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The assessment of risk based on historical data faces many challenges, in particular due to the limited amount of available data, lack of stationarity, and heavy tails. While estimation on a short-term horizon for less extreme percentiles…
As is known, factor analysis is a popular method to reduce dimension for high-dimensional data. For matrix data, the dimension reduction can be more effectively achieved through both row and column directions. In this paper, we introduce a…
We study the relation between a threshold-force based model at the microscopic scale and mode I fracture at the macroscopic scale in a system of discrete interacting springs. Specifically, we idealize the contact between two surfaces as…
Wavelet thresholding generally assumes independent, identically distributed normal errors when estimating functions in a nonparametric regression setting. VisuShrink and SureShrink are just two of the many common thresholding methods based…
Hermite polynomials and functions have extensive applications in scientific and engineering problems. Although it is recognized that employing the scaled Hermite functions rather than the standard ones can remarkably enhance the…
Shrinkage estimators that possess the ability to produce sparse solutions have become increasingly important to the analysis of today's complex datasets. Examples include the LASSO, the Elastic-Net and their adaptive counterparts.…
This paper proposes and analyzes fully data driven methods for inference about the mean function of a stochastic process from a sample of independent trajectories of the process, observed at discrete time points and corrupted by additive…
We propose a scaling ansatz for the elastic energy of a system near the critical jamming transition in terms of three relevant fields: the compressive strain $\Delta \phi$ relative to the critical jammed state, the shear strain $\epsilon$,…
We consider the estimation of the slope function in functional linear regression, where scalar responses are modeled in dependence of random functions. Cardot and Johannes [J. Multivariate Anal. 101 (2010) 395-408] have shown that a…
Many researchers have investigated first hitting times as models for survival data. First hitting times arise naturally in many types of stochastic processes, ranging from Wiener processes to Markov chains. In a survival context, the state…
Preprocessing data is an important step before any data analysis. In this paper, we focus on one particular aspect, namely scaling or normalization. We analyze various scaling methods in common use and study their effects on different…
An important challenge in statistical analysis concerns the control of the finite sample bias of estimators. For example, the maximum likelihood estimator has a bias that can result in a significant inferential loss. This problem is…
Thresholding--the pruning of nodes or edges based on their properties or weights--is an essential preprocessing tool for extracting interpretable structure from complex network data, yet existing methods face several key limitations.…
In this paper, we investigate threshold effects associated with swapping of signal and noise subspaces in estimating signal parameters from compressed noisy data. The term threshold effect refers to a sharp departure of mean-squared error…
There has been much recent work on inference after model selection when the noise level is known, however, $\sigma$ is rarely known in practice and its estimation is difficult in high-dimensional settings. In this work we propose using the…
Yield stress materials flow if a sufficiently large shear stress is ap- plied. Although such materials are ubiquitous and relevant for indus- try, there is no accepted microscopic description of how they yield, even in the simplest…
Scaling describes how a given quantity $Y$ that characterizes a system varies with its size $P$. For most complex systems it is of the form $Y\sim P^\beta$ with a nontrivial value of the exponent $\beta$, usually determined by regression…
Threshold selection is a critical issue for extreme value analysis with threshold-based approaches. Under suitable conditions, exceedances over a high threshold have been shown to follow the generalized Pareto distribution (GPD)…
Multiple signal classification algorithm (MUSICAL) exploits temporal fluctuations in fluorescence intensity to perform super-resolution microscopy by computing the value of a super-resolving indicator function across a fine sample grid. A…
As predictive algorithms grow in popularity, using the same dataset to both train and test a new model has become routine across research, policy, and industry. Sample-splitting attains valid inference on model properties by using separate…