Is Each NPMLE of a Continuous Bivariate Distribution Function with Singly Right-Censored Data Really Inconsistent?

We consider non-parametric estimation of a continuous cdf of a random vector (X ₁, X ₂). With bivariate RC data, it is stated in van der Laan (1996 Van der Laan , M. J. ( 1996 ) Efficient estimation in the bivariate censoring model and repairing NPMLE . Ann. Statist. 24 : 596 – 627 .[Crossref], [Web of Science ®] , [Google Scholar], p. 598¹⁰, Ann. Statist.), Quale et al. (2006 Quale , C. M. , van der Laan , M. J. , Robins , J. R. ( 2006 ). Locally efficient estimation with bivariate right-censored data . JASA. 101 : 1076 – 1084 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar], JASA) etc. that “it is well known that the NPMLE for continuous data is inconsistent (Tsai et al. (1986 Tsai , W. Y. , Leurgans , S. , Crowley , J. ( 1986 ). Nonparametric estimation of a bivariate survival function in the presence of censoring . Ann. Statist. 14 : 1351 – 1365 .[Crossref], [Web of Science ®] , [Google Scholar])).” The claim is based on a result in Tsai et al. (1986 Tsai , W. Y. , Leurgans , S. , Crowley , J. ( 1986 ). Nonparametric estimation of a bivariate survival function in the presence of censoring . Ann. Statist. 14 : 1351 – 1365 .[Crossref], [Web of Science ®] , [Google Scholar], p.1352, Ann. Statist.) that if X ₁ is right censored but not X ₂, then common ways for defining one NPMLE lead to inconsistency. If X ₁ is right censored and X ₂ is type I right-censored (which includes the case in Tsai et al.), we present a consistent NPMLE. The result corrects a common misinterpretation of Tsai's example (Tsai et al., 1986 Tsai , W. Y. , Leurgans , S. , Crowley , J. ( 1986 ). Nonparametric estimation of a bivariate survival function in the presence of censoring . Ann. Statist. 14 : 1351 – 1365 .[Crossref], [Web of Science ®] , [Google Scholar], Ann. Statist.).     

New Confidence Intervals for the Proportion of Interest in One-Sample Correlated Binary Data

Correlated binary data is obtained in many fields of biomedical research. When constructing a confidence interval for the proportion of interest, asymptotic confidence intervals have already been developed. However, such asymptotic confidence intervals are unreliable in small samples. To improve the performance of asymptotic confidence intervals in small samples, we obtain the Edgeworth expansion of the distribution of the studentized mean of beta-binomial random variables. Then, we propose new asymptotic confidence intervals by correcting the skewness in the Edgeworth expansion in one direct and two indirect ways. New confidence intervals are compared with the existing confidence intervals in simulation studies.     

Dependence Models Arising from the Lagrangian Probability Distributions

In this article, we propose a method based on the Lagrangian probability distributions for developing new dependence models. Specifically, a generalized Poisson–gamma dependence model is derived. The maximum likelihood estimation (MLE) technique is proposed for estimating the dependence model parameters. Application of the generalized Poisson–gamma dependence model is illustrated by using an operational risks dataset.     

The Yule–Walker equations as a weighted least-squares problem and the association with tapering

ABSTRACT

A common method for estimating the time-domain parameters of an autoregressive process is to use the Yule–Walker equations. Tapering has been shown intuitively and proven theoretically to reduce the bias of the periodogram in the frequency domain, but the intuition for the similar bias reduction in the time-domain estimates has been lacking. We provide insightful reasoning for why tapering reduces the bias in the Yule–Walker estimates by showing them to be equivalent to a weighted least-squares problem. This leads to the derivation of an optimal taper which behaves similarly to commonly used tapers.     

Probability of correct selection of weibull versus gamma based on livelihood ratio

This paper proposes the use of tne likelihood ratio statistic in choosing between a Neibull or gamma model, values of the probability of correct seeiection are obtained by Monte Carlo simulation. This method provides some basis for decision even when the sample size is small. The technique is applied to four sets of data from the literature.     

Identification of target clusters by using the restricted normal mixture model

This paper addresses the problem of identifying groups that satisfy the specific conditions for the means of feature variables. In this study, we refer to the identified groups as “target clusters” (TCs). To identify TCs, we propose a method based on the normal mixture model (NMM) restricted by a linear combination of means. We provide an expectation–maximization (EM) algorithm to fit the restricted NMM by using the maximum-likelihood method. The convergence property of the EM algorithm and a reasonable set of initial estimates are presented. We demonstrate the method's usefulness and validity through a simulation study and two well-known data sets. The proposed method provides several types of useful clusters, which would be difficult to achieve with conventional clustering or exploratory data analysis methods based on the ordinary NMM. A simple comparison with another target clustering approach shows that the proposed method is promising in the identification.     

Determination of the Selection Statistics and Best Significance Level in Backward Stepwise Logistic Regression

The weighted generalized estimating equation (WGEE), an extension of the generalized estimating equation (GEE) method, is a method for analyzing incomplete longitudinal data. An inappropriate specification of the working correlation structure results in the loss of efficiency of the GEE estimation. In this study, we evaluated the efficiency of WGEE estimation for incomplete longitudinal data when the working correlation structure was misspecified. As a result, we found that the efficiency of the WGEE estimation was lower when an improper working correlation structure was selected, similar to the case of the GEE method. Furthermore, we modified the criterion proposed by Gosho et al. (2011 Gosho, M., Hamada, C. and Yoshimura, I. 2011. Criterion for the selection of a working correlation structure in the generalized estimating equation approach for longitudinal balanced data. Communications in Statistics -Theory and Methods, 40: 3839–3856. [Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]) for selecting a working correlation structure, such that the GEE and WGEE methods can be applied to incomplete longitudinal data, and we investigated the performance of the modified criterion. The results revealed that when the modified criterion was adopted, the proportion that the true correlation structure was selected was likely higher than that in the case of adopting other competing approaches.     

Canonical Correlation Analysis Using Small Number of Samples

Canonical correlation assesses the relationship between two groups of variables. Although it has been a useful tool in a wide variety of research areas, it is not well known that weaker canonical correlations require larger sample sizes to be correctly inferred. In this article, we investigate small sample bias in canonical correlation analysis and apply the jackknife bias correction to the estimation of canonical correlations. We use bootstrap samples to obtain a better confidence interval for the jackknife canonical correlation estimator.     

Mobile safety cameras: estimating casualty reductions and the demand for secondary healthcare

We consider a fully Bayesian analysis of road casualty data at 56 designated mobile safety camera sites in the Northumbria Police Force area in the UK. It is well documented that regression to the mean (RTM) can exaggerate the effectiveness of road safety measures and, since the 1980s, an empirical Bayes (EB) estimation framework has become the gold standard for separating real treatment effects from those of RTM. In this paper we suggest some diagnostics to check the assumptions underpinning the standard estimation framework. We also show that, relative to a fully Bayesian treatment, the EB method is over-optimistic when quantifying the variability of estimates of casualty frequency. Implementing a fully Bayesian analysis via Markov chain Monte Carlo also provides a more flexible and complete inferential procedure. We assess the sensitivity of estimates of treatment effectiveness, as well as the expected monetary value of prevention owing to the implementation of the safety cameras, to different model specifications, which include the estimation of trend and the construction of informative priors for some parameters.