SemiparChangePoint {sac} | R Documentation |
Calculate test statistics, loglikelihood function and estimate unknown parameters in the semiparametric model.
SemiparChangePoint(x, alternative = c("one.change", "epidemic"), adj.Wn = FALSE, tol = 1e-07, maxit = 50, trace = FALSE, ...)
x |
a numeric vector or matrix containing the data, one row per observation; |
alternative |
a character string specifying the alternative hypothesis,
must be one of "one-change" (default) or "epidemic" . You can specify just the initial letter. |
tol |
the desired accuracy (convergence tolerance), an argument of glm.control . |
adj.Wn |
logical indicating if Wn should be adjusted or not
for "epidemic" alternative. |
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 |
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 is separated.
k.hat |
change-point estimate |
m.hat |
second change-point estimate for "epidemic" alternative |
ll |
loglikelihood function |
Sn |
likelihood ratio test statistic for "one-change" alternative |
Vn |
test statistic based integal of weighted likelihood ratio for "epidemic" alternative |
Wn |
test statistic based supremum of weighted likelihood ratio for "epidemic" alternative |
alpha.hat |
estimate of alpha |
beta.hat |
estimate of beta |
Statistic Wn
need be adjusted only for one dimensional observations
and if no bootstrap test is conducted.
Zhong Guan zguan@iusb.edu
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.
schapt
, p.OneChange
, p.Epidemic.Vn
,
p.Epidemic.Wn
require(sac) #load the package # one-change alternative k<-10 n<-30 x<-rnorm(n,0,1) x[(k+1):n]<-x[(k+1):n]+1.5 SemiparChangePoint(x, alternative = "one.change") # epidemic alternative k<-5 m<-10 n<-20 x<-rnorm(n,0,1) x[(k+1):m]<-x[(k+1):m]+1.5 SemiparChangePoint(x, alternative = "epidemic")