Related papers: Sometimes nonparametrics beat parametrics, even wh…
We study parameter estimation and asymptotic inference for sparse nonlinear regression. More specifically, we assume the data are given by $y = f( x^\top \beta^* ) + \epsilon$, where $f$ is nonlinear. To recover $\beta^*$, we propose an…
A critical literature review and comprehensive simulation study is used to show that (a) non-parametric bootstrap is a viable alternative to commonly taught and used methods in basic estimation tasks (mean, variance, quartiles, correlation)…
In this work we are interested in the problems of supervised learning and variable selection when the input-output dependence is described by a nonlinear function depending on a few variables. Our goal is to consider a sparse nonparametric…
We consider nonparametric testing in a non-asymptotic framework. Our statistical guarantees are exact in the sense that Type I and II errors are controlled for any finite sample size. Meanwhile, one proposed test is shown to achieve minimax…
In this paper, we consider an unknown functional estimation problem in a general nonparametric regression model with the feature of having both multiplicative and additive noise.We propose two new wavelet estimators in this general context.…
Modal regression estimates the local modes of the distribution of $Y$ given $X=x$, instead of the mean, as in the usual regression sense, and can hence reveal important structure missed by usual regression methods. We study a simple…
The concept of biased data is well known and its practical applications range from social sciences and biology to economics and quality control. These observations arise when a sampling procedure chooses an observation with probability that…
In the last decade, simplified vine copula models have been an active area of research. They build a high dimensional probability density from the product of marginals densities and bivariate copula densities. Besides parametric models,…
Rapid advancements in data science require us to have fundamentally new frameworks to tackle prevalent but highly non-trivial "irregular" inference problems, to which the large sample central limit theorem does not apply. Typical examples…
Understanding the pathways whereby an intervention has an effect on an outcome is a common scientific goal. A rich body of literature provides various decompositions of the total intervention effect into pathway specific effects.…
In any other circumstance, it might make sense to define the extent of the terrain (Data Science) first, and then locate and describe the landmarks (Principles). But this data revolution we are experiencing defies a cadastral survey. Areas…
In recent years, kernel density estimation has been exploited by computer scientists to model machine learning problems. The kernel density estimation based approaches are of interest due to the low time complexity of either O(n) or…
A common challenge in nonparametric inference is its high computational complexity when data volume is large. In this paper, we develop computationally efficient nonparametric testing by employing a random projection strategy. In the…
We study the asymptotic error of score-based diffusion model sampling in large-sample scenarios from a non-parametric statistics perspective. We show that a kernel-based score estimator achieves an optimal mean square error of…
Asymptotic equivalence results for nonparametric regression experiments have always assumed that the variances of the observations are known. In practice, however the variance of each observation is generally considered to be an unknown…
We consider the kernel partial least squares algorithm for non-parametric regression with stationary dependent data. Probabilistic convergence rates of the kernel partial least squares estimator to the true regression function are…
Linear regression is a fundamental and popular statistical method. There are various kinds of linear regression, such as mean regression and quantile regression. In this paper, we propose a new one called distribution regression, which…
How should researchers analyze randomized experiments in which the main outcome is latent and measured in multiple ways but each measure contains some degree of error? We first identify a critical study-specific noncomparability problem in…
Missing exposure information is a very common feature of many observational studies. Here we study identifiability and efficient estimation of causal effects on vector outcomes, in such cases where treatment is unconfounded but partially…
Several hypothesis testing methods have been proposed to validate the assumption of isotropy in spatial point patterns. A majority of these methods are characterised by an unknown distribution of the test statistic under the null hypothesis…