ddst (version 1.6.11)

ddst.forstochdom.test: Data Driven Smooth Test for Stochastic Dominance in Two Samples

Description

Performs the data driven smooth test for detection of the stochastic ordering, as described in detail in Ledwina and Wyłupek (2012). Suppose that we have random samples from two distributions F and G. The null hypothesis is that F(x) >= G(x) for all x while the alternative is that at F(x) < G(x) for some x. Detailed description of the test statistic is provided in Ledwina and Wylupek (2012).

Usage

ddst.forstochdom.test(
  x,
  y,
  K.N = floor(log(length(x) + length(y), 2)) - 1,
  alpha = 0.05,
  t,
  nr = 1e+05,
  compute.p = TRUE,
  compute.cv = TRUE
)

Arguments

x

a (non-empty) numeric vector of data

y

a (non-empty) numeric vector of data

K.N

an integer specifying a level of complexity of the grid considered, only for advanced users

alpha

a significance level

t

an alpha-dependent tunning parameter in the penalty in the model selection rule

nr

an integer specifying the number of runs for a p-value and a critical value computation if any

compute.p

a logical value indicating whether to compute a p-value or not

compute.cv

a logical value indicating whether to compute a critical value corresponding to the significance level alpha or not

References

Nonparametric tests for stochastic ordering. Ledwina and Wyłupek (2012) <doi:10.1007/s11749-011-0278-7>

Examples

set.seed(7)
library("rmutil", warn.conflicts = FALSE)
# 1. Pareto(1)/Pareto(1.5)
# H0 is false
x <- rpareto(50, 2, 2)
y <- rpareto(50, 1.5, 1.5)
t <- ddst.forstochdom.test(x, y, t = 2.2, K.N = 4)
t
plot(t)

# 2. Laplace(0,1)/Laplace(1,25)
# H0 is false
x <- rlaplace(50, 0, 1)
y <- rlaplace(50, 1, 25)
t <- ddst.forstochdom.test(x, y, t = 2.2, K.N = 4)
t
plot(t)

# 3. LN(0.85,0.6)/LN(1.2,0.2)
# H0 is true
x <- rlnorm(50, 0.85, 0.6)
y <- rlnorm(50, 1.2, 0.2)
t <- ddst.forstochdom.test(x, y, t = 2.2, K.N = 4)
t
plot(t)

if (FALSE) {
# Generate distribution of test statistic
N <- 1000
samp <- replicate(N, {
   x <- runif(30)
   y <- runif(30)
   # statistics with Schwartz penalty
   ddst.forstochdom.test(x, y)$statistic
})
quantile(samp, 0.95)
plot(ecdf(samp))
}