相关论文: Confidence balls in Gaussian regression

The fiducial is not unique in general, but we prove that in a restricted class of models it is uniquely determined by the sampling distribution of the data. It depends in particular not on the choice of a data generating model. The…

The declining response rates in probability surveys along with the widespread availability of unstructured data has led to growing research into non-probability samples. Existing robust approaches are not well-developed for non-Gaussian…

Confidence intervals are an established means of portraying uncertainty about an inferred parameter and can be generated through the use of confidence distributions. For a confidence distribution to be ideal, it must maintain frequentist…

In this short note I apply the methodology of game-theoretic probability to calculating non-asymptotic confidence intervals for the coefficient of a simple first order scalar autoregressive model. The most distinctive feature of the…

Several strategies have been developed recently to ensure valid inference after model selection; some of these are easy to compute, while others fare better in terms of inferential power. In this paper, we consider a selective inference…

We study sequential mean estimation in $\mathbb{R}^d$. In particular, we derive time-uniform confidence spheres -- confidence sphere sequences (CSSs) -- which contain the mean of random vectors with high probability simultaneously across…

We propose, for multivariate Gaussian copula models with unknown margins and structured correlation matrices, a rank-based, semiparametrically efficient estimator for the Euclidean copula parameter. This estimator is defined as a one-step…

We provide a selected overview of methodology and theory for estimation and inference on the edge weights in high-dimensional directed and undirected Gaussian graphical models. For undirected graphical models, two main explicit…

For any compact surface $\Sigma$ with smooth, non-empty boundary, we construct a free boundary minimal immersion into a Euclidean Ball $\mathbb{B}^N$ where $N$ is controlled in terms of the topology of $\Sigma$. We obtain these as…

Non-Bayesian social learning theory provides a framework for distributed inference of a group of agents interacting over a social network by sequentially communicating and updating beliefs about the unknown state of the world through…

A mathematical model is developed, to jointly analyze elastic and inelastic scattering data of fluctuating membranes within a single theoretical framework. The model builds on a non-homogeneously clipped time-dependent Gaussian random…

Under standard regularity assumptions, we provide simple approximations for specific classes of fiducial and confidence distributions and discuss their connections with objective Bayesian posteriors. For a real parameter the approximations…

Given $n=mk$ $iid$ samples from $N(\theta,\sigma^2)$ with $\theta$ and $\sigma^2$ unknown, we have two ways to construct $t$-based confidence intervals for $\theta$. The traditional method is to treat these $n$ samples as $n$ groups and…

We propose two new conformity scores for conformal prediction, in a general multivariate regression framework. The underlying score functions are based on a covariance analysis of the residuals and the input points. We give theoretical…

The Gaussian Correlation Conjecture states that for any two symmetric, convex sets in n-dimensional space and for any centered, Gaussian measure on that space, the measure of the intersection is greater than or equal to the product of the…

Monte Carlo methods are used to approximate the means, $\mu$, of random variables $Y$, whose distributions are not known explicitly. The key idea is that the average of a random sample, $Y_1, ..., Y_n$, tends to $\mu$ as $n$ tends to…

The problem of constructing a simultaneous confidence surface for the 2-dimensional mean function of a non-stationary functional time series is challenging as these bands can not be built on classical limit theory for the maximum absolute…

We study the insulated conductivity problem with inclusions embedded in a bounded domain in $\mathbb R^n$, for $n \ge 3$. The gradient of solutions may blow up as $\varepsilon$, the distance between inclusions, approaches to $0$. We…

Gaussian Process regression is a kernel method successfully adopted in many real-life applications. Recently, there is a growing interest on extending this method to non-Euclidean input spaces, like the one considered in this paper,…

Regression is an essential and fundamental methodology in statistical analysis. The majority of the literature focuses on linear and nonlinear regression in the context of the Euclidean space. However, regression models in non-Euclidean…