# kfn_vectorized: Convolution of Kernel Function K with fn In kader: Kernel Adaptive Density Estimation and Regression

## Description

Vectorized evaluation of the convolution of the kernel function K with fn.

## Usage

 `1` ```kfn_vectorized(u, K, xixj, h, sig) ```

## Arguments

 `u` Numeric vector. `K` Kernel function with vectorized in- & output. `xixj` Numeric matrix. `h` Numeric scalar. `sig` Numeric scalar.

## Details

Vectorized (in u) evaluation of - a more explicit representation of - the integrand K(u) * f_n(… - h^2/σ * u) which is used in the computation of the bias estimator before eq. (2.3) in Srihera & Stute (2011). Also used for the analogous computation of the respective bias estimator in the paragraph after eq. (6) in Eichner & Stute (2013).

## Value

A vector of (K * f_n)(u) evaluated at the values in `u`.

## Note

An alternative implementation could be `K(u) * sapply(h/sig * u, function(v) mean(K(xixj - v))) / h`

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11``` ```require(stats) set.seed(2017); n <- 100; Xdata <- rnorm(n) x0 <- 1; sig <- 1; h <- n^(-1/5) Ai <- (x0 - Xdata)/h Bj <- mean(Xdata) - Xdata # in case of non-robust method AiBj <- outer(Ai, Bj/sig, "+") ugrid <- seq(-10, 10, by = 1) kader:::kfn_vectorized(u = ugrid, K = dnorm, xixj = AiBj, h = h, sig = sig) ```

kader documentation built on May 1, 2019, 10:13 p.m.