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Measurement Error Models

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

A measurement X_t is decomposed into the true value x_t and the measurement error u_t.

When a linear model is constructed as Y_t = β₀ + β₁x_t + e_t but estimated as Y_t = βˆ₀ + βˆ₁X_t = βˆ₀ + βˆ₁(x_t + u_t), then the expected values are characterized by:

And the covariance matrix is specified as:

We assume that x_t, e_t, and u_t are all independent.

The regression coefficient that has been attenuated by measurement error is represented as γ.

The relationship between γ and β₁ is characterized by κ.

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+The regression coefficient that has been attenuated by measurement error is represented as ''γ''.

{{attachment:gamma.svg}}

The relationship between ''γ'' and ''β,,1,,'' is characterized by ''κ''.

{{attachment:kappa.svg}}

Diff for "MeasurementErrorModels"

Measurement Error Models