Related papers: Nonparametric regression based on discretely sampl…
In this paper we examine the use of topological methods for multivariate statistics. Using persistent homology from computational algebraic topology, a random sample is used to construct estimators of persistent homology. This estimation…
In scientific applications, multivariate observations often come in tandem with temporal or spatial covariates, with which the underlying signals vary smoothly. The standard approaches such as principal component analysis and factor…
In a wide range of applications, the stochastic properties of the observed time series change over time. The changes often occur gradually rather than abruptly: the properties are (approximately) constant for some time and then slowly start…
In this paper, we consider a partial deconvolution kernel estimator for nonparametric regression when some covariates are measured with error while others are observed without error. We focus on a general and realistic setting in which the…
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…
This paper is concerned with general nonlinear regression models where the predictor variables are subject to Berkson-type measurement errors. The measurement errors are assumed to have a general parametric distribution, which is not…
This article introduces a general statistical modeling principle called "Density Sharpening" and applies it to the analysis of discrete count data. The underlying foundation is based on a new theory of nonparametric approximation and…
We propose a methodology to analyze data arising from a curve that, over its domain, switches among J states. We consider a sequence of response variables, where each response y depends on a covariate x according to an unobserved state z.…
Modern Bayesian optimization and adaptive sampling methods increasingly rely on nonlinear parametric models, yet theoretical guarantees for such models under adaptive data collection remain limited. Existing analyses largely focus on…
Distribution regression seeks to estimate the conditional distribution of a multivariate response given a continuous covariate. This approach offers a more complete characterization of dependence than traditional regression methods.…
We propose to address the common problem of linear estimation in linear statistical models by using a model selection approach via penalization. Depending then on the framework in which the linear statistical model is considered namely the…
Statistical analysis on compositional data has gained a lot of attention due to their great potential of applications. A feature of these data is that they are multivariate vectors that lie in the simplex, that is, the components of each…
This paper discusses a nonparametric regression model that naturally generalizes neural network models. The model is based on a finite number of one-dimensional transformations and can be estimated with a one-dimensional rate of…
In this paper we develop a nonparametric regression method that is simultaneously adaptive over a wide range of function classes for the regression function and robust over a large collection of error distributions, including those that are…
In this article, we propose a new nonparametric data analysis tool, which we call nonparametric modal regression, to investigate the relationship among interested variables based on estimating the mode of the conditional density of a…
We consider inference procedures, conditional on an observed ancillary statistic, for regression coefficients under a linear regression setup where the unknown error distribution is specified nonparametrically. We establish conditional…
We consider a one-dimensional diffusion process $(X_t)$ which is observed at $n+1$ discrete times with regular sampling interval $\Delta$. Assuming that $(X_t)$ is strictly stationary, we propose nonparametric estimators of the drift and…
We investigate a semiparametric regression model where one gets noisy non linear non invertible functions of the observations. We focus on the application to bearings-only tracking. We first investigate the least squares estimator and prove…
Regularized kernel methods such as, e.g., support vector machines and least-squares support vector regression constitute an important class of standard learning algorithms in machine learning. Theoretical investigations concerning…
Outlying curves often occur in functional or longitudinal datasets, and can be very influential on parameter estimators and very hard to detect visually. In this article we introduce estimators of the mean and the principal components that…