Related papers: Optimal estimation of the mean function based on d…
Causal inference starts with a simple idea: compare groups that differ by treatment, not much else. Traditionally, similar groups are constructed using only observed covariates; however, it remains a long-standing challenge to incorporate…
Mean estimation under differential privacy is a fundamental problem, but worst-case optimal mechanisms do not offer meaningful utility guarantees in practice when the global sensitivity is very large. Instead, various heuristics have been…
In the practical industry, the most commonly used application of statistical analysis for monitoring the process mean is the control chart. Control charts are generated based on the presumption that we have a sample from a stable process.…
Study samples often differ from the target populations of inference and policy decisions in non-random ways. Researchers typically believe that such departures from random sampling -- due to changes in the population over time and space, or…
Functional data analysis has attracted considerable interest and is facing new challenges, one of which is the increasingly available data in a streaming manner. In this article we develop an online nonparametric method to dynamically…
Nowadays, the numerical models of real-world structures are more precise, more complex and, of course, more time-consuming. Despite the growth of a computational effort, the exploration of model behaviour remains a complex task. The…
We study the detection of a sparse change in a high-dimensional mean vector as a minimax testing problem. Our first main contribution is to derive the exact minimax testing rate across all parameter regimes for $n$ independent, $p$-variate…
Optimization algorithms and Monte Carlo sampling algorithms have provided the computational foundations for the rapid growth in applications of statistical machine learning in recent years. There is, however, limited theoretical…
Difference-in-differences (DiD) is a cornerstone of causal inference, yet extending it to functional outcomes is not a routine scalar generalization; rather, it entails three fundamental challenges in identification, inference, and…
Given noisy data, function estimation is considered when the unknown function is known a priori to consist of a small number of regions where the function is either convex or concave. When the number of regions is unknown, the model…
We consider the problem of adaptive stratified sampling for Monte Carlo integration of a differentiable function given a finite number of evaluations to the function. We construct a sampling scheme that samples more often in regions where…
We consider approximation or recovery of functions based on a finite number of function evaluations. This is a well-studied problem in optimal recovery, machine learning, and numerical analysis in general, but many fundamental insights were…
The problem of matching two sets of features appears in various tasks of computer vision and can be often formalized as a problem of permutation estimation. We address this problem from a statistical point of view and provide a theoretical…
A key feature of a sequential study is that the actual sample size is a random variable that typically depends on the outcomes collected. While hypothesis testing theory for sequential designs is well established, parameter and precision…
The problem of quickest detection of a change in the mean of a sequence of independent observations is studied. The pre-change distribution is assumed to be stationary, while the post-change distributions are allowed to be non-stationary.…
We consider the problem of detecting an elevated mean on an interval with unknown location and length in the univariate Gaussian sequence model. Recent results have shown that using scale-dependent critical values for the scan statistic…
A large class of problems in sciences and engineering can be formulated as the general problem of constructing random intervals with pre-specified coverage probabilities for the mean. Wee propose a general approach for statistical inference…
Measurement error is an important problem that has not been very well studied in the context of Functional Data Analysis. To the best of our knowledge, there are no existing methods that address the presence of functional measurement errors…
The problem of the mean-square optimal linear estimation of functionals which depend on the unknown values of a stationary stochastic sequence from observations of the sequence with noise is considered. In the case of spectral certainty,…
Faced with massive data, subsampling is a commonly used technique to improve computational efficiency, and using nonuniform subsampling probabilities is an effective approach to improve estimation efficiency. For computational efficiency,…