Object Reference : Object View and Procedure Reference : Equation
  
 
funcoef
Estimate a functional coefficient regression equation.
Syntax
eq_name.funcoef(options) y x1 [x2 x3 ...] @ funcoef_series
List the funcoef keyword, the dependent variable and a list of the regressor variables, followed by the “@” symbol and the name of the functional coefficient series.
Options
Basic Options
 
kern=arg (default=“epan”)
Kernel type: “epan” (Epanechnikov, default), “trngl” (Triangular), “unif” (Uniform), “gauss” (Normal–Gaussian), “bi” (Biweight–Quartic), “tri” (Triweight).
eval=arg (default=“data”)
Evalution points: observed data (“data”), grid of values (“grid”).
if “eval=grid” you must specify the grid values using “gmin=”, “gmax=” and “glen=”, or using “gvec=”.
gmin = arg
Estimation grid minimum (if “eval=grid”). Must be specified along with “gmax=” and “glen=”.
gmax = arg
Estimation grid maximum (if “eval=grid”). Must be specified along with “gmin=” and “glen=”.
glen = arg
Estimation grid length (if “eval=grid”). Must be specified along with “gmin=” and “gmax=”.
gvec = arg
Estimation grid points in a vector object (if “eval=grid”).
plyk = arg (default = 1)
Estimation polynomial degree for final stage.
auxk = arg (default = 2)
Estimation polynomial degree for pilot stage in excess of final stage.
p
Print results.
Pilot Bandwidth Options
 
plth =arg (default = “cv”)
Pilot bandwidth method: simple rule-of-thumb (“rot”), robust rule-of-thumb (“rotr”), residual squares criterion (“rsc”), modified multi cross-validation (“cv”), user-defined (“user”).
pltbw=arg (default =1)
User-defined bandwidth (if “plth=user”).
plthmin=arg (default = 0.1)
Bandwidth grid search minimum value (if not “plth=user”).
plthmax=arg (default =1)
Bandwidth grid search maximum value (if not “plth=user”).
plthlen=integer (default = 100)
Bandwidth grid search length (if not “plth=user”).
plthinc=integer (default = 10)
Bandwidth grid search increment step percentage increase (if not “plth=user”).
plthcup=integer (default = 10)
Stop rule: consecutive increases of objective function before stop (not available when “plth=user”).
pltm=arg (default = 10)
Modified multifold CV m-value: percentage of sample size used in bandwidth determination (when “plth=cv”).
pltq=integer (default = 4)
Modified multifold CV Q-value: percentage of sample size used in bandwidth determination (when “plth=cv”).
Final Bandwidth Options
 
fnlh =arg (default = “cv”)
Final bandwidth method: simple rule-of-thumb (“rot”), robust rule-of-thumb (“rotr”), residual squares criterion (“rsc”), modified multi cross-validation (“cv”), integrated asymptotic mean square error (“mse”), leave-one-out cross-validation (“loo”), nonparametric AIC (“aic”), user-defined (“user”).
fnlbw=arg
User-defined bandwidth (if “fnlh=user”).
fnlhmin=arg (default = 0.1)
Bandwidth grid search minimum value (if not “fnlh=user”).
fnlhmax=arg (default =1)
Bandwidth grid search maximum value (if not “fnlh=user”).
fnlhlen=integer (default = 100)
Bandwidth grid search length (if not “fnlh=user”).
fnlhinc=integer (default = 10)
Bandwidth grid search increment step percentage increase (if not “fnlh=user”).
fnlhcup=integer (default = 10)
Stop rule: consecutive increases of objective function before stop (if not “fnlh=user”).
fnlm=arg (default = 10)
Modified multifold CV m-value: percentage of sample size used in bandwidth determination (when “fnlh=cv”).
fnlfq=integer (default = 4)
Modified multifold CV Q-value: percentage of sample size used in bandwidth determination (when “fnlh=cv”).
Examples
We consider examples for three equations that estimate FCOEF using UNRATE as the dependent variable, UNRATE(-1 to -2) as independent variables, and LWAGE(-4) as the functional coefficient variable.
eq.funcoef(eval=grid, gmin=0, gmax=10, glen=100) unrate unrate(-1) unrate(-2) @ lwage(-4)
evaluates over a custom uniform grid from 0 to 10 with length 100.
eq.funcoef(eval=grid, gvec=vecgrid) unrate unrate(-1) unrate(-2) @  lwage(-4)
evaluates over a custom grid provided by the values of a workfile vector called VECGRID.
eq.funcoef(plyk=3, auxk=5) unrate unrate(-1) unrate(-2) @ lwage(-4)
estimates using local polynomial fitting with main polynomial degree 3 and auxiliary polynomial degree 5. The latter is employed deriving bias, variance, and bandwidths.
Cross-references
See “Functional Coefficient Regression” for additional discussion of functional coefficients estimation.