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Robust optimization provides a principled framework for decision-making under uncertainty, with broad applications in finance, engineering, and operations research. In portfolio optimization, uncertainty in expected returns and covariances…
Deep neural networks (DNN) has received increasing attention in machine learning applications in the last several years. Recently, a non-asymptotic error bound has been developed to measure the performance of the fully connected DNN…
The bootstrap is a popular and powerful method for assessing precision of estimators and inferential methods. However, for massive datasets which are increasingly prevalent, the bootstrap becomes prohibitively costly in computation and its…
Consider a sequence of estimators $\hat \theta_n$ which converges almost surely to $\theta_0$ as the sample size $n$ tends to infinity. Under weak smoothness conditions, we identify the asymptotic limit of the last time $\hat \theta_n$ is…
Bayesian highest posterior density (HPD) intervals can be estimated directly from simulations via empirical shortest intervals. Unfortunately, these can be noisy (that is, have a high Monte Carlo error). We derive an optimal weighting…
Bootstrap is a useful tool for making statistical inference, but it may provide erroneous results under complex survey sampling. Most studies about bootstrap-based inference are developed under simple random sampling and stratified random…
Nested error regression models are useful tools for analysis of grouped data, especially in the case of small area estimation. This paper suggests a nested error regression model using uncertain random effects in which the random effect in…
Multiple systems estimation using a Poisson loglinear model is a standard approach to quantifying hidden populations where data sources are based on lists of known cases. Information criteria are often used for selecting between the large…
Empirical likelihood is an attractive inferential framework that respects natural parameter boundaries, but existing approaches typically require smoothness of the functional and miscalibrate substantially when these assumptions are…
Accurate uncertainty estimates can significantly improve the performance of iterative design of experiments, as in Sequential and Reinforcement learning. For many such problems in engineering and the physical sciences, the design task…
In this article we present very intuitive, easy to follow, yet mathematically rigorous, approach to the so called data fitting process. Rather than minimizing the distance between measured and simulated data points, we prefer to find such…
The estimation of parameter standard errors for semi-variogram models is challenging, given the two-step process required to fit a parametric model to spatially correlated data. Motivated by an application in the social-epidemiology, we…
Predictive inference under a general regression setting is gaining more interest in the big-data era. In terms of going beyond point prediction to develop prediction intervals, two main threads of development are conformal prediction and…
Time series forecasting is critical for many applications, where deep learning-based point prediction models have demonstrated strong performance. However, in practical scenarios, there is also a need to quantify predictive uncertainty…
Frequentist model averaging has been proposed as a method for incorporating "model uncertainty" into confidence interval construction. Such proposals have been of particular interest in the environmental and ecological statistics…
Corrected confidence intervals are developed for the mean of the second component of a bivariate normal process when the first component is being monitored sequentially. This is accomplished by constructing a first approximation to a…
This paper studies higher-order inference properties of nonparametric local polynomial regression methods under random sampling. We prove Edgeworth expansions for $t$ statistics and coverage error expansions for interval estimators that (i)…
We propose a censored quantile regression estimator motivated by unbiased estimating equations. Under the usual conditional independence assumption of the survival time and the censoring time given the covariates, we show that the proposed…
Nested-error regression models are widely used for analyzing clustered data. For example, they are often applied to two-stage sample surveys, and in biology and econometrics. Prediction is usually the main goal of such analyses, and…
The goal of any estimation study is an interval estimation of a the parameter(s) of interest. These estimations are mostly expressed using empirical confidence intervals that are based on sample point estimates of the corresponding…