Rectangular Confidence Regions

Confidence Hypercubes

Description

R = RCR(S) computes the semi-edge-length of the mean-centered hypercube with 95% probability given S, which is either a covariance matrix or a vector of standard deviations from a multivariate normal distribution. If S is a real, nonnegative vector, RCR(S) is equivalent to RCR(DIAG(S.^2)). Scalar S is treated as a standard deviation.

R = RCR(S,P) computes the semi-edge-length of the hypercube with probability P instead of the default, which is 0.95. R is the two-tailed, equicoordinate quantile corresponding to P. The hypercube edge-length is 2*R.

R = RCR(S,P,NP) uses NP quadrature points instead of the default, which is 2^11. Smaller values of NP result in faster computation, but may yield less accurate results. Use [] as a placeholder to obtain the default value of P.

R = RCR(S,P,NP,M) performs a bootstrap validation with M normally distributed random samples of size 1e6. Use [] as a placeholder to obtain the default value of NP.

R = RCR(S,P,NP,[M N]) performs a bootstrap validation with M normally distributed random samples of size N.

[R,E] = RCR(S,...) returns an error estimate E.

Acknowledgements

The author wishes to acknowledge the following in the creation of this submission:
Confidence Region Radius

• MATLAB release: MATLAB 6.5 (R13)

[Viktor]

Seems to be some error during call to fzero. 'options' seem to be correct. Any ideas?

>> r=rcr(1)
??? Error using ==> optimget
Too many input arguments.

Error in ==> fzero at 143
tol = optimget(options,'TolX',defaultopt,'fast');

Error in ==> rcr at 131
r=abs(fzero(@difference,R0,options,s,p,np));
 

[Tom Davis]

I cannot replicate this problem using MATLAB 7.5.

r = rcr(1)

yields r = 1.9600 as expected.

[Viktor]

Hi. Im using MATLAB 7.7 and the problem persists.

A general question as well which you might know. How hard is it to compute confidence regions for higher dimensions, say n=50, with correlated variables?

[Tom Davis]

Please send me an email message, Viktor. Thanks.

[Tom Davis]

I cannot replicate this problem using MATLAB 7.7.0.471 (Sept. 17, 2008).

r = rcr(1)

yields r = 1.9600 as expected.