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Hard thresholding, LASSO , adaptive LASSO and SCAD point estimators have been suggested for use in the linear regression context when most of the components of the regression parameter vector are believed to be zero, a sparsity type of…
A reasonable confidence interval should have a confidence coefficient no less than the given nominal level and a small expected length to reliably and accurately estimate the parameter of interest, and the bootstrap interval is considered…
Confidence intervals for the means of multiple normal populations are often based on a hierarchical normal model. While commonly used interval procedures based on such a model have the nominal coverage rate on average across a population of…
We consider nonparametric Bayesian estimation inference using a rescaled smooth Gaussian field as a prior for a multidimensional function. The rescaling is achieved using a Gamma variable and the procedure can be viewed as choosing an…
We revisit empirical Bayes discrimination detection, focusing on uncertainty arising from both partial identification and sampling variability. While prior work has mostly focused on partial identification, we find that some empirical…
Robust uncertainty quantification is increasingly important in modern data analysis and is often formalized under Huber's model, which allows an $\varepsilon$-fraction of arbitrary corruptions. In many experimental sciences, however, the…
Bootstrap smoothed (bagged) estimators have been proposed as an improvement on estimators found after preliminary data-based model selection. Efron, 2014, derived a widely applicable formula for a delta method approximation to the standard…
In observational causal inference, domain knowledge often leaves multiple covariate adjustments plausible, yet which sets satisfy ignorability is untestable. Different adjustment sets can yield conflicting estimates of the average treatment…
We provide a new efficient adaptive algorithm for performing phase estimation that does not require that the user infer the bits of the eigenphase in reverse order; rather it directly infers the phase and estimates the uncertainty in the…
We propose a new, two-step empirical Bayes-type of approach for neural networks. We show in context of the nonparametric regression model that the procedure (up to a logarithmic factor) provides optimal recovery of the underlying functional…
When mapping subnational health and demographic indicators, direct weighted estimators of small area means based on household survey data can be unreliable when data are limited. If survey microdata are available, unit level models can…
Tolerance intervals provide bounds that contain a specified proportion of a population with a given confidence level, yet their construction remains challenging when parametric assumptions fail or sample sizes are small. Traditional…
For time series with high temporal correlation, the empirical process converges rather slowly to its limiting distribution. Many statistics in change-point analysis, goodness-of-fit testing and uncertainty quantification admit a…
We advance the theory of parametric bootstrap in constructing highly efficient empirical best (EB) prediction intervals of small area means. The coverage error of such a prediction interval is of the order $O(m^{-3/2})$, where $m$ is the…
Two non-intrusive uncertainty propagation approaches are proposed for the performance analysis of engineering systems described by expensive-to-evaluate deterministic computer models with parameters defined as interval variables. These…
We propose and study three confidence intervals (CIs) centered at an estimator that is intentionally biased to reduce mean squared error. The first CI simply uses an unbiased estimator's standard error; compared to centering at the unbiased…
We offer a general Bayes theoretic framework to derive posterior contraction rates under a hierarchical prior design: the first-step prior serves to assess the model selection uncertainty, and the second-step prior quantifies the prior…
The problem of nonparametric estimation of the conditional density of a response, given a vector of explanatory variables, is classical and of prominent importance in many prediction problems since the conditional density provides a more…
We establish rigorous \emph{a posteriori} error bounds for a space-time finite element method of arbitrary order discretising linear wave problems in second order formulation. The method combines standard finite elements in space and…
It is well known that the empirical likelihood ratio confidence region suffers finite sample under-coverage issue, and this severely hampers its application in statistical inferences.} The root cause of this under-coverage is an upper limit…