Interval estimation for the breakpoint in segmented regression: a smoothed score‐based approach

This paper is concerned with interval estimation for the breakpoint parameter in segmented regression. We present score‐type confidence intervals derived from the score statistic itself and from the recently proposed gradient statistic. Due to lack of regularity conditions of the score, non‐smoothness and non‐monotonicity, naive application of the score‐based statistics is unfeasible and we propose to exploit the smoothed score obtained via induced smoothing. We compare our proposals with the traditional methods based on the Wald and the likelihood ratio statistics via simulations and an analysis of a real dataset: results show that the smoothed score‐like statistics perform in practice somewhat better than competitors, even when the model is not correctly specified.     

Asymptotocally nonparametric tests with censored paired data

A class of asymptotically nonparametric test with contains a test proposed by Wei(1980), is considered for testing the equality of two continuous distribution funcitons when paired observations are subject to arbitrary right censorship. It is shown that under the null hypothesis each test statistic converges in distribution to the standard normal random variable. Furthermore. the Monte Carlo simulation results indicate that some tests in this class are more powerful than Wei's test. A generalization to incomplete censored paired data is also included.     

Locally best invariant test for outliers in a gamma type distribution

It is shown that the locally best invariant test for the existence of outliers for scale parameters of the gamma distribution is given by Bartholomew's test for exponentiality which is the ratio of the sum of squares of the data to the square of the sample mean. The optimality robustness, including null and nonnull robustness of the test is shown. A small simulation study to compare the power among the other eight competitive tests for testing exponentiality is performed. It is seen that the locally best invariant test is not always best but is reasonably good. It is slightly better than Cochran's test and suffers less from the limiting masking effect.     

Nonparametric Estimation of the Number of Drug Users in Hong Kong Using Repeated Multiple Lists

We update a previous approach to the estimation of the size of an open population when there are multiple lists at each time point. Our motivation is 35 years of longitudinal data on the detection of drug users by the Central Registry of Drug Abuse in Hong Kong. We develop a two‐stage smoothing spline approach. This gives a flexible and easily implemented alternative to the previous method which was based on kernel smoothing. The new method retains the property of reducing the variability of the individual estimates at each time point. We evaluate the new method by means of a simulation study that includes an examination of the effects of variable selection. The new method is then applied to data collected by the Central Registry of Drug Abuse. The parameter estimates obtained are compared with the well known Jolly–Seber estimates based on single capture methods.     

Comparison of Interval Estimators of Pr(X < Y) in the Two-parameter Exponential Distribution

We consider confidence intervals for the stress–strength reliability Pr(X< Y) in the two-parameter exponential distribution. We have derived the Bayesian highest posterior density interval using non-informative prior distributions. We have compared its performance with the intervals based on the generalized pivot variable intervals in terms of their coverage probabilities and expected lengths. Our simulation study shows that the Bayesian interval performs better according to the criteria used, especially when the sample sizes are very small. An example is given.     

New Ridge Regression Estimator in Semiparametric Regression Models

In the context of ridge regression, the estimation of shrinkage parameter plays an important role in analyzing data. Many efforts have been put to develop the computation of risk function in different full-parametric ridge regression approaches using eigenvalues and then bringing an efficient estimator of shrinkage parameter based on them. In this respect, the estimation of shrinkage parameter is neglected for semiparametric regression model. Not restricted, but the main focus of this approach is to develop necessary tools for computing the risk function of regression coefficient based on the eigenvalues of design matrix in semiparametric regression. For this purpose the differencing methodology is applied. We also propose a new estimator for shrinkage parameter which is of harmonic type mean of ridge estimators. It is shown that this estimator performs better than all the existing ones for the regression coefficient. For our proposal, a Monte Carlo simulation study and a real dataset analysis related to housing attributes are conducted to illustrate the efficiency of shrinkage estimators based on the minimum risk and mean squared error criteria.     

An exploratory data analysis in scale-space for interval-valued data

We propose an exploratory data analysis approach when data are observed as intervals in a nonparametric regression setting. The interval-valued data contain richer information than single-valued data in the sense that they provide both center and range information of the underlying structure. Conventionally, these two attributes have been studied separately as traditional tools can be readily used for single-valued data analysis. We propose a unified data analysis tool that attempts to capture the relationship between response and covariate by simultaneously accounting for variability present in the data. It utilizes a kernel smoothing approach, which is conducted in scale-space so that it considers a wide range of smoothing parameters rather than selecting an optimal value. It also visually summarizes the significance of trends in the data as a color map across multiple locations and scales. We demonstrate its effectiveness as an exploratory data analysis tool for interval-valued data using simulated and real examples.     

Analysis of Competing Risks by Using Bayesian Smoothing

We consider the competing risks set-up. In many practical situations, the conditional probability of the cause of failure given the failure time is of direct interest. We propose to model the competing risks by the overall hazard rate and the conditional probabilities rather than the cause-specific hazards. We adopt a Bayesian smoothing approach for both quantities of interest. Illustrations are given at the end.     

Penalized Pseudolikelihood Inference in Spatial Interaction Models with Covariates

Given spatially located observed random variables ( x , z = {( x _i , z _i )} _i , we propose a new method for non-parametric estimation of the potential functions of a Markov random field p ( x | z ), based on a roughness penalty approach. The new estimator maximizes the penalized log-pseudolikelihood function and is a natural cubic spline. The calculations involved do not rely on Monte Carlo simulation. We suggest the use of B-splines to stabilize the numerical procedure. An application in Bayesian image reconstruction is described.