CovTest2.2013Cai {CovTools} | R Documentation |
Given two sets of data, it performs 2-sample test for equality of covariance matrices where the null hypothesis is
H_0 : Σ_1 = Σ_2
where Σ_1 and Σ_2 represent true (unknown) covariance
for each dataset based on a procedure proposed by Cai and Ma (2013).
If statistic
> threshold
, it rejects null hypothesis.
CovTest2.2013Cai(X, Y, alpha = 0.05)
X |
an (m\times p) matrix where each row is an observation from the first dataset. |
Y |
an (n\times p) matrix where each row is an observation from the second dataset. |
alpha |
level of significance. |
a named list containing
a test statistic value.
rejection criterion to be compared against test statistic.
a logical; TRUE
to reject null hypothesis, FALSE
otherwise.
Cai TT, Ma Z (2013). “Optimal hypothesis testing for high dimensional covariance matrices.” Bernoulli, 19(5B), 2359–2388. ISSN 1350-7265.
## generate 2 datasets from multivariate normal with identical covariance. pdim = 5 data1 = matrix(rnorm(100*pdim), ncol=pdim) data2 = matrix(rnorm(150*pdim), ncol=pdim) ## run test CovTest2.2013Cai(data1, data2)