Bias-correction of coefficients following general-to-specific model selection

Takes a vector of coefficients (valid for orthogonal variables), their standard errors, the significance level the variables were selected at, and the sample size, to return bias-corrected coefficient estimates to account for the bias induced by model selection.

Usage

biascorr(b, b.se, p.alpha, T)

Arguments

b: a Kx1 vector of coefficients.
b.se: a Kx1 vector of standard errors of the coefficients in 'b'.
p.alpha: numeric value between 0 and 1, the significance level at which selection was conducted.
T: integer, the sample size of the original model selection regression.

Details

The function computes the bias-corrected estimates of coefficients in regression models post general-to-specific model selection using the approach by Hendry and Krolzig (2005). The results are valid for orthogonal regressors only. Bias correction can be applied to the coefficient path in isat models where the only additional covariate besides indicators is an intercept - see Pretis (2015).

Value

Returns a Kx3 matrix, where the first column lists the original coefficients, the second column the one-step corrected coefficients, and the third column the two-step bias-corrected coefficients.

References

Hendry, D.F. and Krolzig, H.M. (2005): 'The properties of automatic Gets modelling'. Economic Journal, 115, C32-C61.

Pretis, F. (2015): 'Testing for time-varying predictive accuracy using bias-corrected indicator saturation'. Oxford Department of Economics Discussion Paper.

Pretis, Felix, Reade, James and Sucarrat, Genaro (2018): 'Automated General-to-Specific (GETS) Regression Modeling and Indicator Saturation for Outliers and Structural Breaks'. Journal of Statistical Software 86, Number 3, pp. 1-44

Author

Felix Pretis, http://www.felixpretis.org/

Examples

###Bias-correction of the coefficient path of the Nile data
#nile <- as.zoo(Nile)
#isat.nile <- isat(nile, sis=TRUE, iis=FALSE, plot=TRUE, t.pval=0.005)
#var <- isatvar(isat.nile)
#biascorr(b=var$const.path, b.se=var$const.se, p.alpha=0.005, T=length(var$const.path))

##Bias-correction of the coefficient path on artificial data
#set.seed(123)
#d <- matrix(0,100,1)
#d[35:55] <- 1
#e <- rnorm(100, 0, 1)
#y <- d*1  +e
  
#ys <- isat(y, sis=TRUE, iis=FALSE, t.pval=0.01)
#var <- isatvar(ys)
#biascorr(b=var$const.path, b.se=var$const.se, p.alpha=0.01, T=length(var$const.path))