R: Kernel Conditional Distribution Estimation with Mixed Data...
npcdist
R Documentation
Kernel Conditional Distribution Estimation with Mixed Data Types
Description
npcdist computes kernel cumulative conditional distribution
estimates on p+q-variate evaluation data, given a set of
training data (both explanatory and dependent) and a bandwidth
specification (a condbandwidth object or a bandwidth vector,
bandwidth type, and kernel type) using the method of Li and Racine
(2008) and Li, Lin, and Racine (2013). The data may be continuous,
discrete (unordered and ordered factors), or some combination thereof.
Usage
npcdist(bws, ...)
## S3 method for class 'formula'
npcdist(bws, data = NULL, newdata = NULL, ...)
## S3 method for class 'call'
npcdist(bws, ...)
## S3 method for class 'condbandwidth'
npcdist(bws,
txdat = stop("invoked without training data 'txdat'"),
tydat = stop("invoked without training data 'tydat'"),
exdat,
eydat,
gradients = FALSE,
...)
## Default S3 method:
npcdist(bws, txdat, tydat, ...)
Arguments
bws
a bandwidth specification. This can be set as a condbandwidth
object returned from a previous invocation of
npcdistbw, or as a p+q-vector of bandwidths,
with each element i up to i=q corresponding to the
bandwidth for column i in tydat, and each element
i from i=q+1 to i=p+q corresponding to the
bandwidth for column i-q in txdat. If specified as a
vector, then additional arguments will need to be supplied as
necessary to specify the bandwidth type, kernel types, training
data, and so on.
gradients
a logical value specifying whether to return estimates of the
gradients at the evaluation points. Defaults to FALSE.
...
additional arguments supplied to specify the bandwidth type, kernel
types, and so on. This is necessary if you specify bws as a
p+q-vector and not a condbandwidth object, and you do
not desire the default behaviours. To do this, you may specify any
of bwmethod, bwscaling, bwtype,
cxkertype, cxkerorder, cykertype,
cykerorder, uxkertype, oxkertype,
oykertype, as described in npcdistbw.
data
an optional data frame, list or environment (or object coercible to
a data frame by as.data.frame) containing the
variables in the model. If not found in data, the variables are
taken from environment(bws), typically the environment from
which npcdistbw was called.
newdata
An optional data frame in which to look for evaluation data. If
omitted, the training data are used.
txdat
a p-variate data frame of sample realizations of explanatory
data (training data). Defaults to the training data used to
compute the bandwidth object.
tydat
a q-variate data frame of sample realizations of dependent
data (training data). Defaults to the training data used to
compute the bandwidth object.
exdat
a p-variate data frame of explanatory data on
which cumulative conditional distributions will be evaluated. By
default, evaluation takes place on the data provided by
txdat.
eydat
a q-variate data frame of dependent data on which
cumulative conditional distributions will be evaluated. By default,
evaluation takes place on the data provided by tydat.
Details
npcdist implements a variety of methods for estimating
multivariate conditional cumulative distributions (p+q-variate)
defined over a set of possibly continuous and/or discrete (unordered,
ordered) data. The approach is based on Li and Racine (2004) 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 nearest-neighbor, and generalized
nearest-neighbor. Adaptive nearest-neighbor bandwidths change with
each sample realization in the set, x[i], when estimating
the cumulative conditional distribution at the point
x. Generalized nearest-neighbor bandwidths change with the point
at which the cumulative conditional distribution is estimated,
x. Fixed bandwidths are constant over the support of x.
Training and evaluation input data may be a
mix of continuous (default), unordered discrete (to be specified in
the data frames using factor), and ordered discrete (to be
specified in the data frames using ordered). Data can be
entered in an arbitrary order and data types will be detected
automatically by the routine (see np for details).
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.
Value
npcdist returns a condistribution object. The generic
accessor functions fitted, se, and
gradients, extract estimated values, asymptotic standard
errors on estimates, and gradients, respectively, from
the returned object. Furthermore, the functions predict,
summary
and plot support objects of both classes. The returned objects
have the following components:
xbw
bandwidth(s), scale factor(s) or nearest neighbours for the
explanatory data, txdat
ybw
bandwidth(s), scale factor(s) or nearest neighbours for the
dependent data, tydat
xeval
the evaluation points of the explanatory data
yeval
the evaluation points of the dependent data
condist
estimates of the conditional cumulative
distribution at the evaluation points
conderr
standard errors of the cumulative conditional distribution
estimates
congrad
if invoked with gradients = TRUE, estimates of
the gradients at the evaluation points
congerr
if invoked with gradients = TRUE, standard
errors of the gradients at the evaluation points
log_likelihood
log likelihood of the cumulative conditional distribution estimate
Usage Issues
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.
Aitchison, J. and C.G.G. Aitken (1976), “Multivariate binary
discrimination by the kernel method,” Biometrika, 63, 413-420.
Hall, P. and J.S. Racine and Q. Li (2004), “Cross-validation and the
estimation of conditional probability densities,” Journal of the
American Statistical Association, 99, 1015-1026.
Li, Q. and J.S. Racine (2007), Nonparametric Econometrics: Theory
and Practice, Princeton University Press.
Li, Q. and J.S. Racine (2008), “Nonparametric estimation of
conditional CDF and quantile functions with mixed categorical and
continuous data,” Journal of Business and Economic Statistics, 26,
423-434.
Li, Q. and J. Lin and J.S. Racine (2013), “Optimal bandwidth
selection for nonparametric conditional distribution and quantile
functions”, Journal of Business and Economic Statistics, 31, 57-65.
Pagan, A. and A. Ullah (1999), Nonparametric Econometrics, Cambridge
University Press.
Scott, D.W. (1992), Multivariate Density Estimation. Theory,
Practice and Visualization, New York: Wiley.
Silverman, B.W. (1986), Density Estimation, London: Chapman and
Hall.
Wang, M.C. and J. van Ryzin (1981), “A class of smooth estimators
for discrete distributions,” Biometrika, 68, 301-309.
See Also
npudens
Examples
## Not run:
# EXAMPLE 1 (INTERFACE=FORMULA): For this example, we load Giovanni
# Baiocchi's Italian GDP panel (see Italy for details), and compute the
# cross-validated bandwidths (default) using a second-order Gaussian
# kernel (default). Note - this may take a minute or two depending on
# the speed of your computer.
data("Italy")
attach(Italy)
# First, compute the bandwidths.
bw <- npcdistbw(formula=gdp~ordered(year))
# Next, compute the condistribution object...
Fhat <- npcdist(bws=bw)
# The object Fhat now contains results such as the estimated cumulative
# conditional distribution function (Fhat$condist) and so on...
summary(Fhat)
# Call the plot() function to visualize the results (<ctrl>-C will
# interrupt on *NIX systems, <esc> will interrupt on MS Windows
# systems).
plot(bw)
detach(Italy)
# EXAMPLE 1 (INTERFACE=DATA FRAME): For this example, we load Giovanni
# Baiocchi's Italian GDP panel (see Italy for details), and compute the
# cross-validated bandwidths (default) using a second-order Gaussian
# kernel (default). Note - this may take a minute or two depending on
# the speed of your computer.
data("Italy")
attach(Italy)
# First, compute the bandwidths.
# Note - we cast `X' and `y' as data frames so that plot() can
# automatically grab names (this looks like overkill, but in
# multivariate settings you would do this anyway, so may as well get in
# the habit).
X <- data.frame(year=ordered(year))
y <- data.frame(gdp)
bw <- npcdistbw(xdat=X, ydat=y)
# Next, compute the condistribution object...
Fhat <- npcdist(bws=bw)
# The object Fhat now contains results such as the estimated cumulative
# conditional distribution function (Fhat$condist) and so on...
summary(Fhat)
# Call the plot() function to visualize the results (<ctrl>-C will
# interrupt on *NIX systems, <esc> will interrupt on MS Windows systems).
plot(bw)
detach(Italy)
# EXAMPLE 2 (INTERFACE=FORMULA): For this example, we load the old
# faithful geyser data from the R `datasets' library and compute the
# conditional distribution function.
library("datasets")
data("faithful")
attach(faithful)
# Note - this may take a few minutes depending on the speed of your
# computer...
bw <- npcdistbw(formula=eruptions~waiting)
summary(bw)
# Plot the conditional cumulative distribution function (<ctrl>-C will
# interrupt on *NIX systems, <esc> will interrupt on MS Windows
# systems).
plot(bw)
detach(faithful)
# EXAMPLE 2 (INTERFACE=DATA FRAME): For this example, we load the old
# faithful geyser data from the R `datasets' library and compute the
# cumulative conditional distribution function.
library("datasets")
data("faithful")
attach(faithful)
# Note - this may take a few minutes depending on the speed of your
# computer...
# Note - we cast `X' and `y' as data frames so that plot() can
# automatically grab names (this looks like overkill, but in
# multivariate settings you would do this anyway, so may as well get in
# the habit).
X <- data.frame(waiting)
y <- data.frame(eruptions)
bw <- npcdistbw(xdat=X, ydat=y)
summary(bw)
# Plot the conditional cumulative distribution function (<ctrl>-C will
# interrupt on *NIX systems, <esc> will interrupt on MS Windows systems)
plot(bw)
detach(faithful)
## End(Not run)