ddst.normbounded.test | R Documentation |
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.
ddst.normbounded.test(
x,
base = ddst.base.legendre,
d.n = 10,
c = 100,
compute.p = TRUE,
alpha = 0.05,
compute.cv = TRUE,
...
)
x |
a (non-empty) numeric vector of data values |
base |
a function which returns an orthonormal system, possible choice: |
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 |
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 |
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.
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)
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