# make_kernel: make_kernel In jlstiles/cateSurvival: blip CDF

## Description

constructs polynomial kernels

## Usage

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

## Arguments

 `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

## Value

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

## Examples

 ``` 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.