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For estimating the unknown parameters in an unstable autoregressive AR(p), the paper proposes sequential least squares estimates with a special stopping time defined by the trace of the observed Fisher information matrix. The limiting…

We propose a novel nonparametric regression framework subject to the positive definiteness constraint. It offers a highly modular approach for estimating covariance functions of stationary processes. Our method can impose positive…

Posterior probabilistic statistical inference without priors is an important but so far elusive goal. Fisher's fiducial inference, Dempster-Shafer theory of belief functions, and Bayesian inference with default priors are attempts to…

Uncertainty quantification of causal effects is crucial for safety-critical applications such as personalized medicine. A powerful approach for this is conformal prediction, which has several practical benefits due to model-agnostic…

Non-stationary approximations of the final value of a converging sequence are discussed, and we show that extremal eigenvalues can be reasonably estimated from the CG iterates without much computation at all. We introduce estimators of…

This paper proposes and analyzes fully data driven methods for inference about the mean function of a stochastic process from a sample of independent trajectories of the process, observed at discrete time points and corrupted by additive…

A conventional Bayesian approach to prediction uses the posterior distribution to integrate out parameters in a density for unobserved data conditional on the observed data and parameters. When the true posterior is intractable, it is…

Projection predictive inference is a decision theoretic Bayesian approach that decouples model estimation from decision making. Given a reference model previously built including all variables present in the data, projection predictive…

We study semiparametric varying-coefficient partially linear models when some linear covariates are not observed, but ancillary variables are available. Semiparametric profile least-square based estimation procedures are developed for…

We introduce a novel uncertainty estimation for classification tasks for Bayesian convolutional neural networks with variational inference. By normalizing the output of a Softplus function in the final layer, we estimate aleatoric and…

We propose DiffusionRollout, a novel selective rollout planning strategy for autoregressive diffusion models, aimed at mitigating error accumulation in long-horizon predictions of physical systems governed by partial differential equations…

This paper considers the problem of forecasting mortality rates. A large number of models have already been proposed for this task, but they generally have the disadvantage of either estimating the model in a two-step process, possibly…

Estimating and detecting faults is crucial in ensuring safe and efficient automated systems. In the presence of disturbances, noise or varying system dynamics, such estimation is even more challenging. To address this challenge, this…

This paper proposes a versatile covariate adjustment method that directly incorporates covariate balance in regression discontinuity (RD) designs. The new empirical entropy balancing method reweights the standard local polynomial RD…

Conformal prediction offers finite-sample coverage guarantees under minimal assumptions. However, existing methods treat the entire modeling process as a black box, overlooking opportunities to exploit and understand modular structure. We…

Exact inference in the linear regression model with spike and slab priors is often intractable. Expectation propagation (EP) can be used for approximate inference. However, the regular sequential form of EP (R-EP) may fail to converge in…

Isotonic regression provides a flexible, tuning-free approach to estimating monotonic functions without imposing global curvature constraints, yet the estimated regression function is inherently a step function. This paper addresses a key…

In randomized experiments, regression adjustment can improve the precision of average treatment effect (ATE) estimation using covariates without requiring a correctly specified outcome model. Although well studied in low-dimensional…

For an arbitrary parameter $p\in [1,+\infty]$, we consider the problem of exponential stabilization in the spatial $L^{p}$-norm, and $W^{1,p}$-norm, respectively, for a class of anti-stable linear parabolic PDEs with space-time-varying…

This paper provides an entire inference procedure for the autoregressive model under (conditional) heteroscedasticity of unknown form with a finite variance. We first establish the asymptotic normality of the weighted least absolute…