Predictive inference under a general regression setting is gaining more interest in the big-data era. In terms of going beyond point prediction to develop prediction intervals, two main threads of development are conformal prediction and Model-free prediction. Recently, a new conformal prediction approach was proposed that exploits the same uniformization procedure as in the well-known Model-free Bootstrap. Hence, it is of interest to compare and further investigate the performance of the two methods. In the paper at hand, we contrast the two approaches via theoretical analysis and numerical experiments with a focus on conditional coverage of prediction intervals. We discuss suitable scenarios for applying each algorithm, underscore the importance of conditional vs. unconditional coverage, and show that, under mild conditions, the Model-free bootstrap yields prediction intervals with guaranteed better conditional coverage compared to quantile estimation. We also extend the concept of ‘pertinence’ of prediction intervals to the nonparametric regression setting, and give concrete examples where its importance emerges under finite sample scenarios. Finally, we define the new notion of ‘conjecture testing’ that is the analog of hypothesis testing as applied to the prediction problem; we also devise a modified conformal score to allow conformal prediction to handle one-sided ‘conjecture tests’, and compare to the Model-free bootstrap.

Distance correlation and Chatterjee's correlation are two highly representative measures of dependence. Their simplicity and desirable properties have attracted much attention over the past years, leading to numerous extensions and in-depth discussions. The theoretical connections between these two measures, however, have remained largely underexplored, despite some empirical comparisons of their statistical power. This paper investigates some connections between Chatterjee's correlation and the rank-based distance correlation. We show that both belong to a class of dependence measures based on non-negative weighted rank differences, but with distinct weight allocations resulting in different asymptotic null distributions. Motivated by this finding, we construct a new rank distance correlation using Gaussian kernel that, quite interestingly, exhibits Chatterjee-like behaviour under finite sample and specific bandwidth conditions.

Complex surveys are important data resources across diverse domains, including social sciences, public health, and market research. When faced with unknown effects and interactions of multiple covariates, analysis using usual parametric regression functions may not be adequate. Moreover, mean regression assuming a Gaussian response is often inappropriate when the response distribution is heavy-tailed or highly skewed. While the ensemble of regression trees has received much attention in recent years, there has been limited attention to nonparametric Bayesian regression functions – specifically for quantile regression and modelling of skewed clustered complex survey data. For clustered survey data with subject-specific survey weights, this paper introduces the Soft Bayesian Additive Regression Trees (SBART) framework for doing quantile regression as well as full modelling of the heavy-tailed and skewed response distribution. We illustrate the advantages of our methods through simulation studies and an analysis of multivariate periodontal responses from the National Health and Nutrition Examination Survey.

We introduce a novel approach for variable selection in the generalised partially linear model (GPLM) by building upon the previous research conducted by Lu Dong, Hu, and Wu [(2023), ‘A unified approach to variable selection for partially linear models’, Journal of Computational and Graphical Statistics, 1–11]. Our proposed method expands on their work by incorporating a local scoring algorithm. This approach enables the selection of linear and nonparametric predictors simultaneously by solving a single optimisation problem. To showcase the effectiveness of our method in practice, we provide simulation examples involving logistic regression and Poisson regression models. Additionally, we present a real-world data example and engage in a discussion surrounding its application.

Causal inference is formulated using the counterfactual framework, enabling direct investigation of causal questions. Causal inference methods can incorporate machine learning techniques into the estimation process, allowing for more flexible models. However, the integration of machine learning methods adds complexity to statistical inference. In this paper, we systematically assess several methods for making causal inference with multiple treatment groups, including the outcome regression, inverse propensity score weighting, double-robust estimators, and their counterparts when employing a super learner in the estimation process, as well as the targeted maximum likelihood estimator (TMLE). We conduct numerical studies with complex data-generating models to evaluate these different estimators. Our results suggest that the double-robust estimator, when combined with machine learning, is the most favourable approach, demonstrating lower biases, a valid variance estimator, and improved coverage probabilities for the 95% confidence interval.

As an alternative to quantile regression, expectile regression can also draw the complete picture of the response and characterise the heterogeneity of the data. However, there is limited study on testing for Granger-causality in expectiles. This paper aims to develop a sup-Wald test for Granger non-causality in an expectile range. The asymptotic null distribution and local power properties of the test are derived for stationary time series. A simulated test procedure is proposed to approximate the critical values by simulating the Gaussian process that characterises the limiting distributions of the test statistic. Simulation studies demonstrate that our test has reasonable size and good power under different model settings. Our test is applied to detect volatility spillover effects between the crude oil and stock markets in the US, Germany and France during the COVID-19 pandemic. The empirical results indicate higher volatility spillovers and significant asymmetric spillover effects between oil and stock markets, with market-specific heterogeneity.

Survival analysis studies the time up to an event of interest assuming that all individuals will undergo the event. In some cases, the event may not happen for all subjects. This condition gives rise to cure models, where a subset of the individuals will experience the event and other part will never suffer it. Estimating the probability of experiencing the event is crucial in these situations. Presmoothing is a technique that improves the efficiency of nonparametric estimates in survival analysis and, therefore, in cure models. We propose to estimate the cure rate nonparametrically using presmoothing. Presmoothing depends on a smoothing parameter which must be chosen appropriately. To understand the effect of presmoothing on the estimation of the probability of cure, a simulation study was carried out. Finally, the methodology was applied to a dataset of breast cancer patients.

The use of surrogate markers to replace a primary outcome in clinical trials has the potential to allow earlier decisions about the effectiveness of a treatment when a direct measurement of the primary outcome is difficult to obtain. However, the surrogate paradox, which occurs when a treatment has a positive effect on the surrogate marker but a negative effect on the primary outcome, may lead researchers to make incorrect conclusions about the treatment benefit. In this paper, we propose a formal nonparametric framework to empirically examine and test assumptions that ensure avoidance of the surrogate paradox. For each assumption, we propose a nonparametric hypothesis test, formally derive the properties of the test, and analyze its performance in finite samples in a variety of simulation settings. We apply our proposed testing framework to data from the the Diabetes Prevention Program clinical trial.

The paper considers the test on the components independence of high-dimensional continuous random vectors based on the Kendall rank correlation coefficient. Under the null hypothesis, it proves that the sum-of-powers type statistics constructed by the Kendall rank correlation coefficient are asymptotically normally distributed and independent when the sum of the orders is odd, and they are also independent with the extreme-value-type test statistics of the Kendall rank correlation coefficient. Based on the asymptotic independence property, it proposes an adaptive test procedure which combines p-values from the sum-of-powers-type test and extreme-value-type test. Some simulations reveal that the proposed test method can significantly enhance the statistical power of the test while keep the type I error well controlled, and it is powerful against a wide range of alternatives (including dense, sparse or moderately sparse signals). To illustrate the use of the proposed adaptive test method, two real data sets are also analysed.