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What If the Disturbances Have Nonzero Expectations or Different Variances?

in Introductory Econometrics: Intuition, Proof, and Practice

Published in print:
2011
Published Online:
June 2013
ISBN:
9780804772624
eISBN:
9780804777209
Item type:
chapter
Publisher:
Stanford University Press
DOI:
10.11126/stanford/9780804772624.003.0008
Subject:
Economics and Finance, Econometrics

This chapter shows that the εi's must have the same expected value for regression to make any sense. However, we cannot tell if the εi's have a constant expected value that is different from zero, ... More


What If the Disturbances Are Correlated?

in Introductory Econometrics: Intuition, Proof, and Practice

Published in print:
2011
Published Online:
June 2013
ISBN:
9780804772624
eISBN:
9780804777209
Item type:
chapter
Publisher:
Stanford University Press
DOI:
10.11126/stanford/9780804772624.003.0009
Subject:
Economics and Finance, Econometrics

This chapter deals with the possibility that the disturbances are correlated with each other. In this case, ordinary least squares (OLS) estimates are still unbiased. However, they are no longer best ... More


Introduction to the Kalman filter

C. Snyder

in Advanced Data Assimilation for Geosciences: Lecture Notes of the Les Houches School of Physics: Special Issue, June 2012

Published in print:
2014
Published Online:
March 2015
ISBN:
9780198723844
eISBN:
9780191791185
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198723844.003.0003
Subject:
Physics, Geophysics, Atmospheric and Environmental Physics

This chapter introduces The Kalman filter, which implements Bayesian data assimilation for linear, Gaussian systems. Its update equations can also be derived as the best linear unbiased estimator ... More


Selected topics in multiscale data assimilation

M. Bocquet, L. Wu, F. Chevallier, and M. R. Kookhan

in Advanced Data Assimilation for Geosciences: Lecture Notes of the Les Houches School of Physics: Special Issue, June 2012

Published in print:
2014
Published Online:
March 2015
ISBN:
9780198723844
eISBN:
9780191791185
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198723844.003.0018
Subject:
Physics, Geophysics, Atmospheric and Environmental Physics

This chapter discusses several approaches to developing original theoretical approaches to assimilate information at a given scale and consistently propagate it to other scales. This is motivated by ... More


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