Related papers: On Semi-Supervised Estimation of Distributions
We study semiparametric efficiency bounds and efficient estimation of parameters defined through general moment restrictions with missing data. Identification relies on auxiliary data containing information about the distribution of the…
We study minimax rates for high-dimensional linear regression with additive errors under the $\ell_p\ (1\leq p<\infty)$-losses, where the regression parameter is of weak sparsity. Our lower and upper bounds agree up to constant factors,…
Suppose that univariate data are drawn from a mixture of two distributions that are equal up to a shift parameter. Such a model is known to be nonidentifiable from a nonparametric viewpoint. However, if we assume that the unknown mixed…
In a multiple testing context, we consider a semiparametric mixture model with two components where one component is known and corresponds to the distribution of $p$-values under the null hypothesis and the other component $f$ is…
The most fundamental problem in statistics is the inference of an unknown probability distribution from a finite number of samples. For a specific observed data set, answers to the following questions would be desirable: (1) Estimation:…
We consider a general multivariate model where univariate marginal distributions are known up to a parameter vector and we are interested in estimating that parameter vector without specifying the joint distribution, except for the…
This survey provides an overview of optimal estimation of linear functionals which depend on the unknown values of a stationary stochastic sequence. Based on observations of the sequence without noise as well as observations of the sequence…
Due to measurement noise, a common problem in in various fields is how to estimate the ratio of two functions. We consider this problem of estimating the ratio of two functions in a nonparametric regression model. Assuming the noise is…
Combining information from multiple samples is often needed in biomedical and economic studies, but the differences between these samples must be appropriately taken into account in the analysis of the combined data. We study estimation for…
We address the problem of aggregating an ensemble of predictors with known loss bounds in a semi-supervised binary classification setting, to minimize prediction loss incurred on the unlabeled data. We find the minimax optimal predictions…
The use of principal component methods to analyze functional data is appropriate in a wide range of different settings. In studies of ``functional data analysis,'' it has often been assumed that a sample of random functions is observed…
Estimations of physical parameters using data usually involve non-uniform experimental efficiencies. In this article, a method of maximum likelihood fit is introduced using the efficiency as a weight, while the probability distribution…
We consider the minimax estimation problem of a discrete distribution with support size $k$ under locally differential privacy constraints. A privatization scheme is applied to each raw sample independently, and we need to estimate the…
The notion of stochastic precedence between two random variables emerges as a relevant concept in several fields of applied probability. When one consider a vector of random variables $X_1,...,X_n$, this notion has a preeminent role in the…
Widely used methods for analyzing missing data can be biased in small samples. To understand these biases, we evaluate in detail the situation where a small univariate normal sample, with values missing at random, is analyzed using either…
Statistical estimation and inference for marginal hazard models with varying coefficients for multivariate failure time data are important subjects in survival analysis. A local pseudo-partial likelihood procedure is proposed for estimating…
Given two populations from which independent binary observations are taken with parameters $p_1$ and $p_2$ respectively, estimators are proposed for the relative risk $p_1/p_2$, the odds ratio $p_1(1-p_2)/(p_2(1-p_1))$ and their logarithms.…
We develop minimax optimal risk bounds for the general learning task consisting in predicting as well as the best function in a reference set $\mathcal{G}$ up to the smallest possible additive term, called the convergence rate. When the…
We introduce missingness-MDPs (miss-MDPs), a novel subclass of partially observable Markov decision processes (POMDPs) that incorporates the theory of missing data. A miss-MDP is a POMDP whose observation function is a missingness function,…
Imbalanced classification tasks are widespread in many real-world applications. For such classification tasks, in comparison with the accuracy rate, it is usually much more appropriate to use non-decomposable performance measures such as…