plots: Visualized Model Diagnostic and Loglikelihood Plot

In sac: Semiparametric Analysis of Change-Point

Description

Plot and compare the empirical likelihood and semiparametric empirical likelihood distribution functions, plot loglikelihood function.

Usage

Graf.Diagnostic(x, k, m, Alpha, Beta, Color, LTY, xlab = "x", 
    ylab = "Estimated DF's", main = "Model Diagnostic", 
    OneLegend = TRUE, lgnd1, lgnd2, arw1, arw2, ...)
Plot.ll(x, ll, col, xaxis.lab = NULL, xlab = "k", ylab = "Loglikelihood", 
    main = "Plot of Loglikelihood",...)

Arguments

x	a numeric vector or matrix containing the data, one row per observation;
ll	loglikelihood function, output of SemiparChangePoint
col	color code or character string for the loglikelihood curve
xaxis.lab	a vector of character strings or numeric values to be placed at the tickpoints as labels of axis
k	the estimated change-point, output of SemiparChangePoint
m	= n, the sample size, for "one-change" alternative, or the estimated second change-point for "epidemic" alternative, an output of SemiparChangePoint
Alpha	estimated parameter alpha, output of SemiparChangePoint
Beta	estimated parameter beta, output of SemiparChangePoint
Color	a vector of character strings or color codes for curves of estimated distribution functions F-hat, F-tilde, G-hat and G-tilde
LTY	vector of lty's, LTY=c(lty1, lty2, lty3, lty4), corresponds to the above color codes
xlab	character string for x-axis lable
ylab	character string for y-axis lable
main	character string for main title
OneLegend	a logical indicating whether plot one or two legend.
lgnd1	a numeric vector of two specify the position of the first legend box
lgnd2	a numeric vector of two specify the position of the second legend box, if OneLegend = FALSE
arw1	a numeric vector of four numbers indicating start and end positions of the first arrows point to curves
arw2	a numeric vector of four numbers indicating start and end positions of the second arrows point to curves
...	other arguments of function plot

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 Changepoints with Epidemic Alternatives.

See Also

schapt

Examples

require(sac) #load the package
k<-30
n<-80
x<-rnorm(n,0,1)
x[(k+1):n]<-x[(k+1):n]+1.5
res<-SemiparChangePoint(x, alternative = "one.change")
Plot.ll(x, res$ll, col="blue")

## Nile data with one change-point: the annual flows drop in 1898 which corresponds 
## to k=28. 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")
Nile.res<-SemiparChangePoint(Nile, alternative = "one.change")
Color<-c(1,2,3,4); LTY<-c(1,2,3,4)

## Plots of estimated distribution functions
Graf.Diagnostic(Nile, Nile.res$k.hat, length(Nile), Nile.res$alpha.hat, 
    Nile.res$beta.hat, Color, LTY, xlab = "x", ylab = "Estimated DF's", 
    main="Model Diagnostic for Nile Data", OneLegend = FALSE, lgnd1 = 
    c(1100, 0.15), lgnd2 = c(600, .99), arw1=c(780, .93, 1010, .9),
    arw2 = c(1165, .15, 1015, .24))

## Plot of loglikelihood function
Plot.ll(Nile, Nile.res$ll, col = "blue")
Plot.ll(Nile, Nile.res$ll, col = "blue", xaxis.lab = seq(1871,1970, length = 100), 
    xlab = "Year")

Example output

change-point =  23 
change-point =  28 
change-point =  28 

sac documentation built on Jan. 27, 2021, 5:11 p.m.