How accurate are CML and Maxlik estimates, and will AD improve their accuracy?
A. For its calculations GAUSS uses only double precision floating point numbers, and in modern computers that translates to about 16 decimal places of accuracy. The floating point number looks like this: x.xxxxxxxxxxxxxxx + yyy where yyy is the exponent. The exponent determines the location of the decimal point which is therefore irrelevant with respect to accuracy. The accuracy of this number is determined by the number of x’s that are correct. When I say that a numerical derivative loses 4 places of accuracy I mean that the result will be x.xxxxxxxxxxxdddd + yyy where the d’s represent inaccurate or incorrect numbers. A numerical Hessian compounds the inaccuracy: x.xxxxxxxdddddddd + yyy. While AD restores the full 16 places of accuracy to the calculation of the gradient, it doesn’t necessarily translate to 16 places of accuracy in the estimates or standard errors. The accuracy of the estimates is largely determined by several factors, the condition number of the Hessian, the accuracy
A. For its calculations GAUSS uses only double precision floating point numbers, and in modern computers that translates to about 16 decimal places of accuracy. The floating point number looks like this: x.xxxxxxxxxxxxxxx + yyy where yyy is the exponent. The exponent determines the location of the decimal point which is therefore irrelevant with respect to accuracy. The accuracy of this number is determined by the number of x’s that are correct. When I say that a numerical derivative loses 4 places of accuracy I mean that the result will be x.xxxxxxxxxxxdddd + yyy where the d’s represent inaccurate or incorrect numbers. A numerical Hessian compounds the inaccuracy: x.xxxxxxxdddddddd + yyy. While AD restores the full 16 places of accuracy to the calculation of the gradient, it doesn’t necessarily translate to 16 places of accuracy in the estimates or standard errors. The accuracy of the estimates is largely determined by several factors, the condition number of the Hessian, the accuracy
