SET NOECHO PROC GAUSS SET NOOUTPUT * ************************************************************************ * Estimation of a function by the Gauss-Newton algorithm * * REFERENCE: Section 12.2.3b of Judge, Hill et al. [1988, p.514-5] * * SHAZAM procedure written by Diana Whistler - January 1994 * * Input requirements: * (1) NCOEF: Number of coefficients to estimate * (2) Starting values named B1, B2, .... * (3) NITER: Maximum number of iterations * (4) DELTA: Convergence criteria - the algorithm stops when * the gradient sum of squares is less than the * value specified. * (5) Y: The left-hand side of the equation * (6) EQRHS: The right-hand side of the equation with * unknown parameters B1, B2, ... * * Run the procedure with the commands: * FILE PROC procedure_filename * EXEC GAUSS * ************************************************************************ SET NODOECHO GEN1 T_=\$N DIM B_ [NCOEF] BOLD_ [NCOEF] Z_ T_ [NCOEF] SSEV_ 10 STEP_ 10 DO #=1,[NCOEF] GEN1 B_:#=B# ENDO DO #=1,[NITER] * Use the DERIV command to get the Z matrix of first derivatives DO %=1,[NCOEF] DERIV B% Z_:%=[EQRHS] ENDO * Residuals GENR E_=[Y] - [EQRHS] * Compute the error sum of squares MATRIX SSE_=E_'E_ * Compute the value of the log-likelihood function GEN1 LLF_=-(T_/2)*LOG(2*\$PI)-(T_/2)-(T_/2)*LOG(SSE_/T_) * Calculate the gradient MATRIX G_=-2*Z_'E_ MATRIX H_=INV(Z_'Z_) * Print results GEN1 ITER_=# PRINT ITER_ SSE_ LLF_ B_ G_ * Convergence test - stop if the gradient is "close" to zero. MATRIX C_=G_'G_ ENDIF (C_.LT.[DELTA]) * Calculate the direction vector MATRIX D_=-0.5*H_*G_ * A grid-search MATRIX BOLD_=B_ DO %=1,10 GEN1 STEP_:%=%/10 GEN1 STEPSZ_=STEP_:% * Updating step MATRIX B_=BOLD_+STEPSZ_*D_ DO !=1,[NCOEF] GEN1 B!=B_:! ENDO GENR E_=[Y] - [EQRHS] MATRIX SSE_=E_'E_ GEN1 SSEV_:%=SSE_ ENDO * Choose an optimal step-size SORT SSEV_ STEP_ / BEG=1 END=10 GEN1 STEPSZ_=STEP_:1 PRINT STEPSZ_ * Update the parameter vector MATRIX B_=BOLD_+STEPSZ_*D_ DO !=1,[NCOEF] GEN1 B!=B_:! ENDO ENDO * Compute the standard errors and print the final results GEN1 SIG2_=SSE_/T_ MATRIX SE_=SQRT(SIG2_*DIAG(H_)) MATRIX TRATIO_=B_/SE_ PRINT SSE_ LLF_ SIG2_ SAMPLE 1 [NCOEF] PRINT B_ SE_ TRATIO_ DELETE / ALL_ SET DOECHO SET ECHO SET OUTPUT PROCEND