npsigtest  R Documentation 
npsigtest
implements a consistent test of significance of an
explanatory variable(s) in a nonparametric regression setting that is
analogous to a simple ttest (Ftest) in a parametric
regression setting. The test is based on Racine, Hart, and Li (2006)
and Racine (1997).
npsigtest(bws, ...) ## S3 method for class 'formula' npsigtest(bws, data = NULL, ...) ## S3 method for class 'call' npsigtest(bws, ...) ## S3 method for class 'npregression' npsigtest(bws, ...) ## Default S3 method: npsigtest(bws, xdat, ydat, ...) ## S3 method for class 'rbandwidth' npsigtest(bws, xdat = stop("data xdat missing"), ydat = stop("data ydat missing"), boot.num = 399, boot.method = c("iid","wild","wildrademacher","pairwise"), boot.type = c("I","II"), pivot=TRUE, joint=FALSE, index = seq(1,ncol(xdat)), random.seed = 42, ...)
bws 
a bandwidth specification. This can be set as a 
data 
an optional data frame, list or environment (or object coercible to
a data frame by 
xdat 
a pvariate data frame of explanatory data (training data) used to calculate the regression estimators. 
ydat 
a one (1) dimensional numeric or integer vector of dependent data,
each element i corresponding to each observation (row) i
of 
boot.method 
a character string used to specify the bootstrap method for
determining the null distribution. 
boot.num 
an integer value specifying the number of bootstrap replications to
use. Defaults to 
boot.type 
a character string specifying whether to use a ‘Bootstrap I’ or
‘Bootstrap II’ method (see Racine, Hart, and Li (2006) for
details). The ‘Bootstrap II’ method reruns crossvalidation for
each bootstrap replication and uses the new crossvalidated
bandwidth for variable i and the original ones for the
remaining variables. Defaults to 
pivot 
a logical value which specifies whether to bootstrap a pivotal
statistic or not (pivoting is achieved by dividing gradient
estimates by their asymptotic standard errors). Defaults to

joint 
a logical value which specifies whether to conduct a joint test or
individual test. This is to be used in conjunction with 
index 
a vector of indices for the columns 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 specify the bandwidth type, kernel types, selection methods, and so on, detailed below. 
npsigtest
implements a variety of methods for computing the
null distribution of the test statistic and allows the user to
investigate the impact of a variety of default settings including
whether or not to pivot the statistic (pivot
), whether pairwise
or residual resampling is to be used (boot.method
), and whether
or not to recompute the bandwidths for the variables being tested
(boot.type
), among others.
Defaults are chosen so as to provide reasonable behaviour in a broad
range of settings and this involves a tradeoff between computational
expense and finitesample performance. However, the default
boot.type="I"
, though computationally expedient, can deliver a
test that can be slightly oversized in small sample settings (e.g.
at the 5% level the test might reject 8% of the time for samples of
size n=100 for some data generating processes). If the default
setting (boot.type="I"
) delivers a Pvalue that is in the
neighborhood (i.e. slightly smaller) of any classical level
(e.g. 0.05) and you only have a modest amount of data, it might be
prudent to rerun the test using the more computationally intensive
boot.type="II"
setting to confirm the original result. Note
also that boot.method="pairwise"
is not recommended for the
multivariate local linear estimator due to substantial size
distortions that may arise in certain cases.
npsigtest
returns an object of type
sigtest
. summary
supports sigtest
objects. It
has the
following components:
In 
the vector of statistics 
P 
the vector of Pvalues for each statistic in 
In.bootstrap 
contains a matrix of the bootstrap
replications of the vector 
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: bootstrap methods are, by their nature, computationally
intensive. This can be frustrating for users possessing large
datasets. For exploratory purposes, you may wish to override the
default number of bootstrap replications, say, setting them to
boot.num=99
. 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.
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.
Li, Q. and J.S. Racine (2007), Nonparametric Econometrics: Theory and Practice, Princeton University Press.
Racine, J.S., J. Hart, and Q. Li (2006), “Testing the significance of categorical predictor variables in nonparametric regression models,” Econometric Reviews, 25, 523544.
Racine, J.S. (1997), “Consistent significance testing for nonparametric regression,” Journal of Business and Economic Statistics 15, 369379.
Wang, M.C. and J. van Ryzin (1981), “A class of smooth estimators for discrete distributions,” Biometrika, 68, 301309.
## Not run: # EXAMPLE 1 (INTERFACE=FORMULA): For this example, we simulate 100 draws # from a DGP in which z, the first column of X, is an irrelevant # discrete variable set.seed(12345) n < 100 z < rbinom(n,1,.5) x1 < rnorm(n) x2 < runif(n,2,2) y < x1 + x2 + rnorm(n) # Next, we must compute bandwidths for our regression model. In this # case we conduct local linear regression. Note  this may take a few # minutes depending on the speed of your computer... bw < npregbw(formula=y~factor(z)+x1+x2,regtype="ll",bwmethod="cv.aic") # We then compute a vector of tests corresponding to the columns of # X. Note  this may take a few minutes depending on the speed of your # computer... we have to generate the null distribution of the statistic # for each variable whose significance is being tested using 399 # bootstrap replications for each... npsigtest(bws=bw) # If you wished, you could conduct the test for, say, variables 1 and 3 # only, as in npsigtest(bws=bw,index=c(1,3)) # EXAMPLE 1 (INTERFACE=DATA FRAME): For this example, we simulate 100 # draws from a DGP in which z, the first column of X, is an irrelevant # discrete variable set.seed(12345) n < 100 z < rbinom(n,1,.5) x1 < rnorm(n) x2 < runif(n,2,2) X < data.frame(factor(z),x1,x2) y < x1 + x2 + rnorm(n) # Next, we must compute bandwidths for our regression model. In this # case we conduct local linear regression. Note  this may take a few # minutes depending on the speed of your computer... bw < npregbw(xdat=X,ydat=y,regtype="ll",bwmethod="cv.aic") # We then compute a vector of tests corresponding to the columns of # X. Note  this may take a few minutes depending on the speed of your # computer... we have to generate the null distribution of the statistic # for each variable whose significance is being tested using 399 # bootstrap replications for each... npsigtest(bws=bw) # If you wished, you could conduct the test for, say, variables 1 and 3 # only, as in npsigtest(bws=bw,index=c(1,3)) ## End(Not run)
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