On one twoepoch linear model with the nuisance parameters

2008 ◽  
Vol 58 (1) ◽  
Author(s):  
Karel Hron
Keyword(s):  
Linear Regression ◽  
Regression Model ◽  
Linear Model ◽  
Linear Regression Model ◽  
Mean Value ◽  
Nuisance Parameters ◽  
Variable Parameters ◽  
Linear Estimators ◽  
Theoretical Results

AbstractThe optimum linear estimators of the useful mean value parameters within a linear regression model with the stable and variable parameters and with the nuisance parameters are derived including their characteristics of accuracy. Some verification of theoretical results is presented.

scholarly journals Impact of Climate Factors in Modeling and Predicting the Transmission of Meningitis in Africa: The Case of Burkina Faso

2020 ◽  
Author(s):  
Haoua Tall ◽  
Issaka Yaméogo ◽  
Ryan Novak ◽  
Lionel L Ouedraogo ◽  
Ousmane Ouedraogo ◽  
...  
Keyword(s):  
Relative Humidity ◽  
Linear Regression ◽  
Regression Model ◽  
Burkina Faso ◽  
Linear Model ◽  
Linear Regression Model ◽  
Multivariate Linear Regression ◽  
Multivariate Linear Regression Model ◽  
Climate Factors ◽  
Multivariate Linear Model

Abstract Background: Meningitis is a major cause of morbidity in the world. Previous studies showed that climate factors influence the occurrence of meningitis. A multiple linear regression model was developed to forecast meningitis cases in Burkina Faso using climate factors. However, the multivariate linear regression model based on times series data may produce fallacious results given the autocorrelation of errors. Aims: The aim of the study is to develop a model to quantify the effect of climate factors on meningitis cases, and then predict the expected weekly incidences of meningitis for each district. Data and methods: The weekly cases of meningitis come from the Ministry of Health and covers the period 2005-2017. Climate data were collected daily in 10 meteorological stations from 2005 to 2017 and were provided by the national meteorological Agency of Burkina Faso. An ARIMAX and a multivariate linear regression model were estimated separately for each district. Results: The multivariate linear model is inappropriate to model the number of meningitis cases due to autocorrelation of errors. With the ARIMAX Model, Temperature is significantly associated with an increase of meningitis cases in 3 of 10 districts, while relative humidity is significantly associated with a decrease of meningitis cases in 3 of the 10 districts. The effect of wind speed and precipitation is not significant at the 5% level in all 10 districts. The prediction of meningitis cases with 8 test observations provides an average absolute error ranging from 0.99 in Boromo and Bogandé to 7.22 in the district of Ouagadougou. Conclusion: The ARIMAX model is more appropriate than the multivariate linear model to analyze the dynamics of meningitis cases. Climatic factors such as temperature and relative humidity have a significant influence on the occurrence of meningitis in Burkina Faso; the temperature influences it positively and the relative humidity influences it negatively.

Impact of Climate Factors in Modeling and Predicting the Transmission of Meningitis in Africa: The Case of Burkina Faso

2020 ◽  
Author(s):  
Haoua Tall ◽  
Issaka Yaméogo ◽  
Ryan Novak ◽  
Lionel L Ouedraogo ◽  
Ousmane Ouedraogo ◽  
...  
Keyword(s):  
Relative Humidity ◽  
Linear Regression ◽  
Regression Model ◽  
Burkina Faso ◽  
Linear Model ◽  
Linear Regression Model ◽  
Multivariate Linear Regression ◽  
Multivariate Linear Regression Model ◽  
Climate Factors ◽  
Multivariate Linear Model

Abstract Background Meningitis is a major cause of morbidity in the world. Previous studies showed that climate factors influence the occurrence of meningitis. A multiple linear regression model was developed to forecast meningitis cases in Burkina Faso using climate factors. However, the multivariate linear regression model based on times series data may produce fallacious results given the autocorrelation of errors.Aims The aim of the study is to develop a model to quantify the effect of climate factors on meningitis cases, and then predict the expected weekly incidences of meningitis for each district.Data and methods The weekly cases of meningitis come from the Ministry of Health and covers the period 2005-2017. Climate data were collected daily in 10 meteorological stations from 2005 to 2017 and were provided by the national meteorological Agency of Burkina Faso. An ARIMAX and a multivariate linear regression model were estimated separately for each district.Results The multivariate linear model is inappropriate to model the number of meningitis cases due to autocorrelation of errors. With the ARIMAX Model, Temperature is significantly associated with an increase of meningitis cases in 3 of 10 districts, while relative humidity is significantly associated with a decrease of meningitis cases in 3 of the 10 districts. The effect of wind speed and precipitation is not significant at the 5% level in all 10 districts. The prediction of meningitis cases with 8 test observations provides an average absolute error ranging from 0.99 in Boromo and Bogandé to 7.22 in the district of Ouagadougou.Conclusion The ARIMAX model is more appropriate than the multivariate linear model to analyze the dynamics of meningitis cases. Climatic factors such as temperature and relative humidity have a significant influence on the occurrence of meningitis in Burkina Faso; the temperature influences it positively and the relative humidity influences it negatively.

THE LIMIT DISTRIBUTION OF THE CUSUM OF SQUARES TEST UNDER GENERAL MIXING CONDITIONS

2008 ◽  
Vol 24 (3) ◽  
pp. 809-822 ◽  
Author(s):  
Ai Deng ◽  
Pierre Perron
Keyword(s):  
Linear Regression ◽  
Regression Model ◽  
Limit Distribution ◽  
Linear Regression Model ◽  
Nuisance Parameters ◽  
Standard Approach ◽  
Mixing Conditions ◽  
Cumulative Sum ◽  
Distribution Free ◽  
Times Series

We consider the cumulative sum (CUSUM) of squares test in a linear regression model with general mixing assumptions on the regressors and the errors. We derive its limit distribution and show how it depends on the nature of the error process. We suggest a corrected version that has a limit distribution free of nuisance parameters. We also discuss how it provides an improvement over the standard approach to testing for a change in the variance in a univariate times series. Simulation evidence is presented to support this.

scholarly journals On the Stochastic Restrictedr-kClass Estimator and Stochastic Restrictedr-dClass Estimator in Linear Regression Model

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Jibo Wu
Keyword(s):  
Linear Regression ◽  
Regression Model ◽  
Linear Regression Model ◽  
Mean Squared Error ◽  
Multiple Linear Regression Model ◽  
Error Matrix ◽  
Squared Error ◽  
The Mean ◽  
Linear Restrictions ◽  
Theoretical Results

The stochastic restrictedr-kclass estimator and stochastic restrictedr-dclass estimator are proposed for the vector of parameters in a multiple linear regression model with stochastic linear restrictions. The mean squared error matrix of the proposed estimators is derived and compared, and some properties of the proposed estimators are also discussed. Finally, a numerical example is given to show some of the theoretical results.

scholarly journals Iterative Estimators of Parameters in Linear Models with Partially Variant Coefficients

2007 ◽  
Vol 17 (2) ◽  
pp. 179-187 ◽  
Author(s):  
Shaolin Hu ◽  
Karl Meinke ◽  
Rushan Chen ◽  
Ouyang Huajiang
Keyword(s):  
Linear Regression ◽  
Regression Model ◽  
Linear Model ◽  
Linear Regression Model ◽  
Generalized Linear Model ◽  
Linear Models ◽  
Iterative Algorithms ◽  
Important Application ◽  
New Model ◽  
Special Case

Iterative Estimators of Parameters in Linear Models with Partially Variant CoefficientsA new kind of linear model with partially variant coefficients is proposed and a series of iterative algorithms are introduced and verified. The new generalized linear model includes the ordinary linear regression model as a special case. The iterative algorithms efficiently overcome some difficulties in computation with multidimensional inputs and incessantly appending parameters. An important application is described at the end of this article, which shows that this new model is reasonable and applicable in practical fields.

Statistical Inference and Application for Partially Linear Models

2015 ◽  
Vol 733 ◽  
pp. 910-913
Author(s):  
Jing Zhang ◽  
Hong Xia Guo
Keyword(s):  
Linear Regression ◽  
Regression Model ◽  
Linear Model ◽  
Linear Regression Model ◽  
Linear Models ◽  
Linear Regression Analysis ◽  
Principal Component ◽  
Partial Linear Model ◽  
Partially Linear Regression Model ◽  
Partially Linear

As partially linear regression model contains parameters part and the nonparametric part, it is better than the linear model. Partially linear regression model is more freedom, flexible, and can seize the characteristics of data. This passage first reduces the dimension of expenditure index data using principal component analysis. Then based on the dimension-reduced data, a partial linear model is established to forecast expenditure on army. The results show a great advantage over those by stepwise linear regression analysis.

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