sporm (version 1.1.1)

newton.theta: Initial theta value by Newton method

Description

Optional initial \(\theta\) value for mrle.sporm based on uniform (0, 1) baseline distrbution and calculated by Newton method.

Usage

newton.theta(y, theta0 = 1, maxit = 100, eps = 1e-10)

Arguments

y

The \(y\)-sample in proportional odds rate model with uniform (0,1) baseline distrbution. If baseline \(F\) is not uniform (0,1) or unknown, use \(y^*_i=F_n(y_j)\), \(j=1,\ldots,n\), where \(F_n\) is the empirical cdf of \(x_1,\ldots,x_m\).

theta0

an initial value of \(\theta\)

maxit

The maximum number of Newton iterations.

eps

Convergence tolerance used in the Newton iteration

Value

Returns the proportionality parameter \(\theta\) of the parametric proportional odds rate model with Uniform(0,1) baseline by Newtom method.

Details

See the reference below.

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.

See Also

mrle.sporm.

Examples

# NOT RUN {
theta<-2
u<-runif(30)
y<-u/(theta-(theta-1)*u)
newton.theta(y)
# }