LSCV: Least-squares cross-validation function for the...

In smoothemplik: Smoothed Empirical Likelihood

Least-squares cross-validation function for the Nadaraya-Watson estimator

Description

Least-squares cross-validation function for the Nadaraya-Watson estimator

Usage

LSCV(
  x,
  y,
  bw,
  weights = NULL,
  same = FALSE,
  degree = 0,
  kernel = "gaussian",
  order = 2,
  PIT = FALSE,
  chunks = 0,
  robust.iterations = 0,
  cores = 1
)

Arguments

x	A numeric vector, matrix, or data frame containing observations. For density, the points used to compute the density. For kernel regression, the points corresponding to explanatory variables.
y	A numeric vector of dependent variable values.
bw	Candidate bandwidth values: scalar, vector, or a matrix (with columns corresponding to columns of x).
weights	A numeric vector of observation weights (typically counts) to perform weighted operations. If null, rep(1, NROW(x)) is used. In all calculations, the total number of observations is assumed to be the sum of weights.
same	Logical: use the same bandwidth for all columns of x?
degree	Integer: 0 for locally constant estimator (Nadaraya–Watson), 1 for locally linear (Cleveland's LOESS), 2 for locally quadratic (use with care, less stable, requires larger bandwidths)
kernel	Character describing the desired kernel type. NB: due to limited machine precision, even Gaussian has finite support.
order	An integer: 2, 4, or 6. Order-2 kernels are the standard kernels that are positive everywhere. Orders 4 and 6 produce some negative values, which reduces bias but may hamper density estimation.
PIT	If TRUE, the Probability Integral Transform (PIT) is applied to all columns of x via ecdf in order to map all values into the [0, 1] range. May be an integer vector of indices of columns to which the PIT should be applied.
chunks	Integer: the number of chunks to split the task into (limits RAM usage but increases overhead). 0 = auto-select (making sure that no matrix has more than 2^27 elements).
robust.iterations	The number of robustifying iterations (due to Cleveland, 1979). If greater than 0, xout is ignored.
cores	Integer: the number of CPU cores to use. High core count = high RAM usage. Note: since LSCV requires zeroing out the diagonals of the weight matrix, repeated observations are combined first; the de-duplication is therefore forced in cross-validation. The only situation where de-duplication can be skipped is passing de-duplicated data sets from outside (e.g. inside optimisers).

Value

A numeric vector of the same length as bw or nrow(bw).

Examples

set.seed(1)  # Creating a data set with many duplicates
n.uniq <- 1000
n <- 4000
inds <- sort(ceiling(runif(n, 0, n.uniq)))
x.uniq <- sort(rnorm(n.uniq))
y.uniq <- 1 + 0.2*x.uniq + 0.3*sin(x.uniq) + rnorm(n.uniq)
x <- x.uniq[inds]
y <- y.uniq[inds]
w <- 1 + runif(n, 0, 2) # Relative importance
data.table::setDTthreads(1) # For measuring pure gains and overhead
RcppParallel::setThreadOptions(numThreads = 1)
bw.grid <- seq(0.1, 1.2, 0.05)
ncores <- if (.Platform$OS.type == "windows") 1 else 2
CV <- LSCV(x, y, bw.grid, weights = w, cores = ncores)  # Parallel capabilities
bw.opt <- bw.grid[which.min(CV)]
g <- seq(-3.5, 3.5, 0.05)
yhat <- kernelSmooth(x, y, xout = g, weights = w,
                     bw = bw.opt, deduplicate.xout = FALSE)
oldpar <- par(mfrow = c(2, 1), mar = c(2, 2, 2, 0)+.1)
plot(bw.grid, CV, bty = "n", xlab = "", ylab = "", main = "Cross-validation")
plot(x.uniq, y.uniq, bty = "n", xlab = "", ylab = "", main = "Optimal fit")
points(g, yhat, pch = 16, col = 2, cex = 0.5)
par(oldpar)

smoothemplik documentation built on Aug. 22, 2025, 1:11 a.m.