new;
/* KERNEL.GPR: Nonparametric Kernel Density and Series Estimation
	       of an Unkown Regression Function
	       By Woocheol Kim, Ylae University, April, 1998 */

load a[1500,2]=dat1.asc;
library pgraph;
graphset;

y   =a[.,1];
x   =a[.,2];
n   =1500;
s   =stdc(x);


/**
*** Nonparametric Estimation
**/
/******************
h  =1.5*s*n^(-1/5);

inc =1;
f ={};

i   =1; do until i gt n;
    p   =1/(n*h).*sumc(pdfn((x[i]-x)./h));
    fp  =1/(n*h).*sumc(y.*pdfn((x[i]-x)./h));
    f  =f|(fp/p);   
    i   =i+inc;i;
endo;

output file=a:\q8\ker.asc reset;
f;
output off;
***********************/
load f[]=a:\q8\ker.asc;

/*_ptek   ="nonpara.tkf";
_pdate  ="";
_plctrl =-1;
_pstype ={1};
_psymsiz={1};
title("Nonparametric Regression(Data2)\LKernel Estimator:");
_plegctl={2,5,1,1};
_plegstr="h=1.5*SD*n^(-1/5)";
xlabel("X");
ylabel("fhat");
xy(x,f);*/


/***
****Series Estimation
***/

xx=ones(n,1)~x;
yh  ={};    @place for the estimated values @
mxp =3;     @maximum power in the series estimation @
j   =2;
do until j gt mxp;
    xx  =xx~x^j;
    b   =inv(xx'xx)*xx'y;
    yh  =yh~xx*b;
    j   =j+1;
endo;
yh=yh[.,2];
/*_plctrl =-1;
_ptek   ="series.tkf";
title("Series Regression\LUsing Data2");
_plegctl={2,4,1,1};
_plegstr="y=b0+b1*x+b2*x^2+b3*x^3+b4*x^4";
xy(x,yh);*/

load beta=a:\q1&2\q_dat1;
yhat = exp( (xx*beta)) ;

title("Fig 4:kernel vs Series vs nonlinear Regression\LUsing Data1");
_plctrl =-1;
_pstype ={1,3,5};
_psymsiz={0.5,1.5,2.5};
/*_ptek   ="compa.tkf";*/
_plegctl={2,4,1,1};
_plegstr="h=1.5*SD*n^(-1/5)\0"\
		"y=b0+b1*x+b2*x^2+b3*x^3+b4*x^4\0"\
		"y=exp(b0+b1*x+b2*x^2+b3*x^3+b4*x^4)";

xy(x,f~yh~yhat);