arXiv subjects

Hanbing Zhu

Publications and source records attributed to Hanbing Zhu.

4 recordsLinked to original sources

arXiv2025

Quantile regression with generalized multiquadric loss function

Quantile regression (QR) is now widely used to analyze the effect of covariates on the conditional distribution of a response variable. It provides a more comprehensive picture of the relationship between a response and covariates compared with classical least squares regression. However, the non-differentiability of the check loss function precludes the use of gradient-based methods to solve the optimization problem in quantile regression estimation. To this end, This paper constructs a smoothed loss function based on multiquadric (MQ) function. The proposed loss function leads to a globally convex optimization problem that can be efficiently solved via (stochastic) gradient descent methods. As an example, we apply the Barzilai-Borwein gradient descent method to obtain the estimation of quantile regression. We establish the theoretical results of the proposed estimator under some regularity conditions, and compare it with other estimation methods using Monte Carlo simulations.

stat.ME↗

arXiv2024

Expectile Periodograms

This paper introduces a novel periodogram-like function, called the expectile periodogram, for modeling spectral features of time series and detecting hidden periodicities. The expectile periodogram is constructed from trigonometric expectile regression, in which a specially designed check function is used to substitute the squared $l_2$ norm that leads to the ordinary periodogram. The expectile periodogram retains the key properties of the ordinary periodogram as a frequency-domain representation of serial dependence in time series, while offering a more comprehensive understanding by examining the data across the entire range of expectile levels. We establish the asymptotic theory and investigate the relationship between the expectile periodogram and the so called expectile spectrum. Simulations demonstrate the efficiency of the expectile periodogram in the presence of hidden periodicities. Finally, by leveraging the inherent two-dimensional nature of the expectile periodogram, we train a deep learning (DL) model to classify earthquake waveform data. Remarkably, our approach outperforms alternative periodogram-based methods in terms of classification accuracy.

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arXiv2023

Generalized Estimating Equations for Hearing Loss Data with Specified Correlation Structures

Due to the nature of pure-tone audiometry test, hearing loss data often has a complicated correlation structure. Generalized estimating equation (GEE) is commonly used to investigate the association between exposures and hearing loss, because it is robust to misspecification of the correlation matrix. However, this robustness typically entails a moderate loss of estimation efficiency in finite samples. This paper proposes to model the correlation coefficients and use second-order generalized estimating equations to estimate the correlation parameters. In simulation studies, we assessed the finite sample performance of our proposed method and compared it with other methods, such as GEE with independent, exchangeable and unstructured correlation structures. Our method achieves an efficiency gain which is larger for the coefficients of the covariates corresponding to the within-cluster variation (e.g., ear-level covariates) than the coefficients of cluster-level covariates. The efficiency gain is also more pronounced when the within-cluster correlations are moderate to strong, or when comparing to GEE with an unstructured correlation structure. As a real-world example, we applied the proposed method to data from the Audiology Assessment Arm of the Conservation of Hearing Study, and studied the association between a dietary adherence score and hearing loss.

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arXiv2021

Semismooth Newton Augmented Lagrangian Algorithm for Adaptive Lasso Penalized Least Squares in Semiparametric Regression

This paper is concerned with a partially linear semiparametric regression model containing an unknown regression coefficient, an unknown nonparametric function, and an unobservable Gaussian distributed random error. We focus on the case of simultaneous variable selection and estimation with a divergent number of covariates under the assumption that the regression coefficient is sparse. We consider the applications of the least squares to semiparametric regression and particularly present an adaptive lasso penalized least squares (PLS) method to select the regression coefficient. We note that there are many algorithms for PLS in various applications, but they seem to be rarely used in semiparametric regression. This paper focuses on using a semismooth Newton augmented Lagrangian (SSNAL) algorithm to solve the dual of PLS which is the sum of a smooth strongly convex function and an indicator function. At each iteration, there must be a strongly semismooth nonlinear system, which can be solved by semismooth Newton by making full use of the penalized term. We show that the algorithm offers a significant computational advantage, and the semismooth Newton method admits fast local convergence rate. Numerical experiments on simulated and real data have demonstrated the effectiveness of the PLS method and the progressiveness of the SSNAL algorithm.

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