arXiv subjects

Yujia Ding

Publications and source records attributed to Yujia Ding.

5 recordsLinked to original sources

arXiv2022

Linear Multifractional Stable Sheets in the Broad Sense: Existence and Joint Continuity of Local Times

We introduce the notion of linear multifractional stable sheets in the broad sense (LMSS) with $α\in(0,2]$, to include both linear multifractional Brownian sheets ($α=2$) and linear multifractional stable sheets ($α<2$). The purpose of the present paper is to study the existence and joint continuity of the local times of LMSS, and also the local Hölder condition of the local times in the set variable. Among the main results of this paper, Theorem 2.4 provides a sufficient and necessary condition for the existence of local times of LMSS; Theorem 3.1 shows a sufficient condition for the joint continuity of local times; and Theorem 4.1 proves a sharp local Hölder condition for the local times in the set variable. All these theorems improve significantly the existing results for the local times of multifractional Brownian sheets and linear multifractional stable sheets in the literature.

math.PR↗

arXiv2021

Variable Selection and Regularization via Arbitrary Rectangle-range Generalized Elastic Net

We introduce the arbitrary rectangle-range generalized elastic net penalty method, abbreviated to ARGEN, for performing constrained variable selection and regularization in high-dimensional sparse linear models. As a natural extension of the nonnegative elastic net penalty method, ARGEN is proved to have variable selection consistency and estimation consistency under some conditions. The asymptotic behavior in distribution of the ARGEN estimators have been studied. We also propose an algorithm called MU-QP-RR-W-$l_1$ to efficiently solve ARGEN. By conducting simulation study we show that ARGEN outperforms the elastic net in a number of settings. Finally an application of S&P 500 index tracking with constraints on the stock allocations is performed to provide general guidance for adapting ARGEN to solve real-world problems.

stat.ML↗

arXiv2021

Series Representation of Jointly S$α$S Distribution via Symmetric Covariations

We introduce the notion of symmetric covariation, which is a new measure of dependence between two components of a symmetric $α$-stable random vector, where the stability parameter $α$ measures the heavy-tailedness of its distribution. Unlike covariation that exists only when $α\in(1,2]$, symmetric covariation is well defined for all $α\in(0,2]$. We show that symmetric covariation can be defined using the proposed generalized fractional derivative, which has broader usages than those involved in this work. Several properties of symmetric covariation have been derived. These are either similar to or more general than those of the covariance functions in the Gaussian case. The main contribution of this framework is the representation of the characteristic function of bivariate symmetric $α$-stable distribution via convergent series based on a sequence of symmetric covariations. This series representation extends the one of bivariate Gaussian.

math.ST↗

arXiv2021

Optimal Control of the SIR Model with Constrained Policy, with an Application to COVID-19

This article considers the optimal control of the SIR model with both transmission and treatment uncertainty. It follows the model presented in Gatto and Schellhorn (2021). We make four significant improvements on the latter paper. First, we prove the existence of a solution to the model. Second, our interpretation of the control is more realistic: while in Gatto and Schellhorn the control $α$ is the proportion of the population that takes a basic dose of treatment, so that $α>1$ occurs only if some patients take more than a basic dose, in our paper, $α$ is constrained between zero and one, and represents thus the proportion of the population undergoing treatment. Third, we provide a complete solution for the moderate infection regime (with constant treatment). Finally, we give a thorough interpretation of the control in the moderate infection regime, while Gatto and Schellhorn focussed on the interpretation of the low infection regime. Finally, we compare the efficiency of our control to curb the COVID-19 epidemic to other types of control.

math.OC↗

arXiv2019

Accelerometer-Based Gait Segmentation: Simultaneously User and Adversary Identification

In this paper, we introduce a new gait segmentation method based on accelerometer data and develop a new distance function between two time series, showing novel and effectiveness in simultaneously identifying user and adversary. Comparing with the normally used Neural Network methods, our approaches use geometric features to extract walking cycles more precisely and employ a new similarity metric to conduct user-adversary identification. This new technology for simultaneously identify user and adversary contributes to cybersecurity beyond user-only identification. In particular, the new technology is being applied to cell phone recorded walking data and performs an accuracy of $98.79\%$ for 6 classes classification (user-adversary identification) and $99.06\%$ for binary classification (user only identification). In addition to walking signal, our approach works on walking up, walking down and mixed walking signals. This technology is feasible for both large and small data set, overcoming the current challenges facing to Neural Networks such as tuning large number of hyper-parameters for large data sets and lacking of training data for small data sets. In addition, the new distance function developed here can be applied in any signal analysis.

eess.SP↗