Related papers: Finite-sample analysis of M-estimators using self-…
An effective two-stage method for an estimation of parameters of the linear regression is considered. For this purpose we introduce a certain quasi-estimator that, in contrast to usual estimator, produces two alternative estimates. It is…
In this article, we construct semiparametrically efficient estimators of linear functionals of a probability measure in the presence of side information using an easy empirical likelihood approach. We use estimated constraint functions and…
We propose an iterative estimating equations procedure for analysis of longitudinal data. We show that, under very mild conditions, the probability that the procedure converges at an exponential rate tends to one as the sample size…
It is well known that estimating the expectation of any given bounded random variable with values in $[-B, B]$ has a sample complexity of $\mathrm{O}(B^2/\epsilon^2)$ that is independent of the underlying probability measure. We show that…
We investigate the nonparametric, composite hypothesis testing problem for arbitrary unknown distributions in the asymptotic regime where both the sample size and the number of hypotheses grow exponentially large. Such asymptotic analysis…
The sample compression theory provides generalization guarantees for predictors that can be fully defined using a subset of the training dataset and a (short) message string, generally defined as a binary sequence. Previous works provided…
A central problem in Binary Hypothesis Testing (BHT) is to determine the optimal tradeoff between the Type I error (referred to as false alarm) and Type II (referred to as miss) error. In this context, the exponential rate of convergence of…
We study robust linear regression in high-dimension, when both the dimension $d$ and the number of data points $n$ diverge with a fixed ratio $\alpha=n/d$, and study a data model that includes outliers. We provide exact asymptotics for the…
In most machine learning tasks, we evaluate a model $M$ on a given data population $S$ by measuring a population-level metric $F(S;M)$. Examples of such evaluation metric $F$ include precision/recall for (binary) recognition, the F1 score…
The inferential model (IM) framework offers alternatives to the familiar probabilistic (e.g., Bayesian and fiducial) uncertainty quantification in statistical inference. Allowing this uncertainty quantification to be imprecise makes it…
Random constraint satisfaction problems (CSPs) such as random $3$-SAT are conjectured to be computationally intractable. The average case hardness of random $3$-SAT and other CSPs has broad and far-reaching implications on problems in…
We investigate a generalized empirical likelihood approach in a two-group setting where the constraints on parameters have a form of U-statistics. In this situation, the summands that consist of the constraints for the empirical likelihood…
When estimating a proportion and only a sample of triplets is given, dependencies within the triplets are to be accounted for. Without assuming a distribution for the success count of the triplet, together with the proportion, as second and…
The naive importance sampling estimator, based on samples from a single importance density, can be numerically unstable. Instead, we consider generalized importance sampling estimators where samples from more than one probability…
We study least-squares trace regression when the parameter is the sum of a $r$-low-rank matrix and a $s$-sparse matrix and a fraction $\epsilon$ of the labels is corrupted. For subgaussian distributions and feature-dependent noise, we…
Being able to reliably assess not only the \emph{accuracy} but also the \emph{uncertainty} of models' predictions is an important endeavour in modern machine learning. Even if the model generating the data and labels is known, computing the…
We propose confidence regions for the parameters of incomplete models with exact coverage of the true parameter in finite samples. Our confidence region inverts a test, which generalizes Monte Carlo tests to incomplete models. The test…
Location estimation is a central problem in functional data analysis. In this paper, we investigate penalized spline estimators of location for discretely sampled functional data under a broad class of convex loss functions. Our framework…
It is well known that if the power spectral density of a continuous time stationary stochastic process does not have a compact support, data sampled from that process at any uniform sampling rate leads to biased and inconsistent spectrum…
An important challenge in statistical analysis concerns the control of the finite sample bias of estimators. This problem is magnified in high-dimensional settings where the number of variables $p$ diverges with the sample size $n$, as well…