the data generated. From tables 1.1 to 1.3, the mean square error (MSE) of 1 are 0.007678, 0.001972 and 0.001253 respectively for sample sizes 20, 40 and 80. Our finding showed that the mean square error (MSE) value varies with the sum of the powers of the input variables.

scholarly journals Robustness Test of the Two Stage K-L Estimator in Models with Multicollinear Regressors and Autocorrelated Error Term

2021 ◽  
pp. 22-33
Author(s):  
Zubair Mohammed Anono ◽  
Adenomon Monday Osagie
Keyword(s):  
Maximum Likelihood ◽  
Mean Square Error ◽  
Linear Regression Analysis ◽  
Real Life ◽  
Multiple Linear Regression Analysis ◽  
Least Square ◽  
Mean Square ◽  
Two Stage ◽  
Data Set ◽  
Real Life Data

In a classical multiple linear regression analysis, multicollinearity and autocorrelation are two main basic assumption violation problems. When multicollinearity exists, biased estimation techniques such as Maximum Likelihood, Restricted Maximum Likelihood and most recent the K-L estimator by Kibria and Lukman [1] are preferable to Ordinary Least Square. On the other hand, when autocorrelation exist in the data, robust estimators like Cochran Orcutt and Prais-Winsten [2] estimators are preferred. To handle these two problems jointly, the study combines the K-L with the Prais-Winsten’s two-stage estimator producing the Two-Stage K-L estimator proposed by Zubair & Adenomon [3]. The Mean Square Error (MSE) and Root Mean Square Error (RMSE) criterion was used to compare the performance of the estimators. Application of the estimators to two (2) real life data set with multicollinearity and autocorrelation problems reveals that the Two Stage K-L estimator is generally the most efficient.

On Asymptotic Prediction Problems for Autoregressive Models with Explosive and Other Roots

1989 ◽  
Vol 38 (1-2) ◽  
pp. 43-56 ◽  
Author(s):  
A. K. Basu ◽  
S. Sen Roy
Keyword(s):  
Mean Square Error ◽  
Asymptotic Properties ◽  
Autoregressive Process ◽  
Autoregressive Models ◽  
Mean Square ◽  
The Mean ◽  
Set Up ◽  
Prediction Problems ◽  
Dependent Error

In this paper the asymptotic properties of the estimated predictor of a k-dimensional, pth order autoregressive process with dependent error variables and a general set-up of the roots have been considered. An expression for the mean-square-error of the estimated predictor has also been obtained.

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 ESTIMASI PARAMETER DISTRIBUSI EKPONENSIAL PADA LOKASI TERBATAS

2007 ◽  
Vol 1 (2) ◽  
pp. 1-7
Author(s):  
Mozart W. Talakua ◽  
Jefri Tipka
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Mean Square Error ◽  
Likelihood Estimation ◽  
Consistent Estimator ◽  
Parameter Distribution ◽  
Mean Square ◽  
The Common ◽  
The Mean ◽  
Best Estimator

The common method in Estimating Parameter Distribution Exponential at Finite Location is Maximum Likelihood Estimation (MLE).The best estimator is consistent estimator. Because of The Mean Square Error (MSE) can be used in comparing some detectable estimators that it had looking for with Maximum Likelihood Estimation (MLE) so can find the consistent estimator in Estimating Parameter Distribution Exponential At Finite Location

The Bordeaux Automatic Meridian Circle

1978 ◽  
Vol 48 ◽  
pp. 227-228
Author(s):  
Y. Requième
Keyword(s):  
Mean Square Error ◽  
Mean Square ◽  
Meridian Circle ◽  
The Mean ◽  
Full Automation

In spite of important delays in the initial planning, the full automation of the Bordeaux meridian circle is progressing well and will be ready for regular observations by the middle of the next year. It is expected that the mean square error for one observation will be about ±0.”10 in the two coordinates for declinations up to 87°.

Limit tolerances for sums of measurement errors

2018 ◽  
Vol 934 (4) ◽  
pp. 59-62
Author(s):  
V.I. Salnikov
Keyword(s):  
Normal Distribution ◽  
Mean Square Error ◽  
Gaussian Distribution ◽  
Measurement Errors ◽  
Theory And Practice ◽  
Mean Square ◽  
The Mean ◽  
Limiting Values ◽  
Limiting Value

The question of calculating the limiting values of residuals in geodesic constructions is considered in the case when the limiting value for measurement errors is assumed equal to 3m, ie ∆рred = 3m, where m is the mean square error of the measurement. Larger errors are rejected. At present, the limiting value for the residual is calculated by the formula 3m√n, where n is the number of measurements. The article draws attention to two contradictions between theory and practice arising from the use of this formula. First, the formula is derived from the classical law of the normal Gaussian distribution, and it is applied to the truncated law of the normal distribution. And, secondly, as shown in [1], when ∆рred = 2m, the sums of errors naturally take the value equal to ?pred, after which the number of errors in the sum starts anew. This article establishes its validity for ∆рred = 3m. A table of comparative values of the tolerances valid and recommended for more stringent ones is given. The article gives a graph of applied and recommended tolerances for ∆рred = 3m.

Sign in / Sign up

Export Citation Format

Share Document