# nadwat: The Classical Nadaraya-Watson Regression Estimator In kader: Kernel Adaptive Density Estimation and Regression

## Description

In its arguments `x` and `dataX` vectorized function to compute the classical Nadaraya-Watson estimator (as it is m_n in eq. (1.1) in Eichner & Stute (2012)).

## Usage

 `1` ```nadwat(x, dataX, dataY, K, h) ```

## Arguments

 `x` Numeric vector with the location(s) at which the Nadaraya-Watson regression estimator is to be computed. `dataX` Numeric vector (X_1, …, X_n) of the x-values from which (together with the pertaining y-values) the estimate is to be computed. `dataY` Numeric vector (Y_1, …, Y_n) of the y-values from which (together with the pertaining x-values) the estimate is to be computed. `K` A kernel function (with vectorized in- & output) to be used for the estimator. `h` Numeric scalar for bandwidth h.

## Details

Implementation of the classical Nadaraya-Watson estimator as in eq. (1.1) in Eichner & Stute (2012) at given location(s) in `x` for data (X_1, Y_1), …, (X_n, Y_n), a kernel function K and a bandwidth h.

## Value

A numeric vector of the same length as `x`.

## 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``` ```require(stats) # Regression function: a polynomial of degree 4 with one maximum (or # minimum), one point of inflection, and one saddle point. # Memo: for p(x) = a * (x - x1) * (x - x2)^3 + b the max. (or min.) # is at x = (3*x1 + x2)/4, the point of inflection is at x = # (x1 + x2)/2, and the saddle point at x = x2. m <- function(x, x1 = 0, x2 = 8, a = 0.01, b = 0) { a * (x - x1) * (x - x2)^3 + b } # Note: for m()'s default values a minimum is at x = 2, a point # of inflection at x = 4, and a saddle point at x = 8. n <- 100 # Sample size. set.seed(42) # To guarantee reproducibility. X <- runif(n, min = -3, max = 15) # X_1, ..., X_n Y <- m(X) + rnorm(length(X), sd = 5) # Y_1, ..., Y_n x <- seq(-3, 15, length = 51) # Where the Nadaraya-Watson estimator # mn of m shall be computed. mn <- nadwat(x = x, dataX = X, dataY = Y, K = dnorm, h = n^(-1/5)) plot(x = X, y = Y); rug(X) lines(x = x, y = mn, col = "blue") # The estimator. curve(m, add = TRUE, col = "red") # The "truth". ```

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