Data Driven Smooth Test for Stochastic Dominance in Two Samples

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).

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) https://doi.org/10.1007/s11749-011-0278-7

Examples

set.seed(7)
library("rmutil", warn.conflicts = FALSE)
#> Registered S3 method overwritten by 'rmutil':
#>   method         from
#>   print.response httr
# 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
#> 
#> 	Data Driven Stochastic Ordering Test
#> 
#> data:  x y, t: 2.2, K.N: 4
#> QT = 124.46, T = 5
#> 
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
#> 
#> 	Data Driven Stochastic Ordering Test
#> 
#> data:  x y, t: 2.2, K.N: 4
#> QT = 129.93, T = 5
#> 
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
#> 
#> 	Data Driven Stochastic Ordering Test
#> 
#> data:  x y, t: 2.2, K.N: 4
#> QT = 0, T = 1
#> 
plot(t)

# \dontrun{
# 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
})
#> Error in test.Q(x, y, m, n, K.N, t): argument "t" is missing, with no default
quantile(samp, 0.95)
#> Error in quantile(samp, 0.95): object 'samp' not found
plot(ecdf(samp))
#> Error in sort(x): object 'samp' not found
# }