Kernel Consistent Density Equality Test with Mixed Data Types

npdeneqtest implements a consistent integrated squared difference test for equality of densities as described in Li, Maasoumi, and Racine (2009).

npdeneqtest(x = NULL,
            y = NULL,
            bw.x = NULL,
            bw.y = NULL,
            boot.num = 399,
            random.seed = 42,
            ...)

Arguments

x,y

data frames for the two samples for which one wishes to test equality of densities. The variables in each data frame must be the same (i.e. have identical names).

bw.x,bw.y

optional bandwidth objects for x,y

boot.num

an integer value specifying the number of bootstrap replications to use. Defaults to 399.

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, and so on. This is used if you do not pass in bandwidth objects and you do not desire the default behaviours. To do this, you may specify any of bwscaling, bwtype, ckertype, ckerorder, ukertype, okertype.

Value

npdeneqtest returns an object of type deneqtest with the following components

Tn

the (standardized) statistic Tn

In

the (unstandardized) statistic In

Tn.bootstrap

contains the bootstrap replications of Tn

In.bootstrap

contains the bootstrap replications of In

Tn.P

the P-value of the Tn statistic

In.P

the P-value of the In statistic

boot.num

number of bootstrap replications

summary supports object of type deneqtest.

References

Li, Q. and E. Maasoumi and J.S. Racine (2009), “A Nonparametric Test for Equality of Distributions with Mixed Categorical and Continuous Data,” Journal of Econometrics, 148, pp 186-200.

Author

Tristen Hayfield tristen.hayfield@gmail.com, Jeffrey S. Racine racinej@mcmaster.ca

Details

npdeneqtest computes the integrated squared density difference between the estimated densities/probabilities of two samples having identical variables/datatypes. See Li, Maasoumi, and Racine (2009) for details.

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.

It is crucial that both data frames have the same variable names.

See also

npdeptest,npsdeptest,npsymtest,npunitest

Examples

if (FALSE) { # \dontrun{
set.seed(1234)

## Distributions are equal

n <- 250

sample.A <- data.frame(x=rnorm(n))
sample.B <- data.frame(x=rnorm(n))

npdeneqtest(sample.A,sample.B,boot.num=99)

Sys.sleep(5)

## Distributions are unequal

sample.A <- data.frame(x=rnorm(n))
sample.B <- data.frame(x=rchisq(n,df=5))

npdeneqtest(sample.A,sample.B,boot.num=99)

## Mixed datatypes, distributions are equal

sample.A <- data.frame(a=rnorm(n),b=factor(rbinom(n,2,.5)))
sample.B <- data.frame(a=rnorm(n),b=factor(rbinom(n,2,.5)))

npdeneqtest(sample.A,sample.B,boot.num=99)

Sys.sleep(5)

## Mixed datatypes, distributions are unequal

sample.A <- data.frame(a=rnorm(n),b=factor(rbinom(n,2,.5)))
sample.B <- data.frame(a=rnorm(n,sd=10),b=factor(rbinom(n,2,.25)))

npdeneqtest(sample.A,sample.B,boot.num=99)
} # }