Related papers: Uniform Inference for Kernel Density Estimators wi…
Bayesian density deconvolution using nonparametric prior distributions is a useful alternative to the frequentist kernel based deconvolution estimators due to its potentially wide range of applicability, straightforward uncertainty…
Kernel mean embeddings are a popular tool that consists in representing probability measures by their infinite-dimensional mean embeddings in a reproducing kernel Hilbert space. When the kernel is characteristic, mean embeddings can be used…
This paper investigates the large sample properties of local regression distribution estimators, which include a class of boundary adaptive density estimators as a prime example. First, we establish a pointwise Gaussian large sample…
Kernel density estimation (KDE) is one of the most widely used nonparametric density estimation methods. The fact that it is a memory-based method, i.e., it uses the entire training data set for prediction, makes it unsuitable for most…
Consistent weighted least square estimators are proposed for a wide class of nonparametric regression models with random regression function, where this real-valued random function of $k$ arguments is assumed to be continuous with…
It has recently been shown that there are substantial differences in the regularity behavior of the empirical process based on scalar diffusions as compared to the classical empirical process, due to the existence of diffusion local time.…
Imputation is a popular technique for handling missing data. We consider a nonparametric approach to imputation using the kernel ridge regression technique and propose consistent variance estimation. The proposed variance estimator is based…
This paper introduces a kernel discrepancy-based framework for rerandomization to enhance the precision of causal inference in controlled experiments. We demonstrate that the kernel discrepancy is the key part of the variance upper bound…
The estimation of information measures of continuous distributions based on samples is a fundamental problem in statistics and machine learning. In this paper, we analyze estimates of differential entropy in $K$-dimensional Euclidean space,…
We consider the problem of deriving uniform confidence bands for the mean of a monotonic stochastic process, such as the cumulative distribution function (CDF) of a random variable, based on a sequence of i.i.d.~observations. Our approach…
Evaluating treatment effect heterogeneity widely informs treatment decision making. At the moment, much emphasis is placed on the estimation of the conditional average treatment effect via flexible machine learning algorithms. While these…
A long-standing problem in the construction of asymptotically correct confidence bands for a regression function $m(x)=E[Y|X=x]$, where $Y$ is the response variable influenced by the covariate $X$, involves the situation where $Y$ values…
Uncertainty quantification is a critical aspect of reinforcement learning and deep learning, with numerous applications ranging from efficient exploration and stable offline reinforcement learning to outlier detection in medical…
Divergence measures have a long association with statistical inference, machine learning and information theory. The density power divergence and related measures have produced many useful (and popular) statistical procedures, which provide…
Statistical inferences for high-dimensional regression models have been extensively studied for their wide applications ranging from genomics, neuroscience, to economics. However, in practice, there are often potential unmeasured…
Coresets have emerged as a powerful tool to summarize data by selecting a small subset of the original observations while retaining most of its information. This approach has led to significant computational speedups but the performance of…
A compound Poisson process whose parameters are all unknown is observed at finitely many equispaced times. Nonparametric estimators of the jump and L\'evy distributions are proposed and functional central limit theorems using the uniform…
Estimating the data density is one of the challenging problems in deep learning. In this paper, we present a simple yet effective method for estimating the data density using a deep neural network and the Donsker-Varadhan variational lower…
The No Unmeasured Confounding Assumption is widely used to identify causal effects in observational studies. Recent work on proximal inference has provided alternative identification results that succeed even in the presence of unobserved…
Kernel estimation of a probability density function supported on the unit interval has proved difficult, because of the well known boundary bias issues a conventional kernel density estimator would necessarily face in this situation.…