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This paper presents an a priori error analysis of the Deep Mixed Residual method (MIM) for solving high-order elliptic equations with non-homogeneous boundary conditions, including Dirichlet, Neumann, and Robin conditions. We examine MIM…

Residual minimization is a widely used technique for solving Partial Differential Equations in variational form. It minimizes the dual norm of the residual, which naturally yields a saddle-point (min-max) problem over the so-called trial…

State-level policy evaluations commonly employ a difference-in-differences (DID) study design; yet within this framework, statistical model specification varies notably across studies. Motivated by applied state-level opioid policy…

Metric learning has attracted extensive interest for its ability to provide personalized recommendations based on the importance of observed user-item interactions. Current metric learning methods aim to push negative items away from the…

Many studies exploit variation in the timing of policy adoption across units as an instrument for treatment. This paper formalizes the underlying identification strategy as an instrumented difference-in-differences (DID-IV). In this design,…

In this paper, we consider some aspects of the numerical analysis of the mathematical model of fractional Duffing with a derivative of variable fractional order of the Riemann-Liouville type. Using numerical methods: an explicit…

This article describes two Monte Carlo methods for calculating confidence intervals on cumulative density function (CDF) based multivariate normal quantiles that allows for controlling the tail regions of a multivariate distribution where…

In this paper, we study the computation of the rate-distortion-perception function (RDPF) for a multivariate Gaussian source under mean squared error (MSE) distortion and, respectively, Kullback-Leibler divergence, geometric Jensen-Shannon…

Derivative-free optimization (DFO) is vital in solving complex optimization problems where only noisy function evaluations are available through an oracle. Within this domain, DFO via finite difference (FD) approximation has emerged as a…

A common issue in learning decision-making policies in data-rich settings is spurious correlations in the offline dataset, which can be caused by hidden confounders. Instrumental variable (IV) regression, which utilises a key unconfounded…

Background: Under competing risks, the commonly used sub-distribution hazard ratio (SHR) is not easy to interpret clinically and is valid only under the proportional sub-distribution hazard (SDH) assumption. This paper introduces an…

Elder people consequence a variety of problems while living Activities of Daily Living (ADL) for the reason of age, sense, loneliness and cognitive changes. These cause the risk to ADL which leads to several falls. Getting real life fall…

This paper proposes a new approach for estimating the failure time distribution using the indicator data. The indicators, which are checked by periodic inspection of a standby redundant system, only convey whether at least one failure…

While in recent years a number of new statistical approaches have been proposed to model group differences with a different assumption on the nature of the measurement invariance of the instruments, the tools for detecting local…

Even though a train/test split of the dataset randomly performed is a common practice, could not always be the best approach for estimating performance generalization under some scenarios. The fact is that the usual machine learning…

Detecting the High impedance fault (HIF) in distribution systems plays an important role in power utilization safety. However, many HIFs are challenging to be identified due to their low currents and diverse characteristics. In particular,…

Considering the case where the response variable is a categorical variable and the predictor is a random function, two novel functional sufficient dimensional reduction (FSDR) methods are proposed based on mutual information and square loss…

Binary endpoints are common in clinical trials and conditional odds ratios have traditionally been used to assess treatment effects. However, the interpretation of odds ratios is difficult, they are non-collapsible and rely on strong…

High-dimensional group inference is an essential part of statistical methods for analysing complex data sets, including hierarchical testing, tests of interaction, detection of heterogeneous treatment effects and inference for local…

Distortion Risk Measures (DRMs) capture risk preferences in decision-making and serve as general criteria for managing uncertainty. This paper proposes gradient descent algorithms for DRM optimization based on two dual representations: the…