| 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, ... | |
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
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