Journal of Nonparametric Statistics最新文献

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.

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.

Accurately estimating data density is crucial for making informed decisions and modeling in various fields. This paper presents a novel nonparametric density estimation procedure that utilizes bivariate penalized spline smoothing over triangulation for data scattered over irregular spatial domains. Our likelihood-based approach incorporates a regularization term addressing the roughness of the logarithm of density using a second-order differential operator. We establish the asymptotic convergence rate of the proposed density estimator in terms of the $L_2$ and $L_{\infty }$ norms under mild natural conditions, providing a solid theoretical foundation. The proposed method demonstrates superior efficiency and flexibility with enhanced smoothness and continuity across the domain compared to existing techniques. We validate our approach through comprehensive simulation studies and apply it to real-world motor vehicle theft data from Portland, Oregon, illustrating its practical advantages in data analysis on spatial domains.

We study the multiplicative hazards model with intermittently observed longitudinal covariates and time-varying coefficients. For such models, the existing ad hoc approach, such as the last value carried forward, is biased. We propose a kernel weighting approach to get an unbiased estimation of the non-parametric coefficient function and establish asymptotic normality for any fixed time point. Furthermore, we construct the simultaneous confidence band to examine the overall magnitude of the variation. Simulation studies support our theoretical predictions and show favorable performance of the proposed method. A data set from Alzheimer's Disease Neuroimaging Initiative study is used to illustrate our methodology.

Surface-based data are prevalent across diverse practical applications in various fields. This paper introduces a novel nonparametric method to discover the underlying signals from data distributed on complex surface-based domains. The proposed approach involves a penalized spline estimator defined on a triangulation of surface patches, enabling effective signal extraction and recovery. The proposed method offers superior handling of "leakage" or "boundary effects" over complex domains, enhanced computational efficiency, and capabilities for analyzing sparse and irregularly distributed data on complex objects. We provide rigorous theoretical guarantees, including convergence rates and asymptotic normality of the estimators. We demonstrate that the convergence rates are optimal within the framework of nonparametric estimation. A bootstrap method is introduced to quantify the uncertainty in the proposed estimators and to provide pointwise confidence intervals. The advantages of the proposed method are demonstrated through simulations and data applications on cortical surface neuroimaging data and oceanic near-surface atmospheric data.