nnregCI(fit, model=fit$best.model, ngrind=250, ntries=100, npol=20, clevel=0.95, cut1=NA, cut2=NA, nfits=500, tol1=1e-06, tol2=1e-09, itmax1=250, itmax2=10000, fdata, fout="nnci.out", seed)
fit
| A nnreg object. |
model
| Model number used in finding joint parameter confidence set. Default is the best model based on GCV(2). |
ngrind
| Number of coarse optimizations. |
ntries
| Number of random starting values for each coarse optimization. |
npol
| Number of coarse fits improved, i.e polish, using smaller minimization tolerance. |
clevel
| Confidence level used in finding joint parameter confidence set. Default is the 0.95 level. |
cut1
| RMSE value corresponding to the clevel confidence level. |
cut2
| RMSE value corresponding to 80% of the RMSE value corresponding to the clevel confidence level. |
nfits
| Number of fits (parameter sets) found in the confidence set. Maximum is 500. |
tol1
| Minimization tolerance for coarse optimizations. |
tol2
| Minimization tolerance for polish optimizations. |
itmax1
| Maximum number of iterations performed in the minimization routine for coarse optimizations. |
itmax2
| Maximum number of iterations performed in the minimization routine for polish optimizations. |
fdata
| Temporary UNIX file name for the data. |
fout
| Temporary UNIX file name for the output. |
seed
| Seed used in generating the random parameter starts. |
The program finds parameter sets which satisfy the above inequality. The value of cut1 is RMSE(theta^hat)*sqrt([1+(p/n-p)*F(p,n-p,alpha)]). The value of cut2 is .8*cut1. Approximately 20% of the fits will have a RMSE of cut1 and the remaining 80% will be uniform between RMSE(theta^hat) and cut1. This distribution of parameter sets is to make sure that the parameter sets cover the confidence region. The actual value of cut2 is used only as a check for the covering of the confidence region. The returned component summary has a count of the fits between cut1 and cut2 and also below cut2.
Parameters of the model are estimated by nonlinear least squares. The parameter space has a large number of local minimum so the strategy is to generate "many" parameter sets at random and iterate these starts with a minimization algorithm. The two function parameters ntries and ngrid are used in generating the many starting parameter sets for nonlinear least squares. Ngrind is the number of cubes growing geometrically over a range of magnitude of parameters. Ntries is the number of parameter sets generated at random by a uniform distribution in each cube. The best parameter set ( out the Ntries ) in each cube is used as the start of a coarse optimization. Npol of these coarse fits are selected for further refinement by a minimization with smaller tolerance.
The target RMS for a fit is generated as described above. The parameter sets for the confidence sets are generated in the polishing stage and in groups of the optional argument npol. The file nnregCI.cut contains information about the polished fits. The 7th column is target RMSE value the 8th column is the difference between target RMSE and the root finder's RMSE. The 9th column is the value of cut1 and the 10th column is the value of cut2.
model
| Component model of class netfit. Includes a list of the dimension of the x matrix, the number of hidden units used in the model, the mean of each column of the x matrix, the mean of the y values, the standard deviation of each column of the x matrix, the standard deviation of the y values, the number of parameters in the model and the parameters of model. |
summary
| Partial Fortan program output. Summary of the nnreg fit. Includes a summary of the specified number of fitted values. |
call
| Call to the function. |
x
| Matrix of independent variables. |
y
| Vector of dependent variables. |
n
| Number of observations or length of y. |
nfits
| Number of fits (parameter sets) found in the confidence set. |
seed
| Seed used in generating the random parameter starts. |
S. Ellner, D.W. Nychka, and A.R. Gallant. 1992. LENNS, a program to estimate the dominant Lyapunov exponent of noisy nonlinear systems from time series data. Institute of Statistics Mimeo Series #2235, Statistics Department, North Carolina State University, Raleigh, NC 27695-8203.
D.W. Nychka, S. Ellner, D. McCaffrey, and A.R. Gallant. 1992. Finding Chaos in Noisy Systems. J. R. Statist. Soc. B 54:399-426.
nnreg(ozone$x,ozone$y,1,2) -> fit # fitting a surface to ozone # measurements, from 1 to 2 hidden units nnregCI(fit) -> fit.ci # finds 500 fits in the .95 confidence set based # on the best model from the above fit