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, 21.9.2000