Kernel quantile regression for semiparametric partially linear time-varying-coefficient model based on a history process of longitudinal data

Chapter 33 - Short Selling Stock Indices on Signals from Implied Volatility Index Changes: Evidence from Quantile Regression-Based Techniques

High-dimensional data sets are often available in genome-enabled predictions. Such data sets include nonlinear relationships with complex dependence structures. For such situations, vine copula-based (quantile) regression is an important tool. However, the current vine copula-based regression approaches do not scale up to high and ultra-high dimensions. To perform high-dimensional sparse vine copula-based regression, we propose 2 methods. First, we show their superiority regarding computational complexity over the existing methods. Second, we define relevant, irrelevant, and redundant explanatory variables for quantile regression. Then, we show our method's power in selecting relevant variables and prediction accuracy in high-dimensional sparse data sets via simulation studies. Next, we apply the proposed methods to the high-dimensional real data, aiming at the genomic prediction of maize traits. Some data processing and feature extraction steps for the real data are further discussed. Finally, we show the advantage of our methods over linear models and quantile regression forests in simulation studies and real data applications.

In this article we consider quantile regression in reproducing kernel Hilbert spaces, which we call kernel quantile regression (KQR). We make three contributions: (1) we propose an efficient algorithm that computes the entire solution path of the KQR, with essentially the same computational cost as fitting one KQR model; (2) we derive a simple formula for the effective dimension of the KQR model, which allows convenient selection of the regularization parameter; and (3) we develop an asymptotic theory for the KQR model.

In this paper, we study a problem of anomaly detection from time series-data. We use kernel quantile regression (KQR) to predict the extreme (such as 0.01 or 0.99) quantiles of the future time-series data distribution. It enables us to tell whether the probability of observing a certain time-series sequence is larger than, say, 1 percent or not. In this paper, we develop an efficient update algorithm of KQR in order to adapt the KQR in on-line manner. We propose a new algorithm that allows us to compute the optimal solution of the KQR when a new training pattern is inserted or deleted. We demonstrate the effectiveness of our methodology through numerical experiment using real-world time-series data.

The paper proposes a novel value-at-risk measurement method based on kernel quantile regression. The method can build linear quantile regression in a reproduced Hilbert kernel space. It makes no assumption on the dependence between quantile functions and the predictors and achieves nonlinear capabilities. In the experiment on daily returns of crude oil, we compare its capability with other four conventional methods: simple moving average, exponential weighted moving average, GARCH and linear quantile regression. The out-of-sample results clearly show that the new method has superiority over other four methods.

Quantile regression is a powerful tool for robust and heterogeneous learning that has seen applications in a diverse range of applied areas. However, its broader application is often hindered by the substantial computational demands arising from the non-smooth quantile loss function. In this article, we introduce a novel algorithm named fastkqr, which significantly advances the computation of quantile regression in reproducing kernel Hilbert spaces. The core of fastkqr is a finite smoothing algorithm that magically produces exact regression quantiles, rather than approximations. To further accelerate the algorithm, we equip fastkqr with a novel spectral technique that carefully reuses matrix computations. In addition, we extend fastkqr to accommodate a flexible kernel quantile regression with a data-driven crossing penalty, addressing the interpretability challenges of crossing quantile curves at multiple levels. We have implemented fastkqr in a publicly available R package on CRAN. Extensive simulations and real applications show that fastkqr matches the accuracy of state-of-the-art algorithms but can operate up to an order of magnitude faster. Supplementary materials for this article are available online.

. To address issues of parameter estimation and variable selection of both random and fixed effects in linear mixed- effect model for longitudinal data, this article introduces a novel linear mixed-effects double penalized L p -quantile regression (LME-DL p QR) model, which combines L p -quantile regression with a double-penalty approach. An iterative Lasso-L p -quantile regression algorithm is proposed to implement LME-DL p QR to estimate parameters and select variables, with penalty parameters chosen using two common criteria. Under certain conditions, LME-DL p QR achieves asymptotic normality of the estimation of regression coefficients. Simulations are conducted to study the performance of LME-DL p QR in coefficient estimation and variable selection across different quantiles, considering variations in signal-to-noise ratios, random effects, and model sparsity. The proposed method exhibits robustness and sensitivity, reflecting the advantages of L p -quantile regression when p taking different values. The study also summarizes the efficiency of selecting important variables for various p values. Under diverse conditions, LME-DL p QR with p values between 1 and 2 outperforms the linear mixed effects double penalized quantile (p = 1) and expectile (p = 2) regression model. Finally, the practical utility of LME-DL p QR is demonstrated for future application research of longitudinal data through its analysis on two real datasets.

This study aims to analyze the influence of global gold prices, crude oil prices, and daily COVID-19 cases on the Indonesian Composite Index (IHSG) before, during, and after the COVID-19 pandemic. The study consists of three independent variables: global gold prices, crude oil prices, and daily COVID-19 cases, with one dependent variable: the IHSG. The data was taken from 2018 to 2023, covering the periods before, during, and after the pandemic. The data processing is divided into four periods: before, during, and after the pandemic, up to the overall period. This paper used the Quantile Regression 0.75 and Generalized Linear Model (GLM) research methods due to the presence of extreme outliers that prevented the data from meeting normality requirements. By using Quantile Regression 0.75 and GLM, data normality can be ruled out. Both research methods showed similar significant results. Gold has a positive effect on the IHSG, and crude oil has a larger coefficient than gold. Meanwhile, COVID-19 has a significant but negative effect, with a small coefficient, suggesting that the daily number of COVID-19 cases has no impact on the IHSG. These findings have practical implications for understanding the dynamics of the IHSG, engaging the reader's interest in the study's relevance.

Quantile regression with a metal oxide sensors array for methane prediction over a municipal solid waste treatment plant

Together with quantile regression methods, such a model would have the potential for clinical utility through automated quantitative comparison of individual cases relative to their age and gender-matched peer group. Our aim was to demonstrate the automated processing of digital clinical head CT data in the development of a clinically useful model of age-related changes of the brain in the first 2 decades of life. A total of 415 (209 female) consecutive, clinical head CTs with radiographically normal findings from patients from birth through 20 years of age were retrospectively selected and subjected to automated segmentation. Brain volume, brain parenchymal fraction, brain radiodensity, and brain radiomass were assessed as a function of patient age. Statistical modeling and quantile regression were performed. Brain volume increased from 400 cm3 at birth to 1350 cm3 at 20 years of age (>3-fold). Males had a slightly steeper growth trajectory than females, with approximately 8% difference in volume between the sexes established in the first few years of life. Brain parenchymal fraction was variable at younger than 2 years of age, stabilizing between 0.85 and 0.92 at 2-3 years of age. Brain mean radiodensity was lower at birth (24 HU) and increased through 3 years of age, after which it stabilized near 30 HU, an approximately 25% increase. The product of brain volume and mean brain radiodensity (radiomass), increased from 700 HU × mL at birth to 3900 HU × mL, a 5.6-fold increase, with approximately 5% difference between males and females at 20 years. Quantile regression enables a given metric to be interpreted relative to an age- and sex-matched peer group. Automated segmentation of clinical head CT images permitted the generation of a reference database for quantitative analysis of pediatric and adolescent brains. Quantile regression facilitates clinical application.

In survival analysis, quantile regression has become a useful approach to account for covariate effects on the distribution of an event time of interest. In this article, we discuss how quantile regression can be extended to model counting processes and thus lead to a broader regression framework for survival data. We specifically investigate the proposed modeling of counting processes for recurrent events data. We show that the new recurrent events model retains the desirable features of quantile regression such as easy interpretation and good model flexibility, while accommodating various observation schemes encountered in observational studies. We develop a general theoretical and inferential framework for the new counting process model, which unifies with an existing method for censored quantile regression. As another useful contribution of this work, we propose a sample-based covariance estimation procedure, which provides a useful complement to the prevailing bootstrapping approach. We demonstrate the utility of our proposals via simulation studies and an application to a dataset from the U.S. Cystic Fibrosis Foundation Patient Registry (CFFPR). Supplementary materials for this article are available online.

Accurate energy demand forecasting is crucial for sustainable and resilient energy development. To meet the Net Zero Representative Concentration Pathways (RCP) 4.5 scenario in the DACH countries, increased renewable energy production, energy storage, and reduced commercial building consumption are needed. This scenario's success depends on hydroelectric capacity and climatic factors. Informed decisions require quantifying uncertainty in forecasts. This study explores a nonparametric method based on reproducing kernel Hilbert spaces (RKHS) , known as kernel quantile regression, for energy prediction. Our experiments demonstrate its reliability and sharpness, and we benchmark it against state-of-the-art methods in load and price forecasting for the DACH region. We offer our implementation in conjunction with additional scripts to ensure the reproducibility of our research.

Approximate nonparametric quantile regression in reproducing kernel Hilbert spaces via random projection

High or ultra-high-dimensional data are becoming increasingly common in various fields. They often display diverse characteristics, including heterogeneity, longitudinal responses, and imbalanced measurements. These complexities make it challenging to integrate different modeling options and their combinations in order to fully leverage this rich data source. This paper provides an easy-to-use, and stand-alone, R package, geeVerse, that can implement any combination of 1) simultaneous variable selection and estimation, 2) quantile regression or mean regression for heterogeneous data, 3) longitudinal or cross-sectional data analysis, 4) balanced or imbalanced data, and 5) moderate, high, or even ultra-high-dimensional data. To accomplish this, we propose computationally efficient implementations of penalized generalized estimating equations (GEE) for quantile and mean regression. We present multiple applications with ultra-high-dimensional data including analysis of a resampled genetic dataset, quantile and mean regressions, analysis of cross-sectional and longitudinal data, differing correlation structures, and differing number of repeated measurements per subject. We also demonstrate our approach on two real data applications.

Unmanned aircraft vehicles (UAV) are widely used for yield estimations in agricultural production. Many significant improvements have been made towards the usage of hyperspectral and thermal sensors. The practical application of these new techniques meanwhile has been limited by the cost of data collection and the complexities of data processing. The objective of this paper is to evaluate the effectiveness of wheat yield estimations based on integrating vegetation indices (VI), solar radiation and crop height (CH), all of which are characterized by lower cost of data collection and processing. The VIs, solar radiation and CH were calculated based on UAV-based multispectral images obtained from two separate plots in Southern Germany and validated with data from a third plot. We compare the individual and joint predictive performance of different VIs, CH, and solar radiation by contrasting the estimated yield with actual yield based on multiple linear regression and quantile regression. The best predictive power was found for a combined estimation with CH, solar radiation and a Normalized Difference Red-edge Index (R2 = 0.75, RMSE = 0.53). This combined estimation resulted in a 15–20% improvement in the prediction of wheat yield accuracy as compared with utilizing any of the indices separately.