plots {sac}

Visualized Model Diagnostic and Loglikelihood Plot

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 \hat F, \tilde F, \hat G and \tilde G

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")