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 locpol

Function: locpoldis
Description: locpoldis computes the local polynomial estimator without mixed terms but allows for including a linear part in the regression model. It is using the quartic kernel.


Usage: locpoldis(x, xg, y, h, logi {, xd})
Input:
x n x d matrix nonlinear inputs
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
xd n x dis matrix optional, inputs for the linear part
Output:
mh m x dd x q matrix regression of the nonlinear part and its v'th derivatives divided by v at xg in the following order: regression function, first derivatives respectively x1, x2, x3, ..., second derivative*0.5 respectively x1, x2, x3, ...

Note:

Example:

logi=1            ; we aim to use local quadratic
d   =2            ; dimension of nonlinear inputs
dis =1            ; dimension of discrete influence
q   =1            ; dimension of response
n   = 100         ; number of observations
;*****  create data *****
x  = uniform(n,d)    
xd = uniform(n,dis) 
xd =  (xd.> (1/3)) 
y  =  1.5*x[,1]^2 -x[,2]^3 +xd*(0.5) +normal(n,1)*0.2   
h  = 0.4*matrix(d,1)          ; bandwidth vector
xs = sort(x~xd~y,1)
x  = xs[,1:d]
xd = xs[,(d+1):(d+dis)]
y  = xs[,d+dis+1] 
xg = x                        ; 'grid'
mh = locpoldis(x,xg,y,h,logi,xd)
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_2 x_2
Result:

Contents of _tmp
[  1,]  -1.0606 
[  2,] -0.14172 
...
[100,]   1.2935 
Contents of _tmp
[  1,]   2.8621 
[  2,]   1.1122 
...
[100,]    1.535 
Contents of _tmp
[  1,]  0.25281 
[  2,] -0.56869 
...
[100,] -0.81995 
Contents of _tmp
[  1,]  -6.4567 
[  2,]  -3.3899 
...
[100,]  -3.0269 
Contents of _tmp
[  1,]   7.9354 
[  2,]  -2.9056 
...
[100,]  -0.3416 

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

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, 28.6.1999