schapt {sac}

Semiparametric Analysis of Changepoint

Description

Semiparametric empirical likelihood ratio based test of changepoint with one-change or epidemic alternatives with data-based model diagnostic

Usage

schapt(x, n.boots = 0, replace = FALSE, alternative = c("one.change",
    "epidemic"), conf.level = 0.95, adj.Wn = FALSE, model.test = FALSE,
    n.model.boots = 0, tol=1.0e-7, maxit=50,trace=FALSE,... )

Arguments

x

a numeric vector or matrix containing the data, one row per observation;

n.boots

number of bootstrap samples for bootstrap test of the change-point, if n.boots =0 , do not perform bootstrap test;

replace

a logical indicating whether bootstrap samples for bootstrap test of the change-point are selected with or without replacement, if replace= FALSE (default), corresponds to permutation test, otherwise, bootstrap test;

alternative

a character string specifying the alternative hypothesis, must be one of "one-change" (default) or "epidemic". You can specify just the initial letter. Epidemic alternative is also called square wave alternative in the literature.

conf.level

confidence level.

adj.Wn

logical indicating if Wn should be adjusted or not for "epidemic" alternative.

model.test

a logical indicating whether the test of model validity is performed.

n.model.boots

number of bootstrap samples for model test, if either n.model.boots = 0 or model.test=FALSE, then model test will not be performed.

tol

the desired accuracy (convergence tolerance), an argument of glm.control.

maxit

the maximum number of iterations, an argument of glm.control.

trace

logical indicating if output should be produced for each iteration, an argument of glm.control.

...

other future arguments

Details

Model: \log\{g(x)/f(x)\}=\exp\{\alpha+\beta'T(x)\}, where f(x) and g(x) are the density (frequency) functions of the two hypothesized populations, and T(x) can be chosen as T(x)=x or T(x)=(x,x^2). The procedure will fail when there is separation in the data in the sense of Albert \& Anderson(1984, Biometrika) and Santner \& Duffy (1986, Biometrika). In this case, the change-point(s) may be detected easily using nonparametric method based on cumsum. Currently, this function does not check whether the data are separated.

Value

data.name

dataset name

parameter

sample size n and degree(s) of freedom of the df of Sn for "one-change" alternative

alternative

the alternative hypothesis

statistic

a list contains Sn for "one-change" alternative, Sn, Vn and Wn for "epidemic" alternative; also contains Delta if model test is performed

estimate

a list contains change-point(s) and alpha and beta

p.value

a list contains p-value(s), p(Sn), of Sn for "one-change" alternative, p(Vn) and p(Wn), of Vn and Wn, repectively, for "epidemic" alternative; also p.boots(model) of Delta if model test is performed, if bootstrap test(s) of the change-point(s) are performed, the it also containts the corresponding p-values, p.boots(Sn), p.boots(Vn) and p.boots(Wn) accordingly.

Note

Statistic Wn need be adjusted only for one dimensional observations and if no bootstrap test is conducted. If returned p-value is 0, this means that the p-value is less than 1.0e-7.

Author(s)

Zhong Guan [e-mail]

References

Guan, Z. (2001). Some Results About Empirical Likelihood Method, Ph.D. Thesis, The University of Toledo.

Guan, Z.(2004) A semiparametric change-point model, Biometrika, 91, 4, 849–862.

Guan, Z. Semiparametric Tests for Change-points with Epidemic Alternatives.

See Also

Graf.Diagnostic, Plot.ll

Examples

require(sac) #load the package
# one-change alternative
## Nile data with one change-point: the annual flows drop in 1898.
## It is believed to be caused by the building of the first Aswan dam.
if(! "package:sac" %in% search()) library(sac)
    #if package sac has not been loaded, load it.
if(! "package:stats" %in% search()) library(stats)
data(Nile)
plot(Nile, type="p")
schapt(Nile, alternative = "one.change")