npsp (version 0.3-6)

locpol: Local polynomial estimation

Description

Estimates a multidimensional regression function (and its first derivatives) using local polynomial kernel smoothing of linearly binned data.

Usage

locpol(x, ...)
  "locpol" (x, y, h = NULL, nbin = NULL, degree = 1 + as.numeric(drv), drv = FALSE, hat.bin = FALSE, ncv = 0, set.NA = FALSE, ...)
  "locpol" (x, h = NULL, degree = 1 + as.numeric(drv), drv = FALSE, hat.bin = FALSE, ncv = 0, ...)
  "locpol" (x, h = NULL, degree = 1, drv = FALSE, hat.bin = TRUE, ncv = 0, ...)
  "locpol" (x, h = NULL, degree = 1 + as.numeric(drv), drv = FALSE, ncv = 0, ...)
  locpolhcv(x, y, nbin = NULL, objective = c("CV", "GCV", "MASE"), degree = 1 + as.numeric(drv), drv = FALSE, hat.bin = FALSE, set.NA = FALSE, ncv = ifelse(objective == "GCV", 0, 1), cov = NULL, ...)

Arguments

x

a (data) object used to select a method.

...

further arguments passed to or from other methods (e.g. to hcv.data).

y

vector of data (response variable).

h

(full) bandwidth matrix (controls the degree of smoothing).

nbin

vector with the number of bins on each dimension.

degree

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

drv

logical; if TRUE, the matrix of estimated first derivatives is returned.

hat.bin

logical; if TRUE, the hat matrix of the binned data is returned.

ncv

integer; determines the number of cells leaved out in each dimension. Defaults to 0 (the full data is used) and it is not normally changed by the user in this setting. See "Details" below.

set.NA

logical. If TRUE, sets binning cells without data to missing.

objective

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

cov

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

Value

Returns an S3 object of class locpol.bin (locpol + bin data + grid par.). A bin.data object with the additional (some optional) 3 components:

est

vector or array (dimension nbin) with the local polynomial estimates.

locpol

a list with 7 components:

• degree degree of the polinomial.
• h bandwidth matrix.
• rm residual mean.
• rss sum of squared residuals.
• ncv number of cells ignored in each direction.
• hat (if requested) hat matrix of the binned data.
• nrl0 (if appropriate) number of cells with data (binw > 0) and missing estimate (est == NA).

deriv

(if requested) matrix of first derivatives.

locpol.svar.bin returns an S3 object of class np.svar (locpol semivar + bin semivar + grid par.).locpol.bin.den returns an S3 object of class np.den (locpol den + bin den + grid par.).

Details

Standard generic function with a default method (interface to the fortran routine lp_raw), in which argument x is a vector or matrix of covariates (e.g. spatial coordinates).

If parameter nbin is not specified is set to rep(25, ncol(x)).

A multiplicative triweight kernel is used to compute the weights.

If ncv > 0, estimates are computed by leaving out 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).

Setting set.NA = TRUE (equivalent to biny[binw == 0] <- NA) may be useful for plotting the binned averages $biny (the hat matrix should be handled with care).

locpolhcv calls hcv.data to obtain an "optimal" bandwith (additional arguments ... are passed to this function). Argument ncv is only used here at the bandwith selection stage (estimation is done with all the data).

References

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

Rupert D. and Wand M.P. (1994) Multivariate locally weighted least squares regression. The Annals of Statistics, 22, 1346-1370.

See Also

binning, data.grid, np.svariso, svar.bin, np.den, bin.den, hcv.data.

Examples

lp <- locpol(earthquakes[, c("lon", "lat")], earthquakes$mag, h = diag(2, 2), nbin = c(41,41))
simage(lp, main = "Smoothed magnitude")
contour(lp, add = TRUE)

bin <- binning(earthquakes[, c("lon", "lat")], earthquakes$mag, nbin = c(41,41))
lp2 <- locpol(bin, h = diag(2, 2))
all.equal(lp, lp2)

## Alternatively:
## lp <- locpolhcv(earthquakes[, c("lon", "lat")], earthquakes$mag, ncv = 4)

den <- locpol(as.bin.den(bin), h = diag(1, 2))
plot(den, log = FALSE, main = 'Estimated density')