\name{Hlscv, Hlscv.diag, hlscv}\alias{Hlscv}\alias{Hlscv.diag}%\alias{hlscv}\title{Least-squares cross-validation (LSCV) bandwidth matrix selector  for multivariate data}\description{LSCV bandwidth for 1- to 6-dimensional data}\usage{Hlscv(x, Hstart)Hlscv.diag(x, Hstart, binned=FALSE, bgridsize)}%hlscv(x, binned=TRUE, bgridsize)\arguments{  \item{x}{vector or matrix of data values}  \item{Hstart}{initial bandwidth matrix, used in numerical    optimisation}  \item{binned}{flag for binned kernel estimation}  \item{bgridsize}{vector of binning grid sizes -   required only if \code{binned=TRUE}}}\value{LSCV bandwidth.}\references{  Bowman, A. (1984) An alternative method of cross-validation for the  smoothing of kernel density estimates. \emph{Biometrika}. \bold{71},  353-360.    Duong, T. \& Hazelton, M.L. (2005) Cross-validation  bandwidth matrices for multivariate kernel density estimation.  \emph{Scandinavian Journal of Statistics}. \bold{32}, 485-506.  Rudemo, M. (1982) Empirical choice of histograms and kernel density  estimators. \emph{Scandinavian Journal of Statistics}. \bold{9},  65-78.    Sain, S.R, Baggerly, K.A \& Scott, D.W. (1994)  Cross-validation of multivariate densities. \emph{Journal of the  American Statistical Association}. \bold{82}, 1131-1146.   }\details{\code{hlscv} is the univariate SCV  selector of Bowman (1984) and Rudemo (1982). \code{Hlscv} is a  multivariate generalisation of this.  Use \code{Hlscv} for full bandwidth matrices and \code{Hlscv.diag}  for diagonal bandwidth matrices.    %For d = 1, the selector \code{hlscv} is always computed as binned  %estimator.  For d = 2, 3, 4 and \code{binned=TRUE},   estimates are computed over a binning grid defined   by \code{bgridsize}. Otherwise it's computed exactly.    If \code{Hstart} is not given then it defaults to  \code{k*var(x)} where k = \eqn{\left[\frac{4}{n(d+2)}\right]^{2/(d+4)}}{4/(n*(d + 2))^(2/(d+ 4))}, n = sample size, d = dimension of data. }\seealso{ \code{\link{Hbcv}}, \code{\link{Hscv}}}\examples{mus <- rbind(c(-1/2,0), c(1/2,0))Sigmas <- rbind(diag(c(1/16, 1)), rbind(c(1/8, 1/16), c(1/16, 1/8)))props <- c(2/3, 1/3)x <- rmvnorm.mixt(1000, mus, Sigmas, props)Hlscv(x)Hlscv.diag(x, binned=TRUE)}\keyword{ smooth }