npscoefbw  R Documentation 
npscoefbw
computes a bandwidth object for a smooth
coefficient kernel regression estimate of a one (1) dimensional
dependent variable on
p+q
variate explanatory data, using the model
Y_i = W_{i}^{\prime} \gamma (Z_i) + u_i
where W_i'=(1,X_i')
given training points (consisting of explanatory data and dependent
data), and a bandwidth specification, which can be a rbandwidth
object, or a bandwidth vector, bandwidth type and kernel type.
npscoefbw(...)
## S3 method for class 'formula'
npscoefbw(formula, data, subset, na.action, call, ...)
## S3 method for class 'NULL'
npscoefbw(xdat = stop("invoked without data 'xdat'"),
ydat = stop("invoked without data 'ydat'"),
zdat = NULL,
bws,
...)
## Default S3 method:
npscoefbw(xdat = stop("invoked without data 'xdat'"),
ydat = stop("invoked without data 'ydat'"),
zdat = NULL,
bws,
nmulti,
random.seed,
cv.iterate,
cv.num.iterations,
backfit.iterate,
backfit.maxiter,
backfit.tol,
bandwidth.compute = TRUE,
bwmethod,
bwscaling,
bwtype,
ckertype,
ckerorder,
ukertype,
okertype,
optim.method,
optim.maxattempts,
optim.reltol,
optim.abstol,
optim.maxit,
...)
## S3 method for class 'scbandwidth'
npscoefbw(xdat = stop("invoked without data 'xdat'"),
ydat = stop("invoked without data 'ydat'"),
zdat = NULL,
bws,
nmulti,
random.seed = 42,
cv.iterate = FALSE,
cv.num.iterations = 1,
backfit.iterate = FALSE,
backfit.maxiter = 100,
backfit.tol = .Machine$double.eps,
bandwidth.compute = TRUE,
optim.method = c("NelderMead", "BFGS", "CG"),
optim.maxattempts = 10,
optim.reltol = sqrt(.Machine$double.eps),
optim.abstol = .Machine$double.eps,
optim.maxit = 500,
...)
formula 
a symbolic description of variables on which bandwidth selection is to be performed. The details of constructing a formula are described below. 
data 
an optional data frame, list or environment (or object
coercible to a data frame by 
subset 
an optional vector specifying a subset of observations to be used in the fitting process. 
na.action 
a function which indicates what should happen when the data contain

call 
the original function call. This is passed internally by

xdat 
a 
ydat 
a one (1) dimensional numeric or integer vector of dependent data, each
element 
zdat 
an optionally specified 
bws 
a bandwidth specification. This can be set as a 
... 
additional arguments supplied to specify the regression type, bandwidth type, kernel types, selection methods, and so on, detailed below. 
bandwidth.compute 
a logical value which specifies whether to do a numerical search for
bandwidths or not. If set to 
bwmethod 
which method was used to select bandwidths. 
bwscaling 
a logical value that when set to 
bwtype 
character string used for the continuous variable bandwidth type,
specifying the type of bandwidth provided. Defaults to

ckertype 
character string used to specify the continuous kernel type.
Can be set as 
ckerorder 
numeric value specifying kernel order (one of

ukertype 
character string used to specify the unordered categorical kernel type.
Can be set as 
okertype 
character string used to specify the ordered categorical kernel type.
Can be set as 
nmulti 
integer number of times to restart the process of finding extrema of
the crossvalidation function from different (random) initial
points. Defaults to 
random.seed 
an integer used to seed R's random number generator. This ensures replicability of the numerical search. Defaults to 42. 
optim.method 
method used by the default method is an implementation of that of Nelder and Mead (1965), that uses only function values and is robust but relatively slow. It will work reasonably well for nondifferentiable functions. method method 
optim.maxattempts 
maximum number of attempts taken trying to achieve successful
convergence in 
optim.abstol 
the absolute convergence tolerance used by 
optim.reltol 
relative convergence tolerance used by 
optim.maxit 
maximum number of iterations used by 
cv.iterate 
boolean value specifying whether or not to perform iterative,
crossvalidated backfitting on the data. See details for limitations
of the backfitting procedure. Defaults to 
cv.num.iterations 
integer specifying the number of times to iterate the backfitting
process over all covariates. Defaults to 
backfit.iterate 
boolean value specifying whether or not to iterate evaluations of
the smooth coefficient estimator, for extra accuracy, during the
crossvalidated backfitting procedure. Defaults to 
backfit.maxiter 
integer specifying the maximum number of times to iterate the
evaluation of the smooth coefficient estimator in the attempt to
obtain the desired accuracy. Defaults to 
backfit.tol 
tolerance to determine convergence of iterated evaluations of the
smooth coefficient estimator. Defaults to 
npscoefbw
implements a variety of methods for semiparametric
regression on multivariate (p+q
variate) explanatory data defined
over a set of possibly continuous data. The approach is based on Li and
Racine (2003) who employ ‘generalized product kernels’ that
admit a mix of continuous and discrete data types.
Three classes of kernel estimators for the continuous data types are
available: fixed, adaptive nearestneighbor, and generalized
nearestneighbor. Adaptive nearestneighbor bandwidths change with
each sample realization in the set, x_i
, when estimating the
density at the point x
. Generalized nearestneighbor bandwidths change
with the point at which the density is estimated, x
. Fixed bandwidths
are constant over the support of x
.
npscoefbw
may be invoked either with a formulalike
symbolic description of variables on which bandwidth selection is to be
performed or through a simpler interface whereby data is passed
directly to the function via the xdat
, ydat
, and
zdat
parameters. Use of these two interfaces is mutually
exclusive.
Data contained in the data frame xdat
may be continuous and in
zdat
may be of mixed type. Data can be entered in an arbitrary
order and data types will be detected automatically by the routine (see
np
for details).
Data for which bandwidths are to be estimated may be specified
symbolically. A typical description has the form dependent
data
~
parametric
explanatory
data

nonparametric
explanatory
data
, where
dependent
data
is a univariate response, and
parametric
explanatory
data
and
nonparametric
explanatory
data
are both series of
variables specified by name, separated by the separation character
'+'. For example, y1 ~ x1 + x2  z1
specifies that the
bandwidth object for the smooth coefficient model with response
y1
, linear parametric regressors x1
and x2
, and
nonparametric regressor (that is, the slopechanging variable)
z1
is to be estimated. See below for further examples. In the
case where the nonparametric (slopechanging) variable is not
specified, it is assumed to be the same as the parametric variable.
A variety of kernels may be specified by the user. Kernels implemented for continuous data types include the second, fourth, sixth, and eighth order Gaussian and Epanechnikov kernels, and the uniform kernel. Unordered discrete data types use a variation on Aitchison and Aitken's (1976) kernel, while ordered data types use a variation of the Wang and van Ryzin (1981) kernel.
if bwtype
is set to fixed
, an object containing
bandwidths (or scale factors if bwscaling = TRUE
) is
returned. If it is set to generalized_nn
or adaptive_nn
,
then instead the k
th nearest neighbors are returned for the
continuous variables while the discrete kernel bandwidths are returned
for the discrete variables. Bandwidths are stored in a vector under the
component name bw
. Backfitted bandwidths are stored under the
component name bw.fitted
.
The functions predict
, summary
, and
plot
support
objects of this class.
If you are using data of mixed types, then it is advisable to use the
data.frame
function to construct your input data and not
cbind
, since cbind
will typically not work as
intended on mixed data types and will coerce the data to the same
type.
Caution: multivariate datadriven bandwidth selection methods are, by
their nature, computationally intensive. Virtually all methods
require dropping the i
th observation from the data set,
computing an object, repeating this for all observations in the
sample, then averaging each of these leaveoneout estimates for a
given value of the bandwidth vector, and only then repeating
this a large number of times in order to conduct multivariate
numerical minimization/maximization. Furthermore, due to the potential
for local minima/maxima, restarting this procedure a large
number of times may often be necessary. This can be frustrating for
users possessing large datasets. For exploratory purposes, you may
wish to override the default search tolerances, say, setting
optim.reltol=.1 and conduct multistarting (the default is to restart
min(5,ncol(zdat)) times). Once the procedure terminates, you can restart
search with default tolerances using those bandwidths obtained from
the less rigorous search (i.e., set bws=bw
on subsequent calls
to this routine where bw
is the initial bandwidth object). A
version of this package using the Rmpi
wrapper is under
development that allows one to deploy this software in a clustered
computing environment to facilitate computation involving large
datasets.
Support for backfitted bandwidths is experimental and is limited in functionality. The code does not support asymptotic standard errors or out of sample estimates with backfitting.
Tristen Hayfield tristen.hayfield@gmail.com, Jeffrey S. Racine racinej@mcmaster.ca
Aitchison, J. and C.G.G. Aitken (1976), “Multivariate binary discrimination by the kernel method,” Biometrika, 63, 413420.
Cai Z. (2007), “Trending timevarying coefficient time series models with serially correlated errors,” Journal of Econometrics, 136, 163188.
Hastie, T. and R. Tibshirani (1993), “Varyingcoefficient models,” Journal of the Royal Statistical Society, B 55, 757796.
Li, Q. and J.S. Racine (2007), Nonparametric Econometrics: Theory and Practice, Princeton University Press.
Li, Q. and J.S. Racine (2010), “Smooth varyingcoefficient estimation and inference for qualitative and quantitative data,” Econometric Theory, 26, 131.
Pagan, A. and A. Ullah (1999), Nonparametric Econometrics, Cambridge University Press.
Li, Q. and D. Ouyang and J.S. Racine (2013), “Categorical semiparametric varyingcoefficient models,” Journal of Applied Econometrics, 28, 551589.
Wang, M.C. and J. van Ryzin (1981), “A class of smooth estimators for discrete distributions,” Biometrika, 68, 301309.
npregbw
, npreg
## Not run:
# EXAMPLE 1 (INTERFACE=FORMULA):
set.seed(42)
n < 100
x < runif(n)
z < runif(n, min=2, max=2)
y < x*exp(z)*(1.0+rnorm(n,sd = 0.2))
bw < npscoefbw(formula=y~xz)
summary(bw)
# EXAMPLE 1 (INTERFACE=DATA FRAME):
n < 100
x < runif(n)
z < runif(n, min=2, max=2)
y < x*exp(z)*(1.0+rnorm(n,sd = 0.2))
bw < npscoefbw(xdat=x, ydat=y, zdat=z)
summary(bw)
## End(Not run)
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