# Semiparametric proportional odds rate model

### Description

A rank-based empirical likelihood approach to two-sample proportional odds model and
its goodness-of-fit. Let *x1,...,xm* and *y1,...,yn*
be two independent samples from distributions *F* and
*G* that satisfy

*
[G(x)/(1-G(x))]/[F(x)(1-F(x))]=G(x)(1-F(x))/[F(x)(1-G(x))]=θ*

Function `mele.theta.p`

returns rank-based maximum likelihood estimates of *θ*,
*θ-hat*, and
probability masses *p1,...,pN* of *F* at the sorted pooled sample values
*z1<...<zN*, *N=m+n*.

### Details

Package: | sporm |

Type: | Package |

Version: | 1.0 |

Date: | 2011-01-01 |

License: | GPL 2.0 or newer |

LazyLoad: | yes |

The most important function is `mrle.sporm`

which returns the maximum rank-based likelihood
estimates the proportionality paramter *θ* and the baseline distribution.
Function `ks.sporm`

is used to do the GOF test of the model assumption using a Kolmogorov-Smirnov type
test statistic; `confid.int.theta`

returns a confidence interval for *θ*;
`test.theta`

does the hypothesis testing for *θ*; `Ell.Theta`

calculates the profile loglikelihood *l(θ)* on interval
*(θ1,θ2)* which contains *θ-hat*; and `plotor`

plot the empirical odds ratio. Functions `newton.theta`

,
`dd.est`

and `phi`

can be used to calculate other initials. There are few internal functions:
`V.theta`

, `H.Binv`

, `grad.hessinv`

, `ks.stat`

, and `elltheta`

. Dataset
`RadarTube`

contains the failure times (in days) of two types of radar tubes.

### Author(s)

Zhong Guan <zguan@iusb.edu>; Cheng Peng <cpeng@usm.maine.edu>

Zhong Guan <zguan@iusb.edu>

### 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.