统计理论

We present a theoretically well-founded deep learning algorithm for nonparametric regression. It uses over-parametrized deep neural networks with logistic activation function, which are fitted to the given data via gradient descent. We…

We study adversarial online nonparametric regression with general convex losses and propose a parameter-free learning algorithm that achieves minimax optimal rates. Our approach leverages chaining trees to compete against H{\"o}lder…

In this note, we discuss the identifiability of a total effect in cluster-DAGs, allowing for cycles within the cluster-DAG (while still assuming the associated underlying DAG to be acyclic). This is presented into two key results: first,…

The Unit-Lindley is a one-parameter family of distributions in $(0,1)$ obtained from an appropriate transformation of the Lindley distribution. In this work, we introduce a class of dynamical time series models for continuous random…

Uncovering genuine relationships between a response variable of interest and a large collection of covariates is a fundamental and practically important problem. In the context of Gaussian linear models, both the Bayesian and non-Bayesian…

Shannon defined the mutual information between two variables. We illustrate why the true mutual information between a variable and the predictions made by a prediction algorithm is not a suitable measure of prediction quality, but the…

Standard practice obtains an unbiased variance estimator by dividing by $N-1$ rather than $N$. Yet if only half the data are used to compute the mean, dividing by $N$ can still yield an unbiased estimator. We show that an alternative mean…

Functional time series (FTS) extend traditional methodologies to accommodate data observed as functions/curves. A significant challenge in FTS consists of accurately capturing the time-dependence structure, especially with the presence of…

Identification of joint dependence among more than two random vectors plays an important role in many statistical applications, where the data may contain sensitive or confidential information. In this paper, we consider the the…

We study the problem of transforming a multi-way contingency table into an equivalent table with uniform margins and same dependence structure. This is an old question which relates to recent advances in copula modeling for discrete random…

This work studies estimation of sparse principal components in high dimensions. Specifically, we consider a class of estimators based on kernel PCA, generalizing the covariance thresholding algorithm proposed by Krauthgamer et al. (2015).…

We present a result according to which certain functions of covariance matrices are maximized at scalar multiples of the identity matrix. In a statistical context in which such functions measure loss, this says that the least favourable…

We consider a Bayesian approach for the recovery of scalar parameters arising in inverse problems. We consider a general signal-in white noise model where we have access to two independent noisy observations of a function, and of a linear…

We consider nonparametric regression with functional covariates, that is, they are elements of an infinite-dimensional Hilbert space. A locally polynomial estimator is constructed, where an orthonormal basis and various tuning parameters…

In this article we redefine various poverty measures in literature in terms of quantile functions instead of distribution functions in the prevailing approach. This enables provision for alternative methodology for poverty measurement and…

The drift sequential parameter estimation problems for the Cox-Ingersoll-Ross (CIR) processes under the limited duration of observation are studied. Truncated sequential estimation methods for both scalar and {two}-dimensional parameter…

Existing research on negations primarily focuses on entropy and extropy. Recently, new functions such as varentropy and varextropy have been developed, which can be considered as extensions of entropy and extropy. However, the impact of…

We consider the task of Gaussian mean testing, that is, of testing whether a high-dimensional vector perturbed by white noise has large magnitude, or is the zero vector. This question, originating from the signal processing community, has…

We study a multivariate Hawkes process as a model for time-continuous relational event networks. The model does not assume the network to be known, it includes covariates, and it allows for both common drivers, parameters common to all the…

We consider high-dimensional estimation problems where the number of parameters diverges with the sample size. General conditions are established for consistency, uniqueness, and asymptotic normality in both unpenalized and penalized…