*! version 12.0.0 20dec2012

Title

vx_dbel -- Novel and Efficient Distribution Free Density Based Empirical Likelihood Procedure for Symmetry and K-sample Comparisons

Syntax

vx_dbel
[varlist]
[, options]

Main
sided define the test as less, greater or two sided;
default is sided("two.sided")

method define the test method as monte carlo, interpolation, or hybrid;
default is method("interpolation")

Monte Carlo
repsnum(#) define the number of monte carlo iterations to obtain the critical value;
default is repsnum(10000)

Bayesian
alpha(#) define significance level for the hybrid method;
default is alpha(0.05)

Description

vx_dbel calculates the vx_dbel statistic and p-value for the STATA variables in
varlist. The test is conducted for one, two or three samples based on the the
number of STATA variables in varlist. A test of symmetry is conducted for one sample,
and a sample comparison test is conducted for two and three samples.
The one and two sample tests are more powerful alternatives to wilcoxon.

Options

Main

sided displays output for one sided or two sided test. greater and less perform a one sided test. two.sided performs a two sided test. Note: The three sample comparison does not have a one sided test.

method Defines the method of the test. mc defines the method as monte carlo. interpolation defines the method as interpolation. hybrid defines the method as a hybrid of monte carlo and interpolation, based on a bayesian approach.

alpha(#) specifies the significance level for the hybrid method. The default is alpha(0.05), meaning that a significance level of 0.05 is used for alpha in the hybrid calculation method.

repsnum(#) specifies the number of repetitions to use in calculating the critical values for the monte carlo method. The default is repsnum(10000), meaning that 10000 repetitions are used to obtain critical values with monte carlo method.

Remarks

For the mc method, the critical values are obtained by monte carlo simulations. For the hybrid and interpolation methods, the critical values are obtained using a table of critical values already prepared using monte carlo. Note: The table of critical values is complete for sample sizes of less than or equal to thirty, but has gaps for sample sizes greater than thirty. If all sample sizes are less than or equal to thirty then the critical values are available in the table, and results are obtained faster. If all sample sizes are not less than thirty then the hybrid or interpolation method is utilized.

If only one sample (say X) is specified in varlist, a test of symmetry is conducted. If the two sided alternative is specified, a test of the null distribution of X being symmetric about zero is performed. If a one sided alternative is specified, a test of the null distribution of X being less or greater than zero is performed.

If only two samples (say X and Y) are specified, a two-sample comparison test is conducted. If the two sided alternative is specified, a test of the null distributions of X and Y being equal is performed. If a one sided alternative is specified, a test of the null distribution of X being stochastically less or greater than Y is performed.

If three samples (say, X, Y, and Z) are specified, a three-sample comparison test is conducted. A test of the null distributions of X, Y and Z being equal is performed.

Examples

Note1: X, Y, and Z represent the names of STATA variables to be tested.

Note2:sided("two.sided") and method("interpolation") are the defaults and need not be specified. For hybrid method, alpha("0.05) is the default and need not be specified. For mc method,
cmd:repsnum(10000)} is the default and need not be specified.

One-sample:

. vx_dbel X, repsnum(20000) sided("greater") method("mc")

. vx_dbel X, repsnum(10000) sided("less") method("mc")

. vx_dbel X, method("mc")

. vx_dbel X, sided("greater") method("interpolation")

. vx_dbel X, sided("less")

. vx_dbel X

. vx_dbel X, alpah(0.05) sided("greater") method("hybrid")

. vx_dbel X, sided("less") method("hybrid")

. vx_dbel X, method("hybrid")

two-sample:

. vx_dbel X Y, repsnum(1000) sided("greater") method("mc")

. vx_dbel X Y, sided("less") method("mc")

. vx_dbel X Y, method("mc")

. vx_dbel X Y, sided("greater") method("interpolation")

. vx_dbel X Y, sided("less")

. vx_dbel X Y

. vx_dbel X Y, sided("greater") method("hybrid")

. vx_dbel X Y, alpah(0.075) sided("less") method("hybrid")

. vx_dbel X Y, sided("two.sided") method("hybrid")

three-sample:

. vx_dbel X Y Z, repsnum(1000) method("mc")

. vx_dbel X Y Z, method("hybrid")

. vx_dbel X Y Z