ddst (version 1.6.11)

ddst.uniform.test: Data Driven Smooth Test for Uniformity

Description

Performs data driven smooth tests for simple hypothesis of uniformity on [0,1]. Embeding null model into the original exponential family introduced by Neyman (1937).

Usage

ddst.uniform.test(
  x,
  base = ddst.base.legendre,
  d.n = 10,
  c = 2.4,
  nr = 1e+05,
  compute.p = TRUE,
  alpha = 0.05,
  compute.cv = TRUE,
  ...
)

Value

An object of class htest

statistic

the value of the test statistic.

parameter

the number of choosen coordinates (k).

method

a character string indicating the parameters of performed test.

data.name

a character string giving the name(s) of the data.

p.value

the p-value for the test, computed only if compute.p=T.

Arguments

x

a (non-empty) numeric vector of data

base

a function which returns an orthonormal system, possible choice: ddst.base.legendre for the Legendre polynomials and ddst.base.cos for the cosine system

d.n

an integer specifying the maximum dimension considered, only for advanced users

c

a calibrating 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

alpha

a significance level

compute.cv

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

...

further arguments

References

Inglot, T., Ledwina, T. (2006). Towards data driven selection of a penalty function for data driven Neyman tests. Linear Algebra and its Appl. 417, 579--590.

Ledwina, T. (1994). Data driven version of Neyman's smooth test of fit. J. Amer. Statist. Assoc. 89 1000-1005.

Neyman, J. (1937). `Smooth test' for goodness of fit. Skand. Aktuarietidskr. 20, 149-199.

Examples

set.seed(7)
# H0 is true
z <- runif(80)
if (FALSE) {
t <- ddst.uniform.test(z, compute.p = TRUE, d.n = 10)
t
plot(t)

# known fixed alternative
z <- rnorm(80,10,16)
t <- ddst.uniform.test(pnorm(z, 10, 16), compute.p = TRUE, d.n = 10)
t
plot(t)

# H0 is false
z <- rbeta(80,4,2)
(t <- ddst.uniform.test(z, compute.p = TRUE, d.n = 10))
t$p.value
plot(t)
}