Local polynomial estimation
Description
Estimates a multidimensional regression function (and its first derivatives) using local polynomial kernel smoothing (and linear binning).
Usage
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23  locpol(x, ...)
## Default S3 method:
locpol(x, y, h = NULL, nbin = NULL, degree = 1 +
as.numeric(drv), drv = FALSE, hat.bin = FALSE, ncv = 0,
set.NA = FALSE, ...)
## S3 method for class 'bin.data'
locpol(x, h = NULL, degree = 1 + as.numeric(drv),
drv = FALSE, hat.bin = FALSE, ncv = 0, ...)
## S3 method for class 'svar.bin'
locpol(x, h = NULL, degree = 1, drv = FALSE,
hat.bin = TRUE, ncv = 0, ...)
## S3 method for class 'bin.den'
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 == "CV", 2, 0), cov.dat = NULL,
...)

Arguments
x 
a (data) object used to select a method. 
... 
further arguments passed to or from other methods (e.g. to 
y 
vector of data (response variable). 
h 
(full) bandwidth matrix (controls the degree of smoothing; only the upper triangular part of h is used). 
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 
hat.bin 
logical; if 
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 
objective 
character; optimal criterion to be used ("CV", "GCV" or "MASE"). 
cov.dat 
covariance matrix of the data or semivariogram model
(of class extending 
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 pmax(25, rule.binning(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 crossvalidation 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).
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 
locpol 
a list with 7 components:

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.).
References
Chu, C.K. and Marron, J.S. (1991) Comparison of Two Bandwidth Selectors with Dependent Errors. The Annals of Statistics, 19, 19061918.
Rupert D. and Wand M.P. (1994) Multivariate locally weighted least squares regression. The Annals of Statistics, 22, 13461370.
See Also
binning
, data.grid
,
np.svariso
, svar.bin
,
np.den
, bin.den
, hcv.data
,
rule.binning
.
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13  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')

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