Markov-Modulated Linear Regression: Tasks and Challenges in Transport Modelling

2018 ◽  
pp. 223-231
Author(s):  
Nadezda Spiridovska
Keyword(s):  
Linear Regression ◽  
Transport Modelling ◽  
Markov Modulated

scholarly journals Markov-Modulated Linear Regression Parameter Estimation Using a Convolution of Exponential Densities

2020 ◽  
Vol 14 ◽  
Keyword(s):  
Linear Regression ◽  
External Environment ◽  
Markov Property ◽  
Estimation Procedure ◽  
Model Parameters ◽  
Additive Process ◽  
Markov Additive Process ◽  
Markov Modulated ◽  
Special Case ◽  
Irreducible Markov Chain

Markov-modulated linear regression model is a special case of the Markov-additive process (𝒀, 𝑱) = {(𝒀(𝒕), 𝑱(𝒕)), 𝒕 ≥ 𝟎}, where component J is called Markov, and component Y is additive and described by a linear regression. The component J is a continuous-time homogeneous irreducible Markov chain with the known transition intensities between the states. Usually this Markov component is called the external environment or background process. Unknown regression coefficients depend on external environment state, but regressors remain constant. This research considers the case, when the Markov property is not satisfied, namely, the sojourn time in each state is not exponentially distributed. Estimation procedure for unknown model parameters is described when it’s possible to represent transition intensities as a convolution of exponential densities. An efficiency of such an approach is evaluated by a simulation.

Review of An Introduction to Linear Regression and Correlation. 2nd ed.

1985 ◽  
Vol 30 (10) ◽  
pp. 824-824
Author(s):  
William L. Hays
Keyword(s):  
Linear Regression
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