Natural (Non‐)Informative Priors for Skew‐symmetric Distributions

In this paper, we present an innovative method for constructing proper priors for the skewness (shape) parameter in the skew‐symmetric family of distributions. The proposed method is based on assigning a prior distribution on the perturbation effect of the shape parameter, which is quantified in terms of the total variation distance. We discuss strategies to translate prior beliefs about the asymmetry of the data into an informative prior distribution of this class. We show via a Monte Carlo simulation study that our non‐informative priors induce posterior distributions with good frequentist properties, similar to those of the Jeffreys prior. Our informative priors yield better results than their competitors from the literature. We also propose a scale‐invariant and location‐invariant prior structure for models with unknown location and scale parameters and provide sufficient conditions for the propriety of the corresponding posterior distribution. Illustrative examples are presented using simulated and real data.     

Quantile residual life regression based on semi-competing risks data

This paper investigates the quantile residual life regression based on semi-competing risk data. Because the terminal event time dependently censors the non-terminal event time, the inference on the non-terminal event time is not available without extra assumption. Therefore, we assume that the non-terminal event time and the terminal event time follow an Archimedean copula. Then, we apply the inverse probability weight technique to construct an estimating equation of quantile residual life regression coefficients. But, the estimating equation may not be continuous in coefficients. Thus, we apply the generalized solution approach to overcome this problem. Since the variance estimation of the proposed estimator is difficult to obtain, we use the bootstrap resampling method to estimate it. From simulations, it shows the performance of the proposed method is well. Finally, we analyze the Bone Marrow Transplant data for illustrations.     

Additive risks regression model for middle censored exponentiated-exponential lifetime data

Jammalamadaka and Mangalam introduced middle censoring which refers to data arising in situations, where the exact lifetime becomes unobservable if it falls within a random censoring interval. In the present article, we propose an additive risks regression model for a lifetime data subject to middle censoring, where the lifetimes are assumed to follow exponentiated exponential distribution. The regression parameters are estimated using the Expectation-Maximization algorithm. Asymptotic normality of the estimator is proposed. We report a simulation study to assess the finite sample properties of the estimator. We then analyze a real-life data on survival times of larynx cancer patients studied by Karduan.     

Likelihood inference based on EM algorithm for the destructive length-biased Poisson cure rate model with Weibull lifetime

In this article, we consider the destructive length-biased Poisson cure rate model, proposed by Rodrigues et al., that presents a realistic and interesting interpretation of the biological mechanism for the recurrence of tumor in a competing causes scenario. Assuming the lifetime to follow the Weibull distribution and censoring mechanism to be non-informative, the necessary steps of the EM algorithm for the determination of the MLEs of the model parameters are developed here based on right censored data. The standard errors of the MLEs are obtained by inverting the observed information matrix. A simulation study is then carried out to examine the method of inference developed here. Finally, the proposed methodology is illustrated with a real melanoma dataset.     

Estimation for the censored partially linear quantile regression models

In this article, we develop estimation procedures for partially linear quantile regression models, where some of the responses are censored by another random variable. The nonparametric function is estimated by basis function approximations. The estimation procedure is easy to implement through existing weighted quantile regression, and it requires no specification of the error distributions. We show the large-sample properties of the resulting estimates, the proposed estimator of the regression parameter is root-n consistent and asymptotically normal and the estimator of the functional component achieves the optimal convergence rate of the nonparametric function. The proposed method is studied via simulations and illustrated with the analysis of a primary biliary cirrhosis (BPC) data.     

An Optimal Semiparametric Method for Two‐group Classification

In the classical discriminant analysis, when two multivariate normal distributions with equal variance–covariance matrices are assumed for two groups, the classical linear discriminant function is optimal with respect to maximizing the standardized difference between the means of two groups. However, for a typical case‐control study, the distributional assumption for the case group often needs to be relaxed in practice. Komori et al. (Generalized t ‐statistic for two‐group classification. Biometrics 2015, 71: 404–416) proposed the generalized t ‐statistic to obtain a linear discriminant function, which allows for heterogeneity of case group. Their procedure has an optimality property in the class of consideration. We perform a further study of the problem and show that additional improvement is achievable. The approach we propose does not require a parametric distributional assumption on the case group. We further show that the new estimator is efficient, in that no further improvement is possible to construct the linear discriminant function more efficiently. We conduct simulation studies and real data examples to illustrate the finite sample performance and the gain that it produces in comparison with existing methods.     

A simple,doubly robust,efficient estimator for survival functions using pseudo observations

Survival functions are often estimated by nonparametric estimators such as the Kaplan‐Meier estimator. For valid estimation, proper adjustment for confounding factors is needed when treatment assignment may depend on confounding factors. Inverse probability weighting is a commonly used approach, especially when there is a large number of potential confounders to adjust for. Direct adjustment may also be used if the relationship between the time‐to‐event and all confounders can be modeled. However, either approach requires a correctly specified model for the relationship between confounders and treatment allocation or between confounders and the time‐to‐event. We propose a pseudo‐observation–based doubly robust estimator, which is valid when either the treatment allocation model or the time‐to‐event model is correctly specified and is generally more efficient than the inverse probability weighting approach. The approach can be easily implemented using standard software. A simulation study was conducted to evaluate this approach under a number of scenarios, and the results are presented and discussed. The results confirm robustness and efficiency of the proposed approach. A real data example is also provided for illustration.     

Nonparametric kernel estimation of the impact of tax policy on the demand for private health insurance in Australia

This paper is motivated by our attempt to answer a policy question: how is private health insurance take‐up in Australia affected by the income threshold at which the Medicare Levy Surcharge (MLS) kicks in? We propose a new difference deconvolution kernel estimator for the location and size of regression discontinuities. We also propose a bootstrapping procedure for estimating the confidence interval for the estimated discontinuity. Performance of the estimator is evaluated by Monte Carlo simulations before it is applied to estimating the effect of the income threshold of MLS on the take‐up of private health insurance in Australia, using contaminated data.     

The flavours of love: A cross‐cultural lexical analysis

Linguists have often remarked upon the polysemous nature of love, whereby the term encompasses a wide diversity of emotional relationships. Several typologies have been constructed to account for this diversity. However, these tend to be restricted in scope, and fail to fully represent the range of experiences signified by the term ‘love’ in discourse. In the interest of generating an expanded typology of love, encompassing its varied forms, an enquiry was conducted into relevant concepts found across the world's cultures, focusing on so‐called untranslatable words. Through a quasi‐systematic search of published and internet sources, 609 relevant words were identified. These were organised through a version of grounded theory into 14 categories, representing 14 different forms or ‘flavours’ of love. The result is an expanded theoretical treatment of love, allowing us to better appreciate the nuances of this most cherished and yet polysemous of concepts.