A popular method for flexible function estimation in nonparametric models is the smoothing spline. When applying the smoothing spline method, the nonparametric function is estimated via penalized least squares, where the penalty imposes a soft constraint on the function to be estimated. The specification of the penalty functional is usually based on a set of assumptions about the function. Choosing a reasonable penalty function is the key to the success of the smoothing spline method. In practice, there may exist multiple sets of widely accepted assumptions, leading to different penalties, which then yield different estimates. We refer to this problem as the problem of ambiguous penalties. Neglecting the underlying ambiguity and proceeding to the model with one of the candidate penalties may produce misleading results. In this article, we adopt a Bayesian perspective and propose a fully Bayesian approach that takes into consideration all the penalties as well as the ambiguity in choosing them. We also propose a sampling algorithm for drawing samples from the posterior distribution. Data analysis based on simulated and real‐world examples is used to demonstrate the efficiency of our proposed method.
This content will become publicly available on April 17, 2025
Identifying the underlying trajectory pattern in the spatial‐temporal data analysis is a fundamental but challenging task. In this paper, we study the problem of simultaneously identifying temporal trends and spatial clusters of spatial‐temporal trajectories. To achieve this goal, we propose a novel method named spatial clustered and sparse nonparametric regression (). Our method leverages the B‐spline model to fit the temporal data and penalty terms on spline coefficients to reveal the underlying spatial‐temporal patterns. In particular, our method estimates the model by solving a doubly‐penalized least square problem, in which we use a group sparse penalty for trend detection and a spanning tree‐based fusion penalty for spatial cluster recovery. We also develop an algorithm based on the alternating direction method of multipliers (ADMM) algorithm to efficiently minimize the penalized least square loss. The statistical consistency properties of estimator are established in our work. In the end, we conduct thorough numerical experiments to verify our theoretical findings and validate that our method outperforms the existing competitive approaches.
more » « less- Award ID(s):
- 2316353
- NSF-PAR ID:
- 10504173
- Publisher / Repository:
- Wiley
- Date Published:
- Journal Name:
- Environmetrics
- ISSN:
- 1180-4009
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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