By L. Godfrey
This quantity includes an available dialogue reading computationally-intensive thoughts and bootstrap tools, supplying how one can increase the finite-sample functionality of recognized asymptotic checks for regression versions. The book uses the linear regression version as a framework for introducing simulation-based exams to aid practice econometric analyses.
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Additional info for Bootstrap Tests for Regression Models (Palgrave Texts in Econometrics)
In a predictive test, estimated parameters derived from an estimation sample are used to generate predicted values for a prediction sample. Let the former contain n1 > k observations and the latter contain n2 38 Bootstrap Tests for Regression Models observations, with n2 < k being the usual case. For simplicity of exposition, it is assumed that the ﬁrst n1 observations comprise the estimation sample. 1) is valid for i = 1, . . , n and, under the alternative, this model is only assumed to hold for i = 1, .
60) in which uˆ is the n-dimensional OLS residual vector obtained when all observations are used for estimation and uˇ is the n1 -dimensional OLS residual vector when only the estimation sample is used. Under the null hypothesis that the same classical assumptions apply to all n observations, P has the F n2 , n1 − k distribution with large values of this test statistic indicating predictive failure. 60) is assessed using right-hand tail critical values of the F n2 , n1 − k distribution, the null model under test includes the assumption that the errors ui are Normally distributed.
Non-standard tests for linear regression models In the discussion above, it has been assumed that the applied worker is using a test statistic that, when the null hypothesis is true, has a 36 Bootstrap Tests for Regression Models known distribution, at least asymptotically. In conventional asymptotically valid tests, the sample values of test statistics can be compared with critical values from standard distributions. These standard distributions are: N(0, 1) and t when the null hypothesis imposes one restriction; and χ 2 and F when several restrictions are to be tested.