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Mathematics
Special Issues
Nonparametric Regression Models: Theory and Applications
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Nonparametric Regression Models: Theory and Applications

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Probability and Statistics".

Deadline for manuscript submissions: 30 September 2024 | Viewed by 3422

Special Issue Editors

Prof. Dr. Antonio Musolesi

E-Mail Website
Guest Editor
Department of Economics and Management (DEM), University of Ferrara and SEEDS, 44121 Ferrara, Italy
Interests: econometric modeling; time series and panel data models; economic policy analysis; nonparametric and semiparametric regression models; productivity and economics of innovation
Dr. Alexandra Soberon

E-Mail Website
Guest Editor
Department of Economics, Universidad de Cantabria, 39005 Santander, Spain
Interests: spans different aspectos of the estimation and testing of nonparametric and semiparametric panel data models; the analisis of the individuals' behavior; empirical microeconomics with applications to firm's technical efficiency, environmental; financial econometrics

Special Issue Information

Dear Colleagues,

Over the last 30 years, nonparametric and semiparametric models have received substantial attention in the theoretical and applied statistics literature. They provide different, more flexible ways to complement more traditional parametric approaches where a particular form of the regression functions is assumed to characterize the relationship between the dependent variable and the explanatory variables and are robust to potential model misspecification. Furthermore, the complexity of econometric models has been greatly enriched by the availability of large data sets.

In this Special Issue we are interested in submissions of all types of nonparametric methods, including kernel, spline, and series. In particular, novel estimation methods with applications in challenging research areas (such as economics and finance, environmental, epidemiology) are especially appreciated.

Prof. Dr. Antonio Musolesi
Dr. Alexandra Soberon
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • nonparametric methods
  • semiparametric methods
  • varying-coefficient models
  • local smoothing
  • splines
  • time series
  • environmental economics
  • financial economics
  • cross-sectional dependence

Published Papers (3 papers)

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Research

21 pages, 1467 KiB  
Article
Asymptotic Properties for Cumulative Probability Models for Continuous Outcomes
by Chun Li, Yuqi Tian, Donglin Zeng and Bryan E. Shepherd
Mathematics 2023, 11(24), 4896; https://doi.org/10.3390/math11244896 - 7 Dec 2023
Cited by 1 | Viewed by 1132
Abstract
Regression models for continuous outcomes frequently require a transformation of the outcome, which is often specified a priori or estimated from a parametric family. Cumulative probability models (CPMs) nonparametrically estimate the transformation by treating the continuous outcome as if it is ordered categorically. [...] Read more.
Regression models for continuous outcomes frequently require a transformation of the outcome, which is often specified a priori or estimated from a parametric family. Cumulative probability models (CPMs) nonparametrically estimate the transformation by treating the continuous outcome as if it is ordered categorically. They thus represent a flexible analysis approach for continuous outcomes. However, it is difficult to establish asymptotic properties for CPMs due to the potentially unbounded range of the transformation. Here we show asymptotic properties for CPMs when applied to slightly modified data where bounds, one lower and one upper, are chosen and the outcomes outside the bounds are set as two ordinal categories. We prove the uniform consistency of the estimated regression coefficients and of the estimated transformation function between the bounds. We also describe their joint asymptotic distribution, and show that the estimated regression coefficients attain the semiparametric efficiency bound. We show with simulations that results from this approach and those from using the CPM on the original data are very similar when a small fraction of the data are modified. We reanalyze a dataset of HIV-positive patients with CPMs to illustrate and compare the approaches. Full article
(This article belongs to the Special Issue Nonparametric Regression Models: Theory and Applications)
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15 pages, 1045 KiB  
Article
Semiparametric Integrated and Additive Spatio-Temporal Single-Index Models
by Hamdy F. F. Mahmoud and Inyoung Kim
Mathematics 2023, 11(22), 4629; https://doi.org/10.3390/math11224629 - 13 Nov 2023
Viewed by 701
Abstract
In this paper, we introduce two semiparametric single-index models for spatially and temporally correlated data. Our first model has spatially and temporally correlated random effects that are additive to the nonparametric function, which we refer to as the “semiparametric spatio-temporal single-index model (ST-SIM)”. [...] Read more.
In this paper, we introduce two semiparametric single-index models for spatially and temporally correlated data. Our first model has spatially and temporally correlated random effects that are additive to the nonparametric function, which we refer to as the “semiparametric spatio-temporal single-index model (ST-SIM)”. The second model integrates the spatially correlated effects into the nonparametric function, and the time random effects are additive to the single-index function. We refer to our second model as the “semiparametric integrated spatio-temporal single-index model (IST-SIM)”. Two algorithms based on a Markov chain expectation maximization are introduced to simultaneously estimate the model parameters, spatial effects, and time effects of the two models. We compare the performance of our models using several simulation studies. The proposed models are then applied to mortality data from six major cities in South Korea. Our results suggest that IST-SIM (1) is more flexible than ST-SIM because the former can estimate various nonparametric functions for different locations, while ST-SIM enforces the mortality functions having the same shape over locations; (2) provides better estimation and prediction, and (3) does not need restrictions for the single-index coefficients to fix the identifiability problem. Full article
(This article belongs to the Special Issue Nonparametric Regression Models: Theory and Applications)
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14 pages, 800 KiB  
Article
A Co-Optimization Algorithm Utilizing Particle Swarm Optimization for Linguistic Time Series
by Nguyen Duy Hieu, Mai Van Linh and Pham Dinh Phong
Mathematics 2023, 11(7), 1597; https://doi.org/10.3390/math11071597 - 25 Mar 2023
Cited by 3 | Viewed by 1048
Abstract
The linguistic time-series forecasting model (LTS-FM), which has been recently proposed, uses linguistic words of linguistic variable domains generated by hedge algebras (HAs) to describe historical numeric time-series data. Then, the LTS-FM was established by utilizing real numeric semantics of words induced by [...] Read more.
The linguistic time-series forecasting model (LTS-FM), which has been recently proposed, uses linguistic words of linguistic variable domains generated by hedge algebras (HAs) to describe historical numeric time-series data. Then, the LTS-FM was established by utilizing real numeric semantics of words induced by the fuzziness parameter values (FPVs) of HAs. In the existing LTS-FMs, just the FPVs of HAs are optimized, while the used word set is still chosen by human experts. This paper proposes a co-optimization method of selecting the optimal used word set that best describes numeric time-series data in parallel with choosing the best FPVs of HAs to improve the accuracy of LTS-FMs by utilizing particle swarm optimization (PSO). In this co-optimization method, the outer loop optimizes the FPVs of HAs, while the inner loop optimizes the used word set. The experimental results on three datasets, i.e., the “enrollments of the University of Alabama” (EUA), the “killed in car road accidents in Belgium” (CAB), and the “spot gold in Turkey” (SGT), showed that our proposed forecasting model outperformed the existing forecasting models in terms of forecast accuracy. Full article
(This article belongs to the Special Issue Nonparametric Regression Models: Theory and Applications)
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