Abstract
When the errors in a regression model are independent and identically distributed, the Gauss-Markov theorem establishes that the ordinary least squares (OLS) estimator is “BLUE” (Best Linear Unbiased Estimator) (see Chap. 2). So far, all of the examples we have encountered in this text have met these assumptions, but in this chapter you will learn how to detect violations of the Gauss-Markov assumptions and address some of the problems that they can create.
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Notes
- 1.
We will use a simple linear regression model (i.e., with a single predictor) throughout this chapter for simplicity, but the issues apply to multiple regression as well.
- 2.
Simulations are sometimes called Monte Carlo simulations. A related technique known as resampling will be discussed in Chap. 7.
- 3.
Unfortunately, there is no established standard for quantifying the severity of heteroscedasticity.
- 4.
Chapter 13 offers more detailed coverage of time series analyses.
- 5.
In fact, 48% of adjacent residuals lie on opposite sides of the midpoint in the left-hand panel of Fig. 6.4, but only 18% do so in the right-hand panel.
- 6.
The Breusch–Godfrey test is sometimes called the Lagrange Multiplier test.
- 7.
The estimation assumes an AR(1) model for the residuals. Methods for estimating higher-order autocorrelations will be discussed in Chap. 13.
- 8.
This will not always be true, however. When the predictor is ordered (e.g., days of the month), the standard errors from OLS estimation will often be smaller than the ones produced by FGLS.
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Brown, J.D. (2018). Generalized Least Squares Estimation. In: Advanced Statistics for the Behavioral Sciences. Springer, Cham. https://doi.org/10.1007/978-3-319-93549-2_6
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