HAC confidence interval for the response

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Hello. One can use Matlab's predict to get estimates of the response or dependent variable and its confidence interval for a desired value of the predictor or independent variable. Can we do somehow the same upon using hac? I'm interested in the default value of the option 'Prediction' being 'curve'.

回答(1 个)

Tamas Bodai
Tamas Bodai 2021-4-26
Maybe the following works. I don't accept this answer because i'm not sure if we can use mdl.DFE.
% Define your own data vectors 'y', 't' first, and then make a table
tbl = table(y,t);
% Fit the linear model to have mdl.DFE
mdl = fitlm(tbl,'y ~ t');
% Consider the response in the middle of the interval
%[ypred,yci] = predict(mdl,t(T/2)); % instead of this, do as follows
[EstCov, se, coeff] = hac(t,y);
[ypred,yci] = mypredict(t(T/2),coeff,EstCov,mdl.DFE,0.05);
% This is a stripped down version of function 'predci' called in function
% 'predictDesign' in CompactLinearModel.m.
function [ypred,yCI] = mypredict(X,beta,Sigma,dfe,alpha)
X = [1 X];
% Compute the predicted values at the new X.
ypred = X * beta;
% confi interval for fitted curve
varpred = sum((X*Sigma) .* X,2);
% pointwise
crit = tinv(1-alpha/2,dfe);
delta = sqrt(varpred) * crit;
yCI = [ypred-delta ypred+delta];
end
  1 个评论
Tamas Bodai
Tamas Bodai 2021-5-13
编辑:Tamas Bodai 2021-5-13
I have found an answer here:
https://www.mathworks.com/help/econ/correct-ols-coefficient-covariance-estimate.html
From the function nlpredci, you can read out the degree of freedom of the t-distribution applied. Mind, however, that for small sample size, it is not a t-distribution, it appears to me, or, the approximate t-distribution is of a different degree of freedom.

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