Description Usage Arguments Details Value References See Also Examples

Calculates p-value of the test for testing equality of two-sample high-dimensional mean vectors proposed by Chen and Qin (2010) based on the asymptotic distribution of the test statistic.

1 | ```
apval_Chen2010(sam1, sam2, eq.cov = TRUE)
``` |

`sam1` |
an n1 by p matrix from sample population 1. Each row represents a |

`sam2` |
an n2 by p matrix from sample population 2. Each row represents a |

`eq.cov` |
a logical value. The default is |

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*. 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*.

Chen and Qin (2010) proposed the following test statistic:

*T_{CQ} = \frac{∑_{i \neq j}^{n_1} X_{1i}^T X_{1j}}{n_1 (n_1 - 1)} + \frac{∑_{i \neq j}^{n_2} X_{2i}^T X_{2j}}{n_2 (n_2 - 1)} - 2 \frac{∑_{i = 1}^{n_1} ∑_{j = 1}^{n_2} X_{1i}^T X_{2j}}{n_1 n_2},*

and its asymptotic distribution is normal 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` |
the equality assumption on the covariances of the two sample populations; this was specified by the argument |

`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 Chen and Qin (2010). |

Chen SX and Qin YL (2010). "A two-sample test for high-dimensional data with applications to gene-set testing." *The Annals of Statistics*, **38**(2), 808–835.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 | ```
library(MASS)
set.seed(1234)
n1 <- n2 <- 50
p <- 200
mu1 <- rep(0, p)
mu2 <- mu1
mu2[1:10] <- 0.2
true.cov <- 0.4^(abs(outer(1:p, 1:p, "-"))) # AR1 covariance
sam1 <- mvrnorm(n = n1, mu = mu1, Sigma = true.cov)
sam2 <- mvrnorm(n = n2, mu = mu2, Sigma = true.cov)
apval_Chen2010(sam1, sam2)
# the two sample populations have different covariances
true.cov1 <- 0.2^(abs(outer(1:p, 1:p, "-")))
true.cov2 <- 0.6^(abs(outer(1:p, 1:p, "-")))
sam1 <- mvrnorm(n = n1, mu = mu1, Sigma = true.cov1)
sam2 <- mvrnorm(n = n2, mu = mu2, Sigma = true.cov2)
apval_Chen2010(sam1, sam2, eq.cov = FALSE)
``` |

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