相关论文: Higher-order asymptotic corrections and their appl…

The Gaussian graphical model, a popular paradigm for studying relationship among variables in a wide range of applications, has attracted great attention in recent years. This paper considers a fundamental question: When is it possible to…

Bayesian nonparametric regression under a rescaled Gaussian process prior offers smoothness-adaptive function estimation with near minimax-optimal error rates. Hierarchical extensions of this approach, equipped with stochastic variable…

We derive inferential procedures for large sample sizes that remain valid under data-dependent significance levels (so-called "post-hoc valid inference"). Classical statistical tools require that the significance level -- the "type-I error"…

In statistical inference, confidence set procedures are typically evaluated based on their validity and width properties. Even when procedures achieve rate-optimal widths, confidence sets can still be excessively wide in practice due to…

This work presents a technique for statistically modeling errors introduced by reduced-order models. The method employs Gaussian-process regression to construct a mapping from a small number of computationally inexpensive `error indicators'…

In this paper we compare and contrast the behavior of the posterior predictive distribution to the risk of the maximum a posteriori estimator for the random features regression model in the overparameterized regime. We will focus on the…

Gaussian processes (GPs) are a powerful tool for probabilistic inference over functions. They have been applied to both regression and non-linear dimensionality reduction, and offer desirable properties such as uncertainty estimates,…

The density weighted average derivative (DWAD) of a regression function is a canonical parameter of interest in economics. Classical first-order large sample distribution theory for kernel-based DWAD estimators relies on tuning parameter…

Evaluating the statistical dimension is a common tool to determine the asymptotic phase transition in compressed sensing problems with Gaussian ensemble. Unfortunately, the exact evaluation of the statistical dimension is very difficult and…

We consider parametric estimation and tests for multi-dimensional diffusion processes with a small dispersion parameter $\varepsilon$ from discrete observations. For parametric estimation of diffusion processes, the main target is to…

For complex latent variable models, the likelihood function is not available in closed form. In this context, a popular method to perform parameter estimation is Importance Weighted Variational Inference. It essentially maximizes the…

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…

In this paper, we provide a general methodology to draw statistical inferences on individual signal coordinates or linear combinations of them in sparse phase retrieval. Given an initial estimator for the targeting parameter (some simple…

Measurement error is a pervasive issue which renders the results of an analysis unreliable. The measurement error literature contains numerous correction techniques, which can be broadly divided into those which aim to produce exactly…

Tuning parameters are parameters involved in an estimating procedure for the purpose of reducing the risk of some other estimator. Examples include the degree of penalization in penalized regression and likelihood problems, as well as the…

In the setting of high-dimensional linear regression models, we propose two frameworks for constructing pointwise and group confidence sets for penalized estimators which incorporate prior knowledge about the organization of the non-zero…

Let $\alpha_n(\cdot)=P\bigl(X_{n+1}\in\cdot\mid X_1,\ldots,X_n\bigr)$ be the predictive distributions of a sequence $(X_1,X_2,\ldots)$ of $p$-dimensional random vectors. Suppose $$\alpha_n= \mathcal{N} _p (M_n,Q_n)$$ where…

We developed a statistical inference method applicable to a broad range of generalized linear models (GLMs) in high-dimensional settings, where the number of unknown coefficients scales proportionally with the sample size. Although a…

Mechanistic simulation models are inverted against observations in order to gain inference on modeled processes. However, with the increasing ability to collect high resolution observations, these observations represent more patterns of…

In the big data era, the need to reevaluate traditional statistical methods is paramount due to the challenges posed by vast datasets. While larger samples theoretically enhance accuracy and hypothesis testing power without increasing false…