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Subsampling and block-based bootstrap methods have been used in a wide range of inference problems for time series. To accommodate the dependence, these resampling methods involve a bandwidth parameter, such as subsampling window width and…
Two new test statistics are introduced to test the null hypotheses that the sampling distribution has an increasing hazard rate on a specified interval [0,a]. These statistics are empirical L_1-type distances between the isotonic estimates,…
Deep learning models have significantly improved prediction accuracy in various fields, gaining recognition across numerous disciplines. Yet, an aspect of deep learning that remains insufficiently addressed is the assessment of prediction…
This paper proposes a novel test method for high-dimensional mean testing regard for the temporal dependent data. Comparison to existing methods, we establish the asymptotic normality of the test statistic without relying on restrictive…
A novel data-driven method for formal verification is proposed to study complex systems operating in safety-critical domains. The proposed approach is able to formally verify discrete-time stochastic dynamical systems against temporal logic…
We consider the problem of constructing confidence intervals (CIs) for the population mean of $N$ values $\{x_1, \ldots, x_N\} \subset \Sigma^N$ based on a random sample of size $n$, denoted by $X^n \equiv (X_1, \ldots, X_n)$, drawn…
Confidence sequences are anytime-valid analogues of classical confidence intervals that do not suffer from multiplicity issues under optional continuation of the data collection. As in classical statistics, asymptotic confidence sequences…
Inference for prediction errors is critical in time series forecasting pipelines. However, providing statistically meaningful uncertainty intervals for prediction errors remains relatively under-explored. Practitioners often resort to…
This article reviews recent progress in high-dimensional bootstrap. We first review high-dimensional central limit theorems for distributions of sample mean vectors over the rectangles, bootstrap consistency results in high dimensions, and…
One of the most commonly used methods for forming confidence intervals for statistical inference is the empirical bootstrap, which is especially expedient when the limiting distribution of the estimator is unknown. However, despite its…
We consider the problem of constructing confidence intervals for nonparametric functional data analysis using empirical likelihood. In this doubly infinite-dimensional context, we demonstrate the Wilks's phenomenon and propose a…
In statistics, forecast uncertainty is often quantified using a specified statistical model, though such approaches may be vulnerable to model misspecification, selection bias, and limited finite-sample validity. While bootstrapping can…
Empirical likelihood serves as a powerful tool for constructing confidence intervals in nonparametric regression and regression discontinuity designs (RDD). The original empirical likelihood framework can be naturally extended to these…
We develop a uniform inference theory for high-dimensional slope parameters in threshold regression models, allowing for either cross-sectional or time series data. We first establish oracle inequalities for prediction errors, and L1…
Double (debiased) machine learning (DML) has seen widespread use in recent years for learning causal/structural parameters, in part due to its flexibility and adaptability to high-dimensional nuisance functions as well as its ability to…
Size distortion can occur if an asymptotic testing procedure requiring diverging sample sizes, is implemented to data with very small sample sizes. In this paper, we consider one-sample and two-sample tests for mean vectors when data are…
A non parametric method based on the empirical likelihood is proposed for detecting the change in the coefficients of high-dimensional linear model where the number of model variables may increase as the sample size increases. This amounts…
Regression problems with bounded continuous outcomes frequently arise in real-world statistical and machine learning applications, such as the analysis of rates and proportions. A central challenge in this setting is predicting a response…
A large class of problems in sciences and engineering can be formulated as the general problem of constructing random intervals with pre-specified coverage probabilities for the mean. Wee propose a general approach for statistical inference…
Stochastic gradient descent (SGD) has emerged as the quintessential method in a data scientist's toolbox. Using SGD for high-stakes applications requires, however, careful quantification of the associated uncertainty. Towards that end, in…