npqcmstest  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","wildrademacher"), 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 
subset 
an optional vector specifying a subset of observations to be used. 
model 
a model object obtained from a call to 
xdat 
a pvariate 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

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. 
bwydat 
a character string used to specify the left hand side variable used
in bandwidth selection. 
boot.method 
a character string used to specify the bootstrap method.

boot.num 
an integer value specifying the number of bootstrap replications to
use. Defaults to 
pivot 
a logical value specifying whether the statistic should be
normalised such that it approaches N(0,1) in
distribution. Defaults to 
density.weighted 
a logical value specifying whether the statistic should be
weighted by the density of 
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 
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 
In 
the statistic 
Omega.hat 
as described in Racine, J.S. (2006). 
q.* 
the various quantiles of the statistic 
P 
the Pvalue of the statistic 
Jn.bootstrap 
if 
In.bootstrap 
if 
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 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.
Koenker, R.W. and G.W. Bassett (1978), “Regression quantiles,” Econometrica, 46, 3350.
Li, Q. and J.S. Racine (2007), Nonparametric Econometrics: Theory and Practice, Princeton University Press.
Murphy, K. M. and F. Welch (1990), “Empirical ageearnings profiles,” Journal of Labor Economics, 8, 202229.
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, 301309.
Zheng, J. (1998), “A consistent nonparametric test of parametric regression models under conditional quantile restrictions,” Econometric Theory, 14, 123138.
## Not run: # 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) # 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)
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