Description Usage Arguments Value Examples

constructs polynomial kernels

1 | ```
make_kernel(order, R)
``` |

`order, ` |
the degree of the 1st non-zero moment, an even number since all these kernels are orthogonal to odd polynomials. If NULL then a uniform kernel is constructed |

`R, ` |
support is -R to R and kernel is smooth at the boundary |

a list containing coefficients of the even polynomial kernel, veck, Range, R, and functions for the kernel and its cdf, kern and kern_cdf.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 | ```
# The order of the kernel is power of the first non-zero moment. Kernels will have support between
# -R and R. Order must be an even number because all kernels are orthogonal to odd polynomials
# since they are symmetric
order = 8
R = 5
k=blipCDF:::make_kernel(order,R)
# check it is a kernel
area = with(k, integrate(kern, lower = -R, upper = R, R = R, veck = veck, subdivisions = 10000)$value)
area
# plot
s = seq(-R,R,.001)
y = with(k, kern(s, R=R, veck=veck))
plot = plot(s,y)
plot
# check orthogonality to a polynomial less than the order
test_fcn = as.data.frame(vapply(0:order, FUN = function(r) {
test_fcn = function(x) (x^r)*with(k, kern(x, R=R, veck = veck))
test_int = integrate(test_fcn, lower = -R, upper = R,subdivisions = 10000)
return(c(test_int$abs.error, test_int$value))
}, FUN.VALUE = c(1,1)))
rownames(test_fcn) = c("abs_error", "integral")
colnames(test_fcn) = as.character(0:(order))
# We see the integral of the kernel times an 8th degree polynomial is non trivial
test_fcn
``` |

jlstiles/cateSurvival documentation built on May 24, 2019, 1:36 a.m.

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