mrle.sporm: Semiparametric proportional odds rate model.

In sporm: Semiparametric Proportional Odds Rate Model

Description

Maximum rank-based likelihood estimates of the proportionality parameter θ and probability masses of the discretized baseline distribution F.

Usage

mrle.sporm(x, y, theta = 1, p = rep(1/(length(x) + length(y)), 
    length(x) + length(y)), tol = 1e-07, maxit = 50) 

Arguments

x, y	Vectors containing the data values of the two samples x1,...,xm and y1,...,yn.
theta	Initial value for proportionality parameter θ.
p	Initial value for probability masses p1,...,pN of the discretized baseline distribution F.
tol	Convergence tolerance used in the Newton iteration
maxit	The maximum number of Newton iterations.

Details

The Newton iteration method is applied to find the maximum rank-based likelihood estimates of the proportionality parameter θ and probability masses p1,...,pN of the discretized baseline distribution F. If the default initial values for theta and/or p do not work, functions newton.theta, dd.est and phi can be used to calculate other initials.

Value

theta	The maximum rank-based likelihood estimate of the proportionality parameter theta.
p	The maximum rank-based likelihood estimate of probability masses p1,...,pN of the discretized baseline distribution F.
ell	The maximum rank-based loglikelihood.
del	Convergent tolerance which is sum of the absolute scores, and absolute changes of the parameters theta and p.

Author(s)

Zhong Guan <[e-mail]>

References

Zhong Guan and Cheng Peng (2011), "A rank-based empirical likelihood approach to two-sample proportional odds model and its goodness-of-fit", Journal of Nonparametric Statistics, to appear.

Examples

# Use radar tube life data
z<-RadarTube$Days
v<-RadarTube$Type
x<-z[v==1]; y<-z[v==2]
# Dabrowska-Doksum's estimate of theta
theta0.hat<-dd.est(x,y)
theta0.hat
vartheta0.hat<-dd.est(y,x)
vartheta0.hat
## mrle
m<-length(x)
n<-length(y)
N<-m+n
lambda<-m/N
phat0<-phi(N, theta0.hat, lambda)/N
mrle.sporm(x, y, theta0.hat, phat0)

sporm documentation built on Jan. 27, 2021, 5:08 p.m.