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When a linear model is constructed as ''Y,,t,, = β,,0,, + β,,1,,x,,t,, + e,,t,,'' but estimated as ''Y,,t,, = β,,0,, + β,,1,,X,,t,, + e,,t,, = β,,0,, + β,,1,,(x,,t,, + u,,t,,) + e,,t,,'', then the expected values are characterized by: When a linear model is constructed as ''Y,,t,, = β,,0,, + β,,1,,x,,t,, + e,,t,,'' but estimated as ''Y,,t,, = βˆ,,0,, + βˆ,,1,,X,,t,, = βˆ,,0,, + βˆ,,1,,(x,,t,, + u,,t,,)'', then the expected values are characterized by:
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We assume that ''x,,t,,'', ''e,,t,,'', and ''u,,t,,'' are all independent.

Measurement Error Models

Measurement Error Models (ISBN: 9780470316665) was written by Wayne A. Fuller in 1987.

A measurement Xt is decomposed into the true value xt and the measurement error ut.

When a linear model is constructed as Yt = β0 + β1xt + et but estimated as Yt = βˆ0 + βˆ1Xt = βˆ0 + βˆ1(xt + ut), then the expected values are characterized by:

exp1.svg

exp2.svg

And the covariance matrix is specified as:

covar.svg

We assume that xt, et, and ut are all independent.


CategoryRicottone

MeasurementErrorModels (last edited 2025-04-29 19:24:42 by DominicRicottone)