mv {semidist}

Mean Variance (MV) statistics

Description

Compute the statistics of mean variance (MV) index, which can measure the dependence between a univariate continuous variable and a categorical variable. See Cui, Li and Zhong (2015); Cui and Zhong (2019) for details.

Usage

mv(x, y, return_mat = FALSE)

Arguments

x

Data of univariate continuous variables, which should be a vector of length n.

y

Data of categorical variables, which should be a factor of length n.

return_mat

A boolean. If FALSE (the default), only the calculated statistic is returned. If TRUE, also return the matrix of the indicator for x <= x_i, which is useful for the permutation test.

Value

The value of the corresponding sample statistic.

If the argument return_mat of mv() is set as TRUE, a list with elements

• mv: the MV index statistic;

• mat_x: the matrices of the distances of the indicator for x <= x_i;

will be returned.

See Also

• mv_test() for implementing independence test via MV index;

• mv_sis() for implementing feature screening via MV index.

Examples

x <- mtcars[, "mpg"]
y <- factor(mtcars[, "am"])
print(mv(x, y))

# Man-made independent data -------------------------------------------------
n <- 30; R <- 5; prob <- rep(1/R, R)
x <- rnorm(n)
y <- factor(sample(1:R, size = n, replace = TRUE, prob = prob), levels = 1:R)
print(mv(x, y))

# Man-made functionally dependent data --------------------------------------
n <- 30; R <- 3
x <- rep(0, n)
x[1:10] <- 0.3; x[11:20] <- 0.2; x[21:30] <- -0.1
y <- factor(rep(1:3, each = 10))
print(mv(x, y))