Simultaneous inference for monotone and smoothly time-varying functions under complex temporal dynamics

TL;DR

This paper introduces a new statistical framework for simultaneous inference of monotone and smoothly changing functions over time, using nonparametric estimation and bootstrap methods, applicable to climate data and regression analysis.

Contribution

It develops a novel approach combining monotone rearrangement and Gaussian approximation for constructing confidence bands in complex temporal settings.

Findings

Proposed SCBs have narrower widths than existing methods.

Validated the approach through theoretical analysis and extensive simulations.

Successfully applied to climate trend analysis and environmental impact testing.

Abstract

We propose a new framework for the simultaneous inference of monotone and smoothly time-varying functions under complex temporal dynamics. This will be done utilizing the monotone rearrangement and the nonparametric estimation. We capitalize the Gaussian approximation for the nonparametric monotone estimator and construct the asymptotically correct simultaneous confidence bands (SCBs) using designed bootstrap methods. We investigate two general and practical scenarios. The first is the simultaneous inference of monotone smooth trends from moderately high-dimensional time series. The proposed algorithm has been employed for the joint inference of temperature curves from multiple areas. Specifically, most existing methods are designed for a single monotone smooth trend. In such cases, our proposed SCB empirically exhibits the narrowest width among existing approaches while maintaining confidence levels. It has also been used for testing several hypotheses tailored to global warming. The second scenario involves simultaneous inference of monotone and smoothly time-varying regression coefficients in time-varying coefficient linear models. The proposed algorithm has been utilized for testing the impact of sunshine duration on temperature which is believed to be increasing due to severe greenhouse effect. The validity of the proposed methods has been justified in theory as well as by extensive simulations.