arXiv subjects

Miaoshiqi Liu

Publications and source records attributed to Miaoshiqi Liu.

3 recordsLinked to original sources

arXiv2025

Wasserstein and Convex Gaussian Approximations for Non-stationary Time Series of Diverging Dimensionality

In high-dimensional time series analysis, Gaussian approximation (GA) schemes under various distance measures or on various collections of subsets of the Euclidean space play a fundamental role in a wide range of statistical inference problems. To date, most GA results for high-dimensional time series are established on hyper-rectangles and their equivalence. In this paper, by considering the 2-Wasserstein distance and the collection of all convex sets, we establish a general GA theory for a broad class of high-dimensional non-stationary (HDNS) time series, extending the scope of problems that can be addressed in HDNS time series analysis. For HDNS time series of sufficiently weak dependence and light tail, the GA rates established in this paper are either nearly optimal with respect to the dimensionality and time series length, or they are nearly identical to the corresponding best-known GA rates established for independent data. A multiplier bootstrap procedure is utilized and theoretically justified to implement our GA theory. We demonstrate by two previously undiscussed time series applications the use of the GA theory and the bootstrap procedure as unified tools for a wide range of statistical inference problems in HDNS time series analysis.

math.ST↗

arXiv2024

Self-convolved Bootstrap for M-regression under Complex Temporal Dynamics

The paper considers simultaneous nonparametric inference for a wide class of M-regression models with time-varying coefficients. The covariates and errors of the regression model are tackled as a general class of nonstationary time series and are allowed to be cross-dependent. A novel and easy-to-implement self-convolved bootstrap procedure is proposed. With only one tuning parameter, the bootstrap facilitates a $\sqrt{n}$-consistent inference of the cumulative regression function for the M-estimators under complex temporal dynamics, even under the possible presence of breakpoints in time series. Our methodology leads to a unified framework to conduct general classes of Exact Function Tests, Lack-of-fit Tests, and Qualitative Tests for the time-varying coefficients. These tests enable one to, among many others, conduct variable selection, check for constancy and linearity, as well as verify shape assumptions, including monotonicity and convexity. As applications, our method is utilized to study the time-varying properties of global climate data and Microsoft stock return, respectively.

stat.ME↗

arXiv2021

On Some Problems of Confidence Region Construction

The general problem of constructing confidence regions is unsolved in the sense that there is no algorithm that provides such a region with guaranteed coverage for an arbitrary parameter $ψ\inΨ.$ Moreover, even when such a region exists, it may be absurd in the sense that either the set $Ψ$ or the null set $ϕ$ is reported with positive probability. An approach to the construction of such regions with guaranteed coverage and which avoids absurdity is applied here to several problems that have been discussed in the recent literature and for which some standard approaches produce absurd regions.

math.ST↗