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This study examines the optimal selections of bandwidth and semi-metric for a functional partial linear model. Our proposed method begins by estimating the unknown error density using a kernel density estimator of residuals, where the…
For multi-variable finite measure spaces, we present in this paper a new framework for non-orthogonal $L^2$ Fourier expansions. Our results hold for probability measures $\mu$ with finite support in $\mathbb{R}^d$ that satisfy a certain…
We introduce a general notion of fractional (noninteger) derivative for functions defined on arbitrary time scales. The basic tools for the time-scale fractional calculus (fractional differentiation and fractional integration) are then…
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…
Functional regression is very crucial in functional data analysis and a linear relationship between scalar response and functional predictor is often assumed. However, the linear assumption may not hold in practice, which makes the methods…
While functional magnetic resonance imaging (fMRI) is important for healthcare/neuroscience applications, it is challenging to classify or interpret due to its multi-dimensional structure, high dimensionality, and small number of samples…
Functional data analysis is a fast evolving branch of modern statistics and the functional linear model has become popular in recent years. However, most estimation methods for this model rely on generalized least squares procedures and…
In recent years, there has been a remarkable development of simulation-based inference (SBI) algorithms, and they have now been applied across a wide range of astrophysical and cosmological analyses. There are a number of key advantages to…
As its name suggests, sufficient dimension reduction (SDR) targets to estimate a subspace from data that contains all information sufficient to explain a dependent variable. Ample approaches exist to SDR, some of the most recent of which…
While most time series are non-stationary, it is inevitable for models to face the distribution shift issue in time series forecasting. Existing solutions manipulate statistical measures (usually mean and std.) to adjust time series…
Purpose: Long scan time in phase encoding for forming complete K-space matrices is a critical drawback of MRI, making patients uncomfortable and wasting important time for diagnosing emergent diseases. This paper aims to reducing the scan…
Finite Mixture Regression (FMR) refers to the mixture modeling scheme which learns multiple regression models from the training data set. Each of them is in charge of a subset. FMR is an effective scheme for handling sample heterogeneity,…
The main features of the statistical approach to inverse problems are described on the example of a linear model with additive noise. The approach does not use any Bayesian hypothesis regarding an unknown object; instead, the standard…
Fractional derivative relaxation type equations (FREs) including fractional diffusion equation and fractional relaxation equation, have been widely used to describe anomalous phenomena in physics. To utilize the characteristics of…
Recently, the prediction-correction method has been developed to solve nonlinear convex optimization problems. However, its convergence rate is often poor since large regularization parameters are set to ensure convergence conditions. In…
A data-driven framework is proposed for online estimation of quadrotor motor efficiency via residual minimization. The problem is formulated as a constrained nonlinear optimization that minimizes trajectory residuals between measured flight…
Diffusion models have become a leading paradigm for image super-resolution (SR), but existing methods struggle to guarantee both the high-frequency perceptual quality and the low-frequency structural fidelity of generated images. Although…
Diffusion models (DMs) have made significant progress in the fields of image, audio, and video generation. One downside of DMs is their slow iterative process. Recent algorithms for fast sampling are designed from the perspective of…
The recent focus on Fine-Grained Sketch-Based Image Retrieval (FG-SBIR) has shifted towards generalising a model to new categories without any training data from them. In real-world applications, however, a trained FG-SBIR model is often…
Over the last decade, it has been demonstrated that many systems in science and engineering can be modeled more accurately by fractional-order than integer-order derivatives, and many methods are developed to solve the problem of fractional…