Related papers: Finite-Sample Analysis of Fixed-k Nearest Neighbor…
Nearest neighbor (NN) matching as a tool to align data sampled from different groups is both conceptually natural and practically well-used. In a landmark paper, Abadie and Imbens (2006) provided the first large-sample analysis of NN…
We design a data-dependent metric in $\mathbb R^d$ and use it to define the $k$-nearest neighbors of a given point. Our metric is invariant under all affine transformations. We show that, with this metric, the standard $k$-nearest neighbor…
Nearest neighbor methods are a popular class of nonparametric estimators with several desirable properties, such as adaptivity to different distance scales in different regions of space. Prior work on convergence rates for nearest neighbor…
Asymptotic properties of three estimators of probability density function of sample maximum $f_{(m)}:=mfF^{m-1}$ are derived, where $m$ is a function of sample size $n$. One of the estimators is the parametrically fitted by the…
We introduce a rank-statistic approximation of $f$-divergences that avoids explicit density-ratio estimation by working directly with the distribution of ranks. For a resolution parameter $K$, we map the mismatch between two univariate…
This paper presents how to perform minimax optimal classification, regression, and density estimation based on fixed-$k$ nearest neighbor (NN) searches. We consider a distributed learning scenario, in which a massive dataset is split into…
The k Nearest Neighbors (kNN) method has received much attention in the past decades, where some theoretical bounds on its performance were identified and where practical optimizations were proposed for making it work fairly well in high…
A new nonparametric estimator of a convex regression function in any dimension is proposed and its convergence properties are studied. We start by using any estimator of the regression function and we \emph{convexify} it by taking the…
Trustworthiness in model predictions is crucial for safety-critical applications in the real world. However, deep neural networks often suffer from the issues of uncertainty estimation, such as miscalibration. In this study, we propose…
We propose a general methodology for the construction and analysis of minimax estimators for a wide class of functionals of finite dimensional parameters, and elaborate on the case of discrete distributions, where the alphabet size $S$ is…
We consider the estimation of two-sample integral functionals, of the type that occur naturally, for example, when the object of interest is a divergence between unknown probability densities. Our first main result is that, in wide…
The k-Nearest Neighbor (kNN) classification approach is conceptually simple - yet widely applied since it often performs well in practical applications. However, using a global constant k does not always provide an optimal solution, e.g.,…
The ratio between two probability density functions is an important component of various tasks, including selection bias correction, novelty detection and classification. Recently, several estimators of this ratio have been proposed. Most…
The problem of estimation of density functionals like entropy and mutual information has received much attention in the statistics and information theory communities. A large class of estimators of functionals of the probability density…
Biased sampling and missing data complicates statistical problems ranging from causal inference to reinforcement learning. We often correct for biased sampling of summary statistics with matching methods and importance weighting. In this…
We propose a novel approach for density estimation with exponential families for the case when the true density may not fall within the chosen family. Our approach augments the sufficient statistics with features designed to accumulate…
This paper is concerned with forecasting probability density functions. Density functions are nonnegative and have a constrained integral; thus, they do not constitute a vector space. Implementing unconstrained functional time-series…
In a previous article, a least square regression estimation procedure was proposed: first, we condiser a family of functions and study the properties of an estimator in every unidimensionnal model defined by one of these functions; we then…
The $K$-function is arguably the most important functional summary statistic for spatial point processes. It is used extensively for goodness-of-fit testing and in connection with minimum contrast estimation for parametric spatial point…
Let $\textbf{X} = (X_1,\ldots, X_p)$ be a stochastic vector having joint density function $f_{\textbf{X}}(x)$ with partitions $\textbf{X}_1 = (X_1,\ldots, X_k)$ and $\textbf{X}_2 = (X_{k+1},\ldots, X_p)$. A new method for estimating the…