Sensitivity of T-Statistic (Asymptotic thumb rule)

Rule of Thumb: t-statistic being sensitive to nuisance parameters in variance.

Description

[decision, RHO,ASY_MEAN,ASY_VARIANCE] =t_sens(X,C,T)
% Rule of Thumb: Banerjee, A.N. and J.R. Magnus (2000)
% Testing for restriction C \beta = c0
% The t-statistic is sensitive (at the 50% level)
% to covariance misspecification if and only if
% \phi/c>0.40
% input: X = the matrix of independent data (n x k)
% C = the restriction k x 1
% T = the Derivative of the covariance matrix at \theta = 0
% In this demo the derivative matrix A is the derivative of
% variance covariance matrix of AR(1)(same as MA(1))) at the \theta =0
% where \theta is the AR(1) parameter.
%
% Output : decision = 1 then t-statistic is sensitive to
% nuisance parameter \theta
% = 0 otherwise
% RHO = \phi/c
%
% ASY_MEAN,ASY_VARIANCE = asymptotic mean and variance of RHO
% ------------------------------------------------------------------------
% Reference: Banerjee, A.N. and J.R. Magnus (2000), On the sensitivity of the usual
% t- and F-tests to covariance misspecification, Journal of Econometrics,
% Vol 95(10), pp 157-176.
% ------------------------------------------------------------------------
% ........... PROCEDURES FOR SENSITIVITY ........
%
% Anurag N Banerjee
% Durham University,
% UK
% [e-mail] Date 17/11/2009
% ..............................................................
% This program is in the public domain. While the author disclaims
% any responsibility for the performance of this software, he
% would appreciate receiving any comments.
%
% This written by Anurag N Banerjee and may be distributed as freeware
% for public non-commercial use. Please provide appropriate
% acknowledgment if this supports supports published work.
% ..................................................................

• MATLAB release: MATLAB 6.0 (R12)