power.mvnTest {mvnormalTest}

Power Calculation using the Zhou-Shao's Multivariate Normality Test Statistic (T_n)

Description

Empirical power calculation using the Zhou-Shao's multivariate normality test Statistic T_n.

Usage

power.mvnTest(a, n, p, B = 1000, pct = c(0.01, 0.99), FUN, ...)

Arguments

a

significance level (\alpha).

n

number of rows (observations).

p

number of columns (variables), n>p.

B

number of Monte Carlo simulations, default is 1000 (can increase B to increase the precision).

pct

percentiles of MK to get c1 and c2 described in the reference paper,default is (0.01, 0.99).

FUN

self-defined function for generate multivariate distribution. See example.

...

optional arguments passed to FUN.

Value

Returns a numeric value of the estimated empirical power (value between 0 and 1).

References

Zhou, M., & Shao, Y. (2014). A powerful test for multivariate normality. Journal of applied statistics, 41(2), 351-363.

Examples

set.seed(12345)

## Power calculation against bivariate (p=2) independent Beta(1, 1) distribution ##
## at sample size n=50 for Tn at one-sided alpha = 0.05 ##

power.mvnTest(a = 0.05, n = 50, p = 2,  B = 100, pct = c(0.01, 0.99), FUN=IMMV, D1=runif)