| npqcmstest {np} | R Documentation |
npqcmstest implements a consistent test for correct
specification of parametric quantile regression models (linear or
nonlinear) as described in Racine (2006) which extends the work of
Zheng (1998).
npqcmstest(formula,
data = NULL,
subset,
xdat,
ydat,
model = stop(paste(sQuote("model")," has not been provided")),
tau = 0.5,
distribution = c("bootstrap", "asymptotic"),
bwydat = c("y","varepsilon"),
boot.method=c("iid","wild","wild-rademacher"),
boot.num = 399,
pivot = TRUE,
density.weighted = TRUE,
random.seed = 42,
...)
formula |
a symbolic description of variables on which the test 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 as.data.frame) containing the variables
in the model. If not found in data, the variables are taken from
environment(formula), typically the environment from which the
function is called.
|
subset |
an optional vector specifying a subset of observations to be used. |
model |
a model object obtained from a call to rq. Important: the
call to rq must have the argument model=TRUE or
npqcmstest will not work.
|
xdat |
a p-variate data frame of explanatory data (training data) used to calculate the quantile regression estimators. |
ydat |
a one (1) dimensional numeric or integer vector of dependent data, each
element i corresponding to each observation (row) i of
xdat.
|
tau |
a numeric value specifying the tauth quantile is desired |
distribution |
a character string used to specify the method of estimating the
distribution of the statistic to be calculated. bootstrap
will conduct bootstrapping. asymptotic will use the normal
distribution. Defaults to bootstrap.
|
bwydat |
a character string used to specify ydat used in bandwidth
selection. varepsilon
uses 1-tau,-tau for ydat while
y will use y. Defaults to y.
|
boot.method |
a character string used to specify the bootstrap method.
iid will generate independent identically distributed
draws. wild will use a wild bootstrap. wild-rademacher
will use a wild bootstrap with Rademacher variables. Defaults to
iid.
|
boot.num |
an integer value specifying the number of bootstrap replications to
use. Defaults to 399.
|
pivot |
a logical value specifying whether the statistic should be
normalised such that it approaches N(0,1) in
distribution. data. Defaults to TRUE.
|
density.weighted |
a logical value specifying whether the statistic should be
weighted by the density of xdat. Defaults to TRUE.
|
random.seed |
an integer used to seed R's random number generator. This is to ensure replicability. Defaults to 42. |
... |
additional arguments supplied to control bandwidth selection on the
residuals. One can specify the bandwidth type,
kernel types, and so on. To do this, you may specify any of bwscaling,
bwtype, ckertype, ckerorder, ukertype,
okertype, as described in npregbw.
This is necessary if you specify bws as a p-vector and not
a bandwidth object, and you do not desire the default behaviours.
|
npqcmstest returns an object of type cmstest with the
following components, components will contain information
related to Jn or In depending on the value of pivot:
Jn |
the statistic Jn |
In |
the statistic In |
Omega.hat |
as described in Racine, J.S. (2006). |
q.* |
the various quantiles of the statistic Jn (or
In if
pivot=FALSE) are in
components q.90,
q.95, q.99 (one-sided 1%, 5%, 10% critical values) |
P |
the P-value of the statistic |
Jn.bootstrap |
if pivot=TRUE contains the bootstrap
replications of Jn |
In.bootstrap |
if pivot=FALSE contains the bootstrap
replications of In |
summary supports object of type cmstest.
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.
Tristen Hayfield hayfield@phys.ethz.ch, Jeffrey S. Racine racinej@mcmaster.ca
Aitchison, J. and C.G.G. Aitken (1976), “Multivariate binary discrimination by the kernel method,” Biometrika, 63, 413-420.
Koenker, R.W. and G.W. Bassett (1978), “Regression quantiles”, Econometrica, 46, 33-50.
Li, Q. and J.S. Racine (2007), Nonparametric Econometrics: Theory and Practice, Princeton University Press.
Murphy, K. M. and F. Welch (1990), “Empirical age-earnings profiles,” Journal of Labor Economics, 8, 202-229.
Pagan, A. and A. Ullah (1999), Nonparametric Econometrics, Cambridge University Press.
Racine, J.S. (2006), “Consistent specification testing of heteroskedastic parametric regression quantile models with mixed data,” manuscript.
Wang, M.C. and J. van Ryzin (1981), “A class of smooth estimators for discrete distributions,” Biometrika, 68, 301-309.
Zheng, J. (1998), “A consistent nonparametric test of parametric regression models under conditional quantile restrictions”, Econometric Theory, 14, 123-138.
# EXAMPLE 1: For this example, we conduct a consistent quantile regression
# model specification test for a parametric wage quantile regression
# model that is quadratic in age. The work of Murphy and Welch (1990)
# would suggest that this parametric quantile regression model is
# misspecified.
library("quantreg")
data("cps71")
attach(cps71)
model <- rq(logwage~age+I(age^2), tau=0.5, model=TRUE)
plot(age, logwage)
lines(age, fitted(model))
X <- data.frame(age)
# Note - this may take a few minutes depending on the speed of your
# computer...
npqcmstest(model = model, xdat = X, ydat = logwage, tau=0.5)
## Not run:
# Sleep for 5 seconds so that we can examine the output...
Sys.sleep(5)
# Next try Murphy & Welch's (1990) suggested quintic specification.
model <- rq(logwage~age+I(age^2)+I(age^3)+I(age^4)+I(age^5), model=TRUE)
plot(age, logwage)
lines(age, fitted(model))
X <- data.frame(age)
# Note - this may take a few minutes depending on the speed of your
# computer...
npqcmstest(model = model, xdat = X, ydat = logwage, tau=0.5)
detach(cps71)
## End(Not run)