Related papers: Delta Theorem in the Age of High Dimensions
We provide general adaptive upper bounds for estimating nonparametric functionals based on second order U-statistics arising from finite dimensional approximation of the infinite dimensional models. We then provide examples of functionals…
The linear delta expansion is applied to the 3-dimensional O(N) scalar field theory at its critical point in a way that is compatible with the large-N limit. For a range of the arbitrary mass parameter, the linear delta expansion for…
For the last two decades, high-dimensional data and methods have proliferated throughout the literature. Yet, the classical technique of linear regression has not lost its usefulness in applications. In fact, many high-dimensional…
In this paper, the asymptotic distributions of estimators for the regularized functional canonical correlation and variates of the population are derived. The method is based on the possibility of expressing these regularized quantities as…
Many statistical estimators are defined as the fixed point of a data-dependent operator, with estimators based on minimizing a cost function being an important special case. The limiting performance of such estimators depends on the…
We consider the multiparameter random simplicial complex on a vertex set $\{ 1,\dots,n \}$, which is parameterized by multiple connectivity probabilities. Our key results concern the topology of this complex of dimensions higher than the…
Large deviation theory offers a powerful and general statistical framework to study the asymptotic dynamical properties of rare events. The application of the formalism to concrete experimental situations is, however, often restricted by…
In two previous papers the author introduced a multiplication of distributions in one dimension and he proved that two one-dimensional Dirac delta functions and their derivatives can be multiplied, at least under certain conditions. Here,…
Nonparametric mean function regression with repeated measurements serves as a cornerstone for many statistical branches, such as longitudinal/panel/functional data analysis. In this work, we investigate this problem using fully connected…
Results of extensive computations of moments of the Riemann zeta function on the critical line are presented. Calculated values are compared with predictions motivated by random matrix theory. The results can help in deciding between those…
Many economic and scientific problems involve the analysis of high-dimensional functional time series, where the number of functional variables $p$ diverges as the number of serially dependent observations $n$ increases. In this paper, we…
We study lower and upper bounds for the density of a diffusion process in ${\mathbb{R}}^n$ in a small (but not asymptotic) time, say $\delta$. We assume that the diffusion coefficients $\sigma_1,\ldots,\sigma_d$ may degenerate at the…
While there is considerable work on change point analysis in univariate time series, more and more data being collected comes from high dimensional multivariate settings. This paper introduces the asymptotic concept of high dimensional…
We study the distribution of hard-, soft-, and adaptive soft-thresholding estimators within a linear regression model where the number of parameters k can depend on sample size n and may diverge with n. In addition to the case of known…
For many tasks of data analysis, we may only have the information of the explanatory variable and the evaluation of the response values are quite expensive. While it is impractical or too costly to obtain the responses of all units, a…
Parameter sharing has proven to be a parameter-efficient approach. Previous work on Transformers has focused on sharing parameters in different layers, which can improve the performance of models with limited parameters by increasing model…
This chapter presents key concepts and theoretical results for analyzing estimation and inference in high-dimensional models. High-dimensional models are characterized by having a number of unknown parameters that is not vanishingly small…
Reliable evaluation protocols are of utmost importance for reproducible NLP research. In this work, we show that sometimes neither metric nor conventional human evaluation is sufficient to draw conclusions about system performance. Using…
The argmax theorem is a useful result for deriving the limiting distribution of estimators in many applications. The conclusion of the argmax theorem states that the argmax of a sequence of stochastic processes converges in distribution to…
Beta regression models are employed to model continuous response variables in the unit interval, like rates, percentages, or proportions. Their applications rise in several areas, such as medicine, environment research, finance, and natural…