arXiv subjects

Zhiqiang Liao

Publications and source records attributed to Zhiqiang Liao.

4 recordsLinked to original sources

arXiv2025

Structured Lasso for convex nonparametric least squares: An application to Swedish electricity distribution networks

We study the problem of variable selection in convex nonparametric least squares (CNLS). Whereas the least absolute shrinkage and selection operator (Lasso) is a popular technique for least squares, its variable selection performance is unknown in CNLS problems. In this work, we investigate the performance of the Lasso estimator and find out it is usually unable to select variables efficiently. Exploiting the unique structure of the subgradients in CNLS, we develop a structured Lasso method by combining $\ell_1$-norm and $\ell_{\infty}$-norm. The relaxed version of the structured Lasso is proposed for achieving model sparsity and predictive performance simultaneously, where we can control the two effects--variable selection and model shrinkage--using separate tuning parameters. A Monte Carlo study is implemented to verify the finite sample performance of the proposed approaches. We also use real data from Swedish electricity distribution networks to illustrate the effects of the proposed variable selection techniques. The results from the simulation and application confirm that the proposed structured Lasso performs favorably, generally leading to sparser and more accurate predictive models, relative to the conventional Lasso methods in the literature.

stat.ME↗

arXiv2024

Overfitting Reduction in Convex Regression

Convex regression is a method for estimating the convex function from a data set. This method has played an important role in operations research, economics, machine learning, and many other areas. However, it has been empirically observed that convex regression produces inconsistent estimates of convex functions and extremely large subgradients near the boundary as the sample size increases. In this paper, we provide theoretical evidence of this overfitting behavior. To eliminate this behavior, we propose two new estimators by placing a bound on the subgradients of the convex function. We further show that our proposed estimators can reduce overfitting by proving that they converge to the underlying true convex function and that their subgradients converge to the gradient of the underlying function, both uniformly over the domain with probability one as the sample size is increasing to infinity. An application to Finnish electricity distribution firms confirms the superior performance of the proposed methods in predictive power over the existing methods.

stat.ME↗

arXiv2024

Economic growth of cities: Does resource allocation matter?

We study how efficient resource reallocation across cities affects potential aggregate growth. Using optimal resource allocation models and data on 284 China's prefecture-level cities in the years 2003--2019, we quantitatively measure the cost of misallocation of resources. We show that average aggregate output gains from reallocating resources across nationwide cities to their efficient use are 1.349- and 1.287-fold in the perfect and imperfect allocation scenarios. We further provide evidence on the effects of administrative division adjustments and local allocation. This suggests that city-level adjustments can yield more aggregate gain and that the output gain from nationwide allocation is likely to be more substantial than that from local allocation. Policy implications are proposed to improve the resource allocation efficiency in China.

econ.GN↗

arXiv2022

Convex Support Vector Regression

Nonparametric regression subject to convexity or concavity constraints is increasingly popular in economics, finance, operations research, machine learning, and statistics. However, the conventional convex regression based on the least squares loss function often suffers from overfitting and outliers. This paper proposes to address these two issues by introducing the convex support vector regression (CSVR) method, which effectively combines the key elements of convex regression and support vector regression. Numerical experiments demonstrate the performance of CSVR in prediction accuracy and robustness that compares favorably with other state-of-the-art methods.

stat.ME↗