Related papers: Optimal Subsampling Bootstrap for Massive Data
Stochastic gradient descent (SGD) or stochastic approximation has been widely used in model training and stochastic optimization. While there is a huge literature on analyzing its convergence, inference on the obtained solutions from SGD…
The partially linear binary choice model can be used for estimating structural equations where nonlinearity may appear due to diminishing marginal returns, different life cycle regimes, or hectic physical phenomena. The inference procedure…
Subsampling methods have been recently proposed to speed up least squares estimation in large scale settings. However, these algorithms are typically not robust to outliers or corruptions in the observed covariates. The concept of influence…
Model selection requires repeatedly evaluating models on a given dataset and measuring their relative performances. In modern applications of machine learning, the models being considered are increasingly more expensive to evaluate and the…
Sampling techniques are used in many fields, including design of experiments, image processing, and graphics. The techniques in each field are designed to meet the constraints specific to that field such as uniform coverage of the range of…
An important challenge in statistical analysis concerns the control of the finite sample bias of estimators. For example, the maximum likelihood estimator has a bias that can result in a significant inferential loss. This problem is…
We investigate the validity of two resampling techniques when carrying out inference on the underlying unknown copula using a recently proposed class of smooth, possibly data-adaptive nonparametric estimators that contains empirical…
Model averaging techniques based on resampling methods (such as bootstrapping or subsampling) have been utilized across many areas of statistics, often with the explicit goal of promoting stability in the resulting output. We provide a…
In frequency domain analysis for spatial data, spectral averages based on the periodogram often play an important role in understanding spatial covariance structure, but also have complicated sampling distributions due to complex variances…
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…
We consider the properties of the bootstrap as a tool for inference concerning the eigenvalues of a sample covariance matrix computed from an $n\times p$ data matrix $X$. We focus on the modern framework where $p/n$ is not close to 0 but…
A weighted regression procedure is proposed for regression type problems where the innovations are heavy-tailed. This method approximates the least absolute regression method in large samples, and the main advantage will be if the sample is…
We present a new fitting technique based on the parametric bootstrap method, which relies on the idea to produce artificial measurements using the estimated probability distribution of the experimental data. In order to investigate the main…
Ensuring that analyses performed on a dataset are representative of the entire population is one of the central problems in statistics. Most classical techniques assume that the dataset is independent of the analyst's query and break down…
During the past few years, mediation analysis has gained increasing popularity across various research fields. The primary objective of mediation analysis is to examine the direct impact of exposure on outcome, as well as the indirect…
Sampling is a fundamental problem in computer science and statistics. However, for a given task and stream, it is often not possible to choose good sampling probabilities in advance. We derive a general framework for adaptively changing the…
Bootstrap methods are increasingly accepted as one of the common approaches in constructing confidence intervals in bibliometric studies. Typical bootstrap methods assume that the statistical population is infinite. When the statistical…
Many modern estimators require bootstrapping to calculate confidence intervals because either no analytic standard error is available or the distribution of the parameter of interest is non-symmetric. It remains however unclear how to…
In this paper, we propose a stochastic optimization method that adaptively controls the sample size used in the computation of gradient approximations. Unlike other variance reduction techniques that either require additional storage or the…
A general approach to selective inference is considered for hypothesis testing of the null hypothesis represented as an arbitrary shaped region in the parameter space of multivariate normal model. This approach is useful for hierarchical…