Keywords - Function groups - @ A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

Group: Statistical Data Analysis
Topic: Nonparametric Methods
See also: sker rmed lowess locpoldis

Function: locpol
Description: locpol computes the local polynomial estimator. It is using the quartic kernel.


Usage: locpol(x, xg, y, h, logi)
Input:
x n x d matrix explanatory variables
xg m x d matrix grid points at which the estimation will be done
y n x q matrix dependent variable
h d x 1 matrix vector of bandwidthes
logi logical scalar 0 if linear, 1 if quadratic polynomials are wished
Output:
mh m x dd x q matrix regression function and its v'th derivatives divided by v at xg in the following order: regression function, first derivatives respectively x1, x2, x3, ... , derivatives respectively x1x1, x1x2, ..., x2x2, x2x3, ...

Note:

Example:



logi=1            ; we aim to use local quadratic

d   =2            ; dimension of nonlinear inputs

q   =1            ; dimension of response

n   = 100         ; number of observations

;*****  create data *****

x  = uniform(n,d)    

y  =  1.5*x[,1]^2 -x[,2]^3 +normal(n,1)*0.2   

h  = 0.4*matrix(d,1)          ; bandwidth vector

xs = sort(x~y,1)

x  = xs[,1:d]

y  = xs[,d+1] 

xg = x                        ; 'grid'

mh = locpol(x,xg,y,h,logi)

mh[,1]                        ; regression function

mh[,2]                        ; derivative resp. to x_1

mh[,3]                        ; derivative resp. to x_2

mh[,4]                        ; derivative*0.5 resp. to x_1 x_1

mh[,5]                        ; ...                     x_1 x_2  

mh[,6]                        ; ...                     x_2 x_2

Result:



Contents of _tmp

[  1,] -0.13671 

[  2,] -0.080934

...

[100,]   1.5635 

Contents of _tmp

[  1,] -0.84599 

[  2,] -0.70103 

...

[100,]   6.0576 

Contents of _tmp

[  1,]  -1.2913 

[  2,]  0.19572 

...

[100,]   3.9349 

Contents of _tmp

[  1,]   3.0074 

[  2,]   4.5472 

...

[100,]     8.44 

Contents of _tmp

[  1,]  0.038032 

[  2,]  -1.7854 

...

[100,]   1.2624 

Contents of _tmp

[  1,] -0.89065 

[  2,]  0.93055 

...

[100,]  -13.268 


Group: Statistical Data Analysis
Topic: Nonparametric Methods
See also: sker rmed lowess locpoldis

Keywords - Function groups - @ A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

(C) MD*TECH Method and Data Technologies, 21.9.2000