GaussianNadarayaWatsonEstimator: Nadaraya-Watson estimator with Gaussian kernel
In henrykye/semiBRM: Semiparametric Binary Response Models in R

Description Usage Arguments Details Value Examples

This estimates nonparametric conditional expectation E[y|x=args] using the Nadaraya-Watson estimator with Gaussian kernel.

1	GaussianNadarayaWatsonEstimator(x, y, h, args = NULL)

`x`	a numeric vector or matrix of explanatory variable(s).
`y`	a numeric vector of outcome (or dependent) variable.
`h`	a numeric vector indicating bandwidth size(s) for each explanatory variable in `x`.
`args`	a numeric vector or matrix of arguments at which nonparametric conditional expectations are evaluated.

This is the Nadaraya-Watson estimator taking as arguments data x and y, bandwidth h, and target points args. If args are not given, it will return the leave-one-out version. The dimension of h should be the same as that of x, i.e., bandwidths need to be separately specified for each explanatory variable. A popular choice of bandwidth is the Silverman's rule of thumb, h = sd(x)*N^(-1/r) with r = 4 + q, where N is the sample size and q is the dimension of x.

a numeric vector of nonparametric estimates of conditional expectation E[y|x=args].

# data generating process
N <- 500L
x1 <- stats::rnorm(N)
x2 <- stats::rnorm(N)
x3 <- stats::rnorm(N)
x <- cbind(x1, x2, x3)
v <- (x1 + x2 + x3)/sqrt(3)
y <- v + rnorm(N)

# univariate case
h_u <- stats::sd(v)*N^(-1/5)
vargs <- stats::quantile(v)

yhat_univ_1 <- GaussianNadarayaWatsonEstimator(v, y, h_u, vargs)
yhat_univ_2 <- GaussianNadarayaWatsonEstimator(v, y, h_u) # leave-one-out version

# multivariate case
h_m <- apply(matrix(stats::rnorm(150), 50, 3), 2, stats::sd)*N^(-1/7)
xargs <- apply(matrix(stats::rnorm(150), 50, 3), 2, stats::quantile)

yhat_multi_1 <- GaussianNadarayaWatsonEstimator(x, y, h_m, xargs)
yhat_multi_2 <- GaussianNadarayaWatsonEstimator(x, y, h_m) # leave-one-out version