Effects of the estimation of covariance matrix parameters in the generalized multivariate linear model

1984 ◽  
Vol 13 (5) ◽  
pp. 639-650 ◽  
Author(s):  
Gregory C. Reinsel
Keyword(s):  
Linear Model ◽  
Covariance Matrix ◽  
Multivariate Linear Model

scholarly journals Properties of an MLE algorithm for the multivariate linear model with a separable covariance matrix structure

2021 ◽  
Vol 58 (1) ◽  
pp. 69-79
Author(s):  
Anna Szczepańska-Álvarez ◽  
Bogna Zawieja ◽  
Adolfo Álvarez
Keyword(s):  
Maximum Likelihood ◽  
Linear Model ◽  
Covariance Matrix ◽  
Simulation Study ◽  
Maximum Likelihood Estimators ◽  
Matrix Structure ◽  
Multivariate Linear Model ◽  
Compound Symmetry ◽  
Symmetry Structure

Summary In this paper we present properties of an algorithm to determine the maximum likelihood estimators of the covariance matrix when two processes jointly affect the observations. Additionally, one process is partially modeled by a compound symmetry structure. We perform a simulation study of the properties of an iteratively determined estimator of the covariance matrix.

Structural distributions in the multivariate linear model

Optimization ◽  
1976 ◽  
Vol 7 (5) ◽  
pp. 679-683
Author(s):  
Michael Nussbaum
Keyword(s):  
Linear Model ◽  
Multivariate Linear Model

scholarly journals Estimates of MM type for the multivariate linear model

2011 ◽  
Vol 102 (9) ◽  
pp. 1280-1292 ◽  
Author(s):  
Nadia L. Kudraszow ◽  
Ricardo A. Maronna
Keyword(s):  
Linear Model ◽  
Multivariate Linear Model

The Multivariate Linear Model

2017 ◽  
pp. 491-529
Author(s):  
Marvin H. J. Gruber
Keyword(s):  
Linear Model ◽  
Multivariate Linear Model

The Multivariate Linear Model

2008 ◽  
pp. 221-250
Keyword(s):  
Linear Model ◽  
Multivariate Linear Model

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.

A note on reduction of the number of parameters in linear statistical models

2012 ◽  
Vol 62 (1) ◽  
Author(s):  
Lubomír Kubáček
Keyword(s):  
Statistical Analysis ◽  
Linear Model ◽  
Covariance Matrix ◽  
Statistical Models ◽  
Approximate Model ◽  
Model Matrix ◽  
The Mean ◽  
Linear Statistical Models

AbstractIn certain settings the mean response is modeled by a linear model using a large number of parameters. Sometimes it is desirable to reduce the number of parameters prior to conducting the experiment and prior to the actual statistical analysis. Essentially, it means to formulate a simpler approximate model to the original “ideal” one. The goal is to find conditions (on the model matrix and covariance matrix) under which the reduction does not influence essentially the data fit. Here we try to develop such conditions in regular linear model without and with linear restraints. We emphasize that these conditions are independent of observed data.

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.

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