npsp (version 0.3-6)

h.cv: Cross-validation methods for bandwidth selection

Description

Selects the bandwidth of a local polynomial kernel (regression, density or variogram) estimator using (standart or modified) CV, GCV or MASE criteria.

Usage

h.cv(bin, ...)
  "h.cv" (bin, objective = c("CV", "GCV", "MASE"), h.start = NULL, h.lower = NULL, h.upper = NULL, degree = 1, ncv = ifelse(objective == "GCV", 0, 1), cov.bin = NULL, DEalgorithm = FALSE, warn = FALSE, ...)
  "h.cv" (bin, h.start = NULL, h.lower = NULL, h.upper = NULL, degree = 1, ncv = 1, DEalgorithm = FALSE, warn = FALSE, ...)
  hcv.data(bin, objective = c("CV", "GCV", "MASE"), h.start = NULL, h.lower = NULL, h.upper = NULL, degree = 1, ncv = ifelse(objective == "GCV", 0, 1), cov = NULL, DEalgorithm = FALSE, warn = FALSE, ...)

Arguments

bin

object used to select a method (binned data, binned density or binned semivariogram).

...

further arguments passed to or from other methods (e.g. parameters of the optimization routine).

objective

character; optimal criterion to be used ("CV", "GCV" or "MASE").

h.start

vector; initial values for the parameters (diagonal elements) to be optimized over. If DEalgorithm == FALSE (otherwise not used), defaults to (3 + ncv) * lag, where lag = bin$grid$lag.

h.lower

vector; lower bounds on each parameter (diagonal elements) to be optimized. Defaults to (1.5 + ncv) * bin$grid$lag.

h.upper

vector; upper bounds on each parameter (diagonal elements) to be optimized. Defaults to 1.5 * dim(bin) * bin$grid$lag.

DEalgorithm

logical; if TRUE, the differential evolution optimization algorithm in package DEoptim is used.

ncv

integer; determines the number of cells leaved out in each dimension. (0 to GCV considering all the data, $>0$ to traditional or modified cross-validation). See "Details" bellow.

cov.bin

covariance matrix of the binned data. Defaults to identity.

warn

logical; sets the handling of warning messages (normally due to the lack of data in some neighborhoods). If FALSE (the default) all warnings are ignored.

cov

covariance matrix of the data. Defaults to identity (uncorrelated data).

degree

degree of the local polynomial used. Defaults to 1 (local linear estimation).

Value

Returns a list containing the following 3 components:

h

the best (diagonal) bandwidth matrix found.

value

the value of the objective function corresponding to h.

objective

the criterion used.

Details

Currently, only diagonal windows are supported.

h.cv methods use binning approximations to the objective function values. If ncv > 0, estimates are computed by leaving out binning cells with indexes within the intervals $[x_i - ncv + 1, x_i + ncv - 1]$, at each dimension i, where $x$ denotes the index of the estimation position. $ncv = 1$ corresponds with traditional cross-validation and $ncv > 1$ with modified CV (see e.g. Chu and Marron, 1991, for the one dimensional case). For standard GCV, set ncv = 0 (the full data is used). For theoretical MASE, set y = trend.teor, cov = cov.teor and ncv = 0.

If DEalgorithm == FALSE, the "L-BFGS-B" method in optim is used.

hcv.data evaluates the objective functions at the original data (combining a binning approximation to the nonparametric estimates with a linear interpolation). If ncv > 1 (modified CV), a similar algorithm to that in h.cv.bin.data is used, estimates are computed by leaving out binning cells with indexes within the intervals $[x_i - ncv + 1, x_i + ncv - 1]$.

References

Chu, C.K. and Marron, J.S. (1991) Comparison of Two Bandwidth Selectors with Dependent Errors. The Annals of Statistics, 19, 1906-1918.

Francisco-Fernandez M. and Opsomer J.D. (2005) Smoothing parameter selection methods for nonparametric regression with spatially correlated errors. Canadian Journal of Statistics, 33, 539-558.

See Also

locpol, locpolhcv, binning, np.svar.

Examples

bin <- binning(earthquakes[, c("lon", "lat")], earthquakes$mag, nbin = c(30,30))
hcv <- h.cv(bin, ncv = 2)
lp <- locpol(bin, h = hcv$h)
## Alternatively:
## lp <- locpolhcv(earthquakes[, c("lon", "lat")], earthquakes$mag, nbin = c(30,30), ncv = 2)

simage(lp, main = 'Smoothed magnitude')
contour(lp, add = TRUE)
with(earthquakes, points(lon, lat, pch = 20))

## Density estimation
hden <- h.cv(as.bin.den(bin))
den <- np.den(bin, h = hden$h)

plot(den, main = 'Estimated log(density)')