Related papers: Uniform strong consistency of a frontier estimator…
We study policy evaluation of offline contextual bandits subject to unobserved confounders. Sensitivity analysis methods are commonly used to estimate the policy value under the worst-case confounding over a given uncertainty set. However,…
The use of second order boundary kernels for distribution function estimation was recently addressed in the literature (C. Tenreiro, 2013, Boundary kernels for distribution function estimation, REVSTAT-Statistical Journal, 11, 169-190). In…
In this paper, we analyze the asymptotic behavior of the main characteristics of the mean-variance efficient frontier employing random matrix theory. Our particular interest covers the case when the dimension $p$ and the sample size $n$…
We generalize standard credal set models for imprecise probabilities to include higher order credal sets -- confidences about confidences. In doing so, we specify how an agent's higher order confidences (credal sets) update upon observing…
The problem of convergence of moments of a sequence of random variables to the moments of its asymptotic distribution is important in many applications. These include the determination of the optimal training sample size in the cross…
We consider kernel smoothed Grenander-type estimators for a monotone hazard rate and a monotone density in the presence of randomly right censored data. We show that they converge at rate $n^{2/5}$ and that the limit distribution at a fixed…
Kernel smoothers are considered near the boundary of the interval. Kernels which minimize the expected mean square error are derived. These kernels are equivalent to using a linear weighting function in the local polynomial regression. It…
We generalize a method for proving uniform in bandwidth consistency results for kernel type estimators developed by the two last named authors. Such results are shown to be useful in establishing consistency of local polynomial estimators…
Recent research has established sufficient conditions for finite mixture models to be identifiable from grouped observations. These conditions allow the mixture components to be nonparametric and have substantial (or even total) overlap.…
For the kernel estimator of the quantile density function (the derivative of the quantile function), I show how to perform the boundary bias correction, establish the rate of strong uniform consistency of the bias-corrected estimator, and…
Convergence rates of kernel density estimators for stationary time series are well studied. For invertible linear processes, we construct a new density estimator that converges, in the supremum norm, at the better, parametric, rate…
We are interested in the rate of consistency of kernel density estimators with respect to the weighted sup-norm determined by some unbounded weight function. This problem has been considered by Gine, Koltchinskii and Zinn (2004) for a…
Let $X$ be a Bernoulli random variable with the success probability $p$. We are interested in tight bounds on $\mathbb{E}[f(X_1,X_2)]$, where $X_i=\mathbb{E}[X| \mathcal{F}_i]$ and $\mathcal{F}_i$ are some sigma-algebras. This problem is…
In many contemporary statistical and machine learning methods, one needs to optimize an objective function that depends on the discrepancy between two probability distributions. The discrepancy can be referred to as a metric for…
We consider (robust) inference in the context of a factor model for tensor-valued sequences. We study the consistency of the estimated common factors and loadings space when using estimators based on minimising quadratic loss functions.…
Providing non-conservative uncertainty quantification for function estimates derived from noisy observations remains a fundamental challenge in statistical machine learning, particularly for applications in safety-critical domains. In this…
We introduce a general method to prove uniform in bandwidth consistency of kernel-type function estimators. Examples include the kernel density estimator, the Nadaraya-Watson regression estimator and the conditional empirical process. Our…
We provide a theoretical foundation for non-parametric estimation of functions of random variables using kernel mean embeddings. We show that for any continuous function $f$, consistent estimators of the mean embedding of a random variable…
In this paper, we present a study of a kernel-based consensual aggregation on randomly projected high-dimensional features of predictions for regression. The aggregation scheme is composed of two steps: the high-dimensional features of…
Estimating the innovation probability density is an important issue in any regression analysis. This paper focuses on functional autoregressive models. A residual-based kernel estimator is proposed for the innovation density. Asymptotic…