arXiv subjects

Tianpai Luo

Publications and source records attributed to Tianpai Luo.

3 recordsLinked to original sources

arXiv2026

ConquerNet: Convolution-Smoothed Quantile ReLU Neural Networks with Minimax Guarantees

Quantile regression is a fundamental tool for distributional learning but poses significant optimization challenges for deep models due to the non-smoothness of the pinball loss. We propose ConquerNet, a class of \textbf{con}volution-smoothed \textbf{qu}antil\textbf{e} \textbf{R}eLU neural \textbf{net}works, which yield smooth objectives while preserving the underlying quantile structure. We establish general nonasymptotic risk bounds for ConquerNet under mild conditions, providing minimax guarantees over Besov function classes. In numerical studies, we demonstrate that the proposed approach outperforms standard quantile neural networks at multiple quantile levels, showing improved estimation accuracy and training efficiency across the board, with particularly pronounced advantages at high and low quantiles.

stat.ML↗

arXiv2026

Simultaneous Inference for Nonlinear Time Series, a Sieve M-regression Approach

This paper studies simultaneous inference of conditional distributions in nonlinear time series from a sieve M-regression perspective. Existing literature on sieve M-regression has primarily focused on pointwise asymptotics, leaving the development of uncertainty quantification over the entire predictor space unexplored. We address this gap by establishing a uniform Bahadur representation for the sieve M-estimator, accommodating dependent data and a growing number of sieve basis functions. A novel high-dimensional empirical process theory is developed for temporally dependent data, and a specifically designed M-decomposition method is utilized to control high-dimensional complexities. Building on this representation, we develop a convex Gaussian approximation to characterize the asymptotic behavior of the estimator and construct valid simultaneous confidence regions (SCRs). To facilitate practical implementation, we introduce a self-convolved bootstrap algorithm that accurately approximates the distribution of the maximal deviation. Our inferential framework is supported by rigorous error bounds and validated through numerical simulations and real data applications.

math.ST↗

arXiv2023

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

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.

math.ST↗