ddst (version 1.6.11)

ddst.upwardtrend.test: Data Driven Smooth Test for Upward Trend Alternatives

Description

Performs data driven smooth test for upward trend in k-sample problem. Suppose that we have random samples from k distributions F_i where i = 1, ..., k. The null hypothesis is that there is lack of trend, i.e. F_1 >= ... >= F_k and F_i != F_j for some i and j. The alternative is that there is a trend i.e. F_1 >= ... >= F_k and F_i != F_j for some i and j. This test is implemented as a special case of an umbrella test.

Usage

ddst.upwardtrend.test(
  x,
  r.N = rep(4, length(x) - 1),
  alpha = 0.05,
  t.p,
  t.n,
  nr = 1e+05,
  compute.cv = TRUE
)

Arguments

x

a list of k (non-empty) numeric vectors of data

r.N

a (k-1)-dimensional vector specifying the levels of complexity of the grids considered, only for advanced users

alpha

a significance level

t.p

an alpha-dependent (k-1)-dimensional vector of the tunning parameters in the penalties in the model selection rules T.o

t.n

an alpha-dependent (k-1)-dimensional vector of the tunning parameters in the penalties in the model selection rules T.tilde

nr

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

compute.cv

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

t

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

References

An automatic test for the umbrella alternatives. Wylupek (2016) https://onlinelibrary.wiley.com/doi/abs/10.1111/sjos.12231

Examples

set.seed(7)
# H0 is true
x = runif(80)
y = runif(80) + 0.2
z = runif(80) + 0.4
t <- ddst.upwardtrend.test(list(x, y, z), t.p = 2.2, t.n = 2.2)
t
plot(t)

# H0 is false
# known fixed alternative
x1 = rnorm(80)
x2 = rnorm(80) + 2
x3 = rnorm(80) + 4
x4 = rnorm(80) + 3
t <- ddst.upwardtrend.test(list(x1, x2, x3, x4), t.p = 2.2, t.n = 2.2)
t
plot(t)