| npsigtest {np} | R Documentation |
npsigtest implements a consistent test of significance of
an explanatory variable in a nonparametric regression setting that is
analogous to a simple t-test 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","wild-rademacher"),
boot.type=c("I","II"),
index=seq(1,ncol(xdat)),
random.seed = 42,
...)
bws |
a bandwidth specification. This can be set as a rbandwidth
object returned from a previous invocation, or as a vector of
bandwidths, with each element i corresponding to the bandwidth
for column i in xdat. In either case, the bandwidth
supplied will serve as a starting point in the numerical search for
optimal bandwidths when using boot.type="II". If specified
as a vector, then additional arguments will need to be supplied as
necessary to specify the bandwidth type, kernel types, selection
methods, and so on.
|
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
npregbw was called.
|
xdat |
a p-variate 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
xdat.
|
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.
|
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 re-runs cross-validation for
each bootstrap replication and uses the new cross-validated
bandwidth for variable i and the original ones for the
remaining variables. Defaults to boot.type="I".
|
index |
a vector of indices for the columns of xdat for which the
test of significance is to be conducted. Defaults to (1,2,...,p)
where p is the number of columns in xdat.
|
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 returns an object of type
sigtest. summary supports sigtest objects. It
has the
following components:
In |
the vector of statistics In |
P |
the vector of P-values for each statistic in In |
In.bootstrap |
contains a matrix of the bootstrap
replications of the vector In, each column corresponding to
replications associated with explanatory variables in xdat
indexed by index (e.g., if you selected index = c(1,4)
then In.bootstrap will have two columns, the first being the
bootstrap replications of In associated with variable
1, the second with variable 4). |
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 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.
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, 523-544.
Racine, J.S. (1997), “Consistent significance testing for nonparametric regression,” Journal of Business and Economic Statistics 15, 369-379.
Wang, M.C. and J. van Ryzin (1981), “A class of smooth estimators for discrete distributions,” Biometrika, 68, 301-309.
# 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) ## Not run: # 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)