ddst (version 1.6.11)

ddst.normbounded.test: Data Driven Smooth Test for Normality; Bounded Basis Functions

Description

Performs data driven smooth test for composite hypothesis of normality Null density is given by \( f(z;\gamma)=1/(\sqrt{2 \pi}\gamma_2) \exp(-(z-\gamma_1)^2/(2 \gamma_2^2))\) for \(z \in R\). We model alternatives similarly as in Kallenberg and Ledwina (1997 a,b) using Legendre's polynomials or cosine basis.

Usage

ddst.normbounded.test(
  x,
  base = ddst.base.legendre,
  d.n = 10,
  c = 100,
  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 = TRUE.

Arguments

x

a (non-empty) numeric vector of data values

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

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

Chen, L., Shapiro, S.S. (1995). An alternative test for normality based on normalized spacings. J. Statist. Comput. Simulation 53, 269--288.

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.

Janic, A. and Ledwina, T. (2008). Data-driven tests for a location-scale family revisited. J. Statist. Theory. Pract. Special issue on Modern Goodness of Fit Methods..

Kallenberg, W.C.M., Ledwina, T. (1997 a). Data driven smooth tests for composite hypotheses: Comparison of powers. J. Statist. Comput. Simul. 59, 101--121.

Kallenberg, W.C.M., Ledwina, T. (1997 b). Data driven smooth tests when the hypothesis is composite. J. Amer. Statist. Assoc. 92, 1094--1104.

Examples

set.seed(7)
# H0 is true
z <- rnorm(100)
# let's look on first 10 coordinates
d.n <- 10
t <- ddst.normbounded.test(z, compute.p = TRUE, d.n = d.n)
t
plot(t)

# H0 is false
z <- rexp(100, 1)
t <- ddst.normbounded.test(z, compute.p = TRUE, d.n = d.n)
t
plot(t)

# for Tephra data
z <- c(-1.748789, -1.75753, -1.740102, -1.740102, -1.731467, -1.765523,
      -1.761521, -1.72522, -1.80371, -1.745624, -1.872957, -1.729121,
      -1.81529, -1.888637, -1.887761, -1.881645, -1.91518, -1.849769,
      -1.755141, -1.665687, -1.764721, -1.736171, -1.736956, -1.737742,
      -1.687537, -1.804534, -1.790593, -1.808661, -1.784081, -1.729903,
      -1.711263, -1.748789, -1.772755, -1.72756, -1.71358, -1.821116,
      -1.839588, -1.839588, -1.830321, -1.807835, -1.747206, -1.788147,
      -1.759923, -1.786519, -1.726779, -1.738528, -1.754345, -1.781646,
      -1.641949, -1.755936, -1.775175, -1.736956, -1.705103, -1.743255,
      -1.82613, -1.826967, -1.780025, -1.684504, -1.751168)
t <- ddst.normbounded.test(z, compute.p = TRUE, d.n = d.n)
t
plot(t)