Interval-valued data regression using partial linear model

Semi-parametric modelling of interval-valued data is of great practical importance, as exampled by applications in economic and financial data analysis. We propose a flexible semi-parametric modelling of interval-valued data by integrating the partial linear regression model based on the Center & Range method, and investigate its estimation procedure. Furthermore, we introduce a test statistic that allows one to decide between a parametric linear model and a semi-parametric model, and approximate its null asymptotic distribution based on wild Bootstrap method to obtain the critical values. Extensive simulation studies are carried out to evaluate the performance of the proposed methodology and the new test. Moreover, several empirical data sets are analysed to document its practical applications.     

Healthy Barbs: Activism Confronts Mortality

Barbara Brenner, JD, was the Executive Director of Breast Cancer Action (BCA) from 1995–2010. Before that, she was a longtime activist in the anti-war movement and an attorney who, for most of her career, practiced public policy law. After she was diagnosed with breast cancer in 1993 at the age of 41, she took the helm of BCA. Under her leadership, the organization moved into a position of national advocacy—demanding research on the causes and prevention of breast cancer, including the role of industrial pollutants. Barbara started the “Think Before You Pink” campaign, encouraging people to question whether companies that display pink ribbons actually produce products that harm women's health or generate any funds to fight breast cancer. Her blog, “Healthy Barbs,” challenged readers to critique routine healthcare practices and policies. Barbara received numerous awards, including a Jefferson Award for Public Service in 2007, the Smith College Medal in 2012, and the ACLU-Northern California's Lola Hanzel Courageous Advocacy Award in 2012. Barbara had a recurrence of breast cancer in 1996. She died of complications associated with amyotrophic lateral sclerosis, ALS, on May 10, 2013.     

Mean shift and influence measures in linear measurement error models with stochastic linear restrictions

We present influence diagnostics for linear measurement error models with stochastic linear restrictions using the corrected likelihood of Nakamura in 1990. The case deletion and mean shift outlier models are developed to identify outlying and influential observations. We derive a corrected score test statistic for outlier detection based on mean shift outlier models. The analogs of Cook's distance and likelihood distance are proposed to determine influential observations based on case deletion models. A parametric bootstrap procedure is used to obtain empirical distributions of the test statistics and a simulation study has been used to evaluate the performance of the proposed estimators based on the mean squares error criterion and the score test statistic. Finally, a numerical example is given to illustrate the theoretical results.     

Permutation tests of scale using deviances

Robust tests for comparing scale parameters, based on deviances—absolute deviations from the median—are examined. Higgins (2004) proposed a permutation test for comparing two treatments based on the ratio of deviances, but the performance of this procedure has not been investigated. A simulation study examines the performance of Higgins’ test relative to other tests of scale utilizing deviances that have been shown in the literature to have good properties. An extension of Higgins’ procedure to three or more treatments is proposed, and a second simulation study compares its performance to other omnibus tests for comparing scale. While no procedure emerged as a preferred choice in every scenario, Higgins’ tests are found to perform well overall with respect to Type I error rate and power.     

Testing variance components in balanced linear growth curve models

It is well known that the testing of zero variance components is a non-standard problem since the null hypothesis is on the boundary of the parameter space. The usual asymptotic chi-square distribution of the likelihood ratio and score statistics under the null does not necessarily hold because of this null hypothesis. To circumvent this difficulty in balanced linear growth curve models, we introduce an appropriate test statistic and suggest a permutation procedure to approximate its finite-sample distribution. The proposed test alleviates the necessity of any distributional assumptions for the random effects and errors and can easily be applied for testing multiple variance components. Our simulation studies show that the proposed test has Type I error rate close to the nominal level. The power of the proposed test is also compared with the likelihood ratio test in the simulations. An application on data from an orthodontic study is presented and discussed.     

Testing for linearity in generalized linear models using kernel smoothing

A test statistic proposed by Li (1999) for testing the adequacy of heteroscedastic nonlinear regression models using nonparametric kernel smoothers is applied to testing for linearity in generalized linear models. Simulation results for models with centered gamma and inverse Gaussian errors are presented to illustrate the performance of the resulting test compared with log-likelihood ratio tests for specific parametric alternatives. The test is applied to a data set of coronary heart disease status (Hosmer and Lemeshow, (1990).     

Two non parametric methods for change-point detection in distribution

The change-point detection problem is determining whether a change has taken place. Two non parametric methods based on empirical likelihood and the likelihood ratio are proposed for detecting a change-point problem in distributions for independent observations. Numerical studies are carried out to evaluate the performance of the proposed methods. The simulation results demonstrate that the proposed methods are robust, that is, they perform well regardless of whether the observations are from the same distribution family.     

纽结的Homflypt多项式

介绍了一类重要的纽结不变量,即Honmflypt多项式,证明了两个环链的Homlypt多项式相等的必要条件是它们的环绕数相等。此外,研究了它同纽结Jones多项式和Vassiliev不变量之间的关系。     

A goodness of fit test for multilevel survival data

No satisfactory goodness of fit test is available for multilevel survival data which occur when survival data are clustered or hierarchical in nature. Hence the aim of this research is to develop a new goodness of fit test for multilevel survival data and to examine the properties of the newly developed test. Simulation studies were carried out to evaluate the type ? error and the power. The results showed that the type I error holds for every combination tested and that the test is powerful against the alternative hypothesis of nonproportional hazards for all combinations tested.     

Pitman closeness,monotonicity and consistency of best linear unbiased and invariant estimators for exponential distribution under Type II censoring

Comparisons of best linear unbiased estimators with some other prominent estimators have been carried out over the last 50 years since the ground breaking work of Lloyd [E.H. Lloyd, Least squares estimation of location and scale parameters using order statistics, Biometrika 39 (1952), pp. 88–95]. These comparisons have been made under many different criteria across different parametric families of distributions. A noteworthy one is by Nagaraja [H.N. Nagaraja, Comparison of estimators and predictors from two-parameter exponential distribution, Sankhyā Ser. B 48 (1986), pp. 10–18], who made a comparison of best linear unbiased (BLUE) and best linear invariant (BLIE) estimators in the case of exponential distribution. In this paper, continuing along the same lines by assuming a Type II right censored sample from a scaled-exponential distribution, we first compare BLUE and BLIE of the exponential mean parameter in terms of Pitman closeness (nearness) criterion. We show that the BLUE is always Pitman closer than the BLIE. Next, we introduce the notions of Pitman monotonicity and Pitman consistency, and then establish that both BLUE and BLIE possess these two properties.