Related papers: Multivariate quantiles and multiple-output regress…
We focus on the construction of confidence corridors for multivariate nonparametric generalized quantile regression functions. This construction is based on asymptotic results for the maximal deviation between a suitable nonparametric…
The problems of computational data processing involving regression, interpolation, reconstruction and imputation for multidimensional big datasets are becoming more important these days, because of the availability of data and their widely…
The analysis of multidimensional data is becoming a more and more relevant topic in statistical and machine learning research. Given their complexity, such data objects are usually reshaped into matrices or vectors and then analysed.…
Tukey depth regions are important notions in nonparametric multivariate data analysis. A $\tau$-th Tukey depth region $\mathcal{D}_{\tau}$ is the set of all points that have at least depth $\tau$. While the Tukey depth regions are easily…
Neural networks appear to have mysterious generalization properties when using parameter counting as a proxy for complexity. Indeed, neural networks often have many more parameters than there are data points, yet still provide good…
The computation of the Tukey depth, also called halfspace depth, is very demanding, even in low dimensional spaces, because it requires the consideration of all possible one-dimensional projections. In this paper we propose a random depth…
We investigate asymptotic properties of least-absolute-deviation or median quantile estimates of the location and scale functions in nonparametric regression models with dependent data from multiple subjects. Under a general dependence…
We study the problem of modeling univariate distributions via their quantile functions. We introduce a flexible family of distributions whose quantile function is a linear combination of basis quantiles. Because the model is linear in its…
Classical regression methods treat covariates as a vector and estimate a corresponding vector of regression coefficients. Modern applications in medical imaging generate covariates of more complex form such as multidimensional arrays…
Mean estimation is a fundamental task in statistics and a focus within differentially private statistical estimation. While univariate methods based on the Gaussian mechanism are widely used in practice, more advanced techniques such as the…
Traditional functional linear regression usually takes a one-dimensional functional predictor as input and estimates the continuous coefficient function. Modern applications often generate two-dimensional covariates, which become matrices…
We propose a bivariate quantile regression method for the bivariate varying coefficient model through a directional approach. The varying coefficients are approximated by the B-spline basis and an $L_{2}$ type penalty is imposed to achieve…
Geometric quantiles are popular location functionals to build rank-based statistical procedures in multivariate settings. They are obtained through the minimization of a non-smooth convex objective function. As a result, the singularity of…
The design of a metric between probability distributions is a longstanding problem motivated by numerous applications in Machine Learning. Focusing on continuous probability distributions on the Euclidean space $\mathbb{R}^d$, we introduce…
Data depths are score functions that quantify in an unsupervised fashion how central is a point inside a distribution, with numerous applications such as anomaly detection, multivariate or functional data analysis, arising across various…
Linear regression is a basic and widely-used methodology in data analysis. It is known that some quantum algorithms efficiently perform least squares linear regression of an exponentially large data set. However, if we obtain values of the…
We propose dual regression as an alternative to the quantile regression process for the global estimation of conditional distribution functions under minimal assumptions. Dual regression provides all the interpretational power of the…
In statistical applications, it is common to encounter parameters supported on a varying or unknown dimensional space. Examples include the fused lasso regression, the matrix recovery under an unknown low rank, etc. Despite the ease of…
Data visualisation helps understanding data represented by multiple variables, also called features, stored in a large matrix where individuals are stored in lines and variable values in columns. These data structures are frequently called…
Quantile regression, a robust method for estimating conditional quantiles, has advanced significantly in fields such as econometrics, statistics, and machine learning. In high-dimensional settings, where the number of covariates exceeds…