Related papers: Delta Theorem in the Age of High Dimensions
One reason why standard formulations of the central limit theorems are not applicable in high-dimensional and non-stationary regimes is the lack of a suitable limit object. Instead, suitable distributional approximations can be used, where…
We consider method-of-quantiles estimators of unknown parameters, namely the analogue of method-of-moments estimators obtained by matching empirical and theoretical quantiles at some probability level lambda in (0,1). The aim is to present…
We propose a new estimator for the high-dimensional linear regression model with observation error in the design where the number of coefficients is potentially larger than the sample size. The main novelty of our procedure is that the…
Given a gamma population with known shape parameter $\alpha$, we develop a general theory for estimating a function $g(\cdot)$ of the scale parameter $\beta$ with bounded variance. We begin by defining a sequential sampling procedure with…
Hypothesis testing in the linear regression model is a fundamental statistical problem. We consider linear regression in the high-dimensional regime where the number of parameters exceeds the number of samples ($p> n$). In order to make…
Determining the number of factors in high-dimensional factor modeling is essential but challenging, especially when the data are heavy-tailed. In this paper, we introduce a new estimator based on the spectral properties of Spearman sample…
Hypothesis testing in high dimensional data is a notoriously difficult problem without direct access to competing models' likelihood functions. This paper argues that statistical divergences can be used to quantify the difference between…
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…
We propose a novel estimation framework for quadratic functionals of precision matrices in high-dimensional settings, particularly in regimes where the feature dimension $p$ exceeds the sample size $n$. Traditional moment-based estimators…
In typical high dimensional statistical inference problems, confidence intervals and hypothesis tests are performed for a low dimensional subset of model parameters under the assumption that the parameters of interest are unconstrained.…
Predict a new response from a covariate is a challenging task in regression, which raises new question since the era of high-dimensional data. In this paper, we are interested in the inverse regression method from a theoretical viewpoint.…
Statistical inferences for sample correlation matrices are important in high dimensional data analysis. Motivated by this, this paper establishes a new central limit theorem (CLT) for a linear spectral statistic (LSS) of high dimensional…
In this paper we obtain an approximation for the multivariate Laplace's integral with a large parameter and estimate error term for two cases, when the maximum of the exponent is in the interior of the domain and on the boundary. We are…
Suppose one has a collection of parameters indexed by a (possibly infinite dimensional) set. Given data generated from some distribution, the objective is to estimate the maximal parameter in this collection evaluated at this distribution.…
Large deviation principles are established for the two-parameter Poisson-Dirichlet distribution and two-parameter Dirichlet process when parameter $\theta$ approaches infinity. The motivation for these results is to understand the…
The advent of modern technology, permitting the measurement of thousands of characteristics simultaneously, has given rise to floods of data characterized by many large or even huge datasets. This new paradigm presents extraordinary…
High-dimensional predictive models, those with more measurements than observations, require regularization to be well defined, perform well empirically, and possess theoretical guarantees. The amount of regularization, often determined by…
Network structure is growing popular for capturing the intrinsic relationship between large-scale variables. In the paper we propose to improve the estimation accuracy for large-dimensional factor model when a network structure between…
In some estimation problems, especially in applications dealing with information theory, signal processing and biology, theory provides us with additional information allowing us to restrict the parameter space to a finite number of points.…
Estimates of the approximate factor model are increasingly used in empirical work. Their theoretical properties, studied some twenty years ago, also laid the ground work for analysis on large dimensional panel data models with cross-section…