How do I find the confidence intervals for the estimated coefficients of a bounded nonlinear regression analysis?

I am performing a nonlinear regression analysis to estimate the coefficients of an equation given observed values. These estimated coefficients are constrained to lie within a range of values, say from 0 to 1. I like to know the confidence intervals around each of these estimated coefficients.

Answer 1

[MathWorks Support Team]

There are no tools in MATLAB 7.5 (R2007b) that allow you to directly calculate the confidence interval on a bounded nonlinear regression analysis.

A useful technique for working around this limitation is to transform your unknown coefficients from the range [0, 1] to (-inf, + inf) via the logistic function. You would then perform an unbounded nonlinear regression on this transformed problem, find the confidence intervals using techniques similar to the Statistic Toolbox's NLPARCI, and then re-transform the estimates and interval back into your original space using the inverse logistic function.