Related papers: The Threshold Breakdown Point
We characterize the fundamental limits of high-dimensional mean testing under arbitrary truncation, where samples are drawn from the conditional distribution $P(\cdot \mid S)$ for an unknown truncation set $S$ that may hide up to an…
In threshold-based anomaly detection, we want to tune the threshold of a detector to achieve an acceptable false alarm rate. However, tuning the threshold is often a non-trivial task due to unknown detector output distributions. A detector…
We consider the problem of constructing robust nonparametric confidence intervals and tests of hypothesis for the median when the data distribution is unknown and the data may contain a small fraction of contamination. We propose a…
A confidence distribution is a complete tool for making frequentist inference for a parameter of interest $\psi$ based on an assumed parametric model. Indeed, it allows to reach point estimates, to assess their precision, to set up tests…
We present a novel distribution-free approach, the data-driven threshold machine (DTM), for a fundamental problem at the core of many learning tasks: choose a threshold for a given pre-specified level that bounds the tail probability of the…
We introduce a new estimator SMUCE (simultaneous multiscale change-point estimator) for the change-point problem in exponential family regression. An unknown step function is estimated by minimizing the number of change-points over the…
We consider the problem of sensitivity of threshold risk, defined as the probability of a function of a random variable falling below a specified threshold level $\delta >0.$ We demonstrate that for polynomial and rational functions of that…
We define two minimum distance estimators for dependent data by minimizing some approximated Maximum Mean Discrepancy distances between the true empirical distribution of observations and their assumed (parametric) model distribution. When…
Change point estimation in its offline version is traditionally performed by optimizing over the data set of interest, by considering each data point as the true location parameter and computing a data fit criterion. Subsequently, the data…
We study the excess minimum risk in statistical inference, defined as the difference between the minimum expected loss in estimating a random variable from an observed feature vector and the minimum expected loss in estimating the same…
Classical semiparametric inference with missing outcome data is not robust to contamination of the observed data and a single observation can have arbitrarily large influence on estimation of a parameter of interest. This sensitivity is…
Multi-stage (designed) procedures, obtained by splitting the sampling budget suitably across stages, and designing the sampling at a particular stage based on information about the parameter obtained from previous stages, are often…
Changepoint detection is commonly formulated by minimizing the sum of in-sample losses to quantify the model's overall fit. However, for flexible modeling procedures -- especially those involving high-dimensional parameter spaces or…
We introduce a class of hybrid M-estimators of multivariate scatter which, analogous to the popular spatial sign covariance matrix (SSCM), possess high breakdown points. We also show that the SSCM can be viewed as an extreme member of this…
Many statistical estimators are defined as the fixed point of a data-dependent operator, with estimators based on minimizing a cost function being an important special case. The limiting performance of such estimators depends on the…
In the statistical inference for long range dependent time series the shape of the limit distribution typically depends on unknown parameters. Therefore, we propose to use subsampling. We show the validity of subsampling for general…
Discovery problems often require deciding whether additional sampling is needed to detect all categories whose prevalence exceeds a prespecified threshold. We study this question under a Bernoulli product (incidence) model, where categories…
We study confidence intervals based on hard-thresholding, soft-thresholding, and adaptive soft-thresholding in a linear regression model where the number of regressors $k$ may depend on and diverge with sample size $n$. In addition to the…
Errors-in-variables is a long-standing, difficult issue in linear regression; and progress depends in part on new identifying assumptions. I characterize measurement error as bad-leverage points and assume that fewer than half the sample…
The issue addressed in this paper is that of testing for common breaks across or within equations of a multivariate system. Our framework is very general and allows integrated regressors and trends as well as stationary regressors. The null…