Description Usage Arguments Details Value Note References See Also Examples
Calculates p-value of the test for testing equality of two-sample high-dimensional mean vectors proposed by Srivastava and Du (2008) based on the asymptotic distribution of the test statistic.
1 | apval_Sri2008(sam1, sam2)
|
sam1 |
an n1 by p matrix from sample population 1. Each row represents a p-dimensional sample. |
sam2 |
an n2 by p matrix from sample population 2. Each row represents a p-dimensional sample. |
Suppose that the two groups of p-dimensional independent and identically distributed samples \{X_{1i}\}_{i=1}^{n_1} and \{X_{2j}\}_{j=1}^{n_2} are observed; we consider high-dimensional data with p \gg n := n_1 + n_2 - 2. Assume that the two groups share a common covariance matrix. The primary object is to test H_{0}: μ_1 = μ_2 versus H_{A}: μ_1 \neq μ_2. Let \bar{X}_{k} be the sample mean for group k = 1, 2. Also, let S = n^{-1} ∑_{k = 1}^{2} ∑_{i = 1}^{n_{k}} (X_{ki} - \bar{X}_k) (X_{ki} - \bar{X}_k)^T be the pooled sample covariance matrix from the two groups.
Srivastava and Du (2008) proposed the following test statistic:
T_{SD} = \frac{(n_1^{-1} + n_2^{-1})^{-1} (\bar{X}_1 - \bar{X}_2)^T D_S^{-1} (\bar{X}_1 - \bar{X}_2) - (n - 2)^{-1} n p}{√{2 (tr R^2 - p^2 n^{-1}) c_{p, n}}},
where D_S = diag (s_{11}, s_{22}, ..., s_{pp}), s_{ii}'s are the diagonal elements of S, R = D_S^{-1/2} S D_S^{-1/2} is the sample correlation matrix and c_{p, n} = 1 + tr R^2 p^{-3/2}. This test statistic follows normal distribution under the null hypothesis.
A list including the following elements:
sam.info |
the basic information about the two groups of samples, including the samples sizes and dimension. |
cov.assumption |
this output reminds users that the two sample populations have a common covariance matrix. |
method |
this output reminds users that the p-values are obtained using the asymptotic distributions of test statistics. |
pval |
the p-value of the test proposed by Srivastava and Du (2008). |
The asymptotic distribution of the test statistic was derived under normality assumption in Bai and Saranadasa (1996). Also, this function assumes that the two sample populations have a common covariance matrix.
Srivastava MS and Du M (2008). "A test for the mean vector with fewer observations than the dimension." Journal of Multivariate Analysis, 99(3), 386–402.
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Loading required package: mvtnorm
$sam.info
n1 n2 p
50 50 200
$cov.assumption
[1] "the two groups have same covariance"
$method
[1] "asymptotic distribution"
$pval
Sri2008
0.61321
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