| kernels | R Documentation |
Implementations of kernel functions
W0(x) W1(x) W2(x) W3(x) WDaniell(x, a = (pi/2)) WParzen(u)
x |
real-valued argument to the function; can be a vector |
a |
real number between 0 and pi |
u |
real number |
Daniell kernel function W0:
1/(2pi) I{|x|<=pi}.
Epanechnikov kernel W1 (i. e., variance minimizing kernel function of order 2):
3/(4pi) (1-x/pi)^2 I{|x|<=pi}.
Variance minimizing kernel function W2 of order 4:
(15/(32 pi) (7 (x/pi)^4 - 10 (x/pi)^2 + 3) I{|x|<=pi}.
Variance minimizing kernel function W3 of order 6:
(35/(256 pi) (-99(x/pi)^6 + 189(x/pi)^4 - 105(x/pi)^2+15) I{|x|<=pi}.
Kernel yield by convolution of two Daniell kernels:
\frac{1}{π+a} \Big(1-\frac{|x|-a}{π-a} I\{a ≤q |x| ≤q π\}\Big).
Parzen Window for lagEstimators
plot(x=seq(-8,8,0.05), y=W0(seq(-8,8,0.05)), type="l") plot(x=seq(-8,8,0.05), y=W1(seq(-8,8,0.05)), type="l") plot(x=seq(-8,8,0.05), y=W2(seq(-8,8,0.05)), type="l") plot(x=seq(-8,8,0.05), y=W3(seq(-8,8,0.05)), type="l") plot(x=seq(-pi,pi,0.05), y=WDaniell(seq(-pi,pi,0.05),a=(pi/2)), type="l") plot(x=seq(-2,2,0.05),y=WParzen(seq(-2,2,0.05)),type = "l")