Linear Regression Function Research Articles

Robust estimation for varying coefficient partially functional linear regression models based on exponential squared loss function

Abstract In this article, we present a new robust estimation procedure based on the exponential squared loss function for varying coefficient partially functional linear regression models, where the slope function and nonparametric coefficients are approximated by functional principal component basis functions and B splines, respectively. Under some mild conditions, the convergence rates of the resulted estimators are obtained. Simulation studies indicate that our proposed method can achieve robustness against outliers or heavy-tail error distributions and perform no worse than the popular least-squares estimation method for the normal error case. Finally, a real data example is used to illustrate the application of the proposed method.

Asynchronous functional linear regression models for longitudinal data in reproducing kernel Hilbert space.

Motivated by the analysis of longitudinal neuroimaging studies, we study the longitudinal functional linear regression model under asynchronous data setting for modeling the association between clinical outcomes and functional (or imaging) covariates. In the asynchronous data setting, both covariates and responses may be measured at irregular and mismatched time points, posing methodological challenges to existing statistical methods. We develop a kernel weighted loss function with roughness penalty to obtain the functional estimator and derive its representer theorem. The rate of convergence, a Bahadur representation, and the asymptotic pointwise distribution of the functional estimator are obtained under the reproducing kernel Hilbert space framework. We propose a penalized likelihood ratio test to test the nullity of the functional coefficient, derive its asymptotic distribution under the null hypothesis, and investigate the separation rate under the alternative hypotheses. Simulation studies are conducted to examine the finite-sample performance of the proposed procedure. We apply the proposed methods to the analysis of multitype data obtained from the Alzheimer's Disease Neuroimaging Initiative (ADNI) study, which reveals significant association between 21 regional brain volume density curves and the cognitive function. Data used in preparation of this paper were obtained from the ADNI database (adni.loni.usc.edu).

Experimental Model of Rainfall Rate Estimation Through the Opportunistic Use of Q-/V-Band Satellite Links

This article addresses the opportunistic use of satellite downlink attenuation measurements for the site-specific estimation of rainfall rate. In particular, this article proposes a regression model characterized by the introduction of correction elements extracted from the frequency-domain analysis of the attenuation time series, and the use of a simple linear regression function with a small modification, which allows to using a negative intercept with the goal of minimizing the maximum error (large underestimation/overestimation). The performance, assessed using attenuation measurements of a satellite downlink in Q/V band shows that the proposed model allows to estimate the rainfall rate with low average error and low maximum error with respect to a more standard ITU model, so as to offer more reliable estimations.

The Influence of Capital and Labor Factors on Coffee Production In The Regency of Pesisir Selatan, West Sumatra Province

Coffee has been a leading commodity in Pesisir Selatan Regency however it has not been able to provide high economic value for the community. This is due to coffee production which has decreased during the 2016-2020 period. So as an effort to improve, it is necessary to optimize production factors in order to maximize production. This study aims to analyze the factors that influence coffee production in Pesisir Selatan Regency. This study uses primary data which was analyzed descriptively quantitatively using the Cobb-Douglas production function and multiple linear regression (OLS) processing methods for 113 respondents who were taken by purposive sampling. The variables of capital and labor will be analyzed to see their effect on coffee production. Based on the results of the study, it was found that partially the capital variable had a significant effect on the amount of coffee production, while the labor variable had no significant effect. But together the variables of capital and labor affect the coffee production produced in Pesisir Selatan Regency.

Empirical estimation based on remote sensing images of insured typhoon-induced economic losses from building damage

Rapid and cost-effective economic loss estimation for buildings in non-life insurance is an important issue for insurance industries in order to provide immediate financial supports to residents affected by natural disasters. This study introduces an empirical approach for economic loss estimation of typhoon-induced building damage from post-disaster remote sensing (RS) images based on insurance records obtained in Osaka and Chiba, Japan affected by the 2018 Typhoon Jebi and the 2019 Typhoon Faxai, respectively. From the insurance records and the analysis of the RS images, we found that area-based loss rates (ALRs) defined as ratio of amount of loss to amount of insured values within a mesh were proportional to building damage ratios (BDRs) identified from number of damaged buildings in the RS images and existing building inventory data, whereas it was still challenging to accurately estimate loss rate for building-by-building even from very high-resolution images. A linear regression function was developed from the relationship between the ALRs and BDRs obtained in this study. We confirmed that the regression function provided a good approximation of the insured losses from the typhoon disasters. The result indicates that typhoon-induced insured losses can be rapidly estimated from the insurance inventory and the analysis of post-disaster RS images without field investigations.

A Simple Band Ratio Library (BRL) Algorithm for Retrieval of Hourly Aerosol Optical Depth Using FY-4A AGRI Geostationary Satellite Data

The Advanced Geostationary Radiation Imager (AGRI) is one of the primary payloads aboard the FY-4A geostationary meteorological satellite, which can provide high-frequency, wide coverage, and multiple spectral channel observations for China and surrounding areas. There are currently few studies on aerosol optical depth (AOD) inversion from FY-4A AGRI data. Based on AGRI data, a new land AOD retrieval algorithm called the band ratio library (BRL) algorithm was proposed in this study. The monthly average surface reflectance band ratio library was established after obtaining the relationship of band surface reflectance ratio from the MODIS combined AOD dataset. In order to calculate the hourly AOD, look-up tables (LUT) for the various aerosol models were constructed using the 6SV model. We quantitatively compared AOD produced from AGRI data with AERONET ground observations to validate the BRL algorithm. AGRI-retrieved AOD is in good agreement with AOD measured by AERONET, which has a correlation coefficient of R is 0.84, the linear regression function is AODAGRI = 0.80 ∗ AODAERONET − 0.004, the root-mean-square error (RMSE) is 0.16, and approximately 60% of the AGRI AOD results fall within the uncertain range of AOD = ±(0.2 × AODAERONET + 0.05). A cross-comparison was made with the MODIS AOD product provided by NASA. The comparison and verification show the proposed algorithm has a good accuracy of land AOD estimation from AGRI data.

Functional linear regression for discretely observed data: from ideal to reality

Summary Despite extensive studies on functional linear regression, there exists a fundamental gap in theory between the ideal estimation from fully observed covariate functions and the reality that one can only observe functional covariates discretely with noise. The challenge arises when deriving a sharp perturbation bound for the estimated eigenfunctions in the latter case, which renders existing techniques for functional linear regression not applicable. We use a pooling method to attain the estimated eigenfunctions and propose a sample-splitting strategy to estimate the principal component scores, which facilitates the theoretical treatment for discretely observed data. The slope function is estimated by approximated least squares, and we show that the resulting estimator attains the optimal convergence rates for both estimation and prediction when the number of measurements per subject reaches a certain magnitude of the sample size. This phase transition phenomenon differs from the known results for the pooled mean and covariance estimation, and reveals the elevated difficulty in estimating the regression function. Numerical experiments, using simulated and real data examples, yield favourable results when compared with existing methods.

Toxicity Assessment of the Binary Mixtures of Aquatic Organisms Based on Different Hypothetical Descriptors.

Modern industrialization has led to the creation of a wide range of organic chemicals, especially in the form of multicomponent mixtures, thus making the evaluation of environmental pollution more difficult by normal methods. In this paper, we attempt to use forward stepwise multiple linear regression (MLR) and nonlinear radial basis function neural networks (RBFNN) to establish quantitative structure–activity relationship models (QSARs) to predict the toxicity of 79 binary mixtures of aquatic organisms using different hypothetical descriptors. To search for the proper mixture descriptors, 11 mixture rules were performed and tested based on preliminary modeling results. The statistical parameters of the best derived MLR model were Ntrain = 62, R2 = 0.727, RMS = 0.494, F = 159.537, Q2LOO = 0.727, and Q2pred = 0.725 for the training set; and Ntest = 17, R2 = 0.721, RMS = 0.508, F = 38.773, and q2ext = 0.720 for the external test set. The RBFNN model gave the following statistical results: Ntrain = 62, R2 = 0.956, RMS = 0.199, F = 1279.919, Q2LOO = 0.955, and Q2pred = 0.855 for the training set; and Ntest = 17, R2 = 0.880, RMS = 0.367, F = 110.980, and q2ext = 0.853 for the external test set. The quality of the models was assessed by validating the relevant parameters, and the final results showed that the developed models are predictive and can be used for the toxicity prediction of binary mixtures within their applicability domain.

Confidence intervals of the Kling-Gupta efficiency

• The confidence intervals of the KG efficiency do not have a closed-form description. • The uncertainty of KG efficiency is attributed to measurement errors of training data. • Statistical inference with an informal goodness-of-fit metric is coined diagnostic regression. • Parameter confidence regions of KG efficiency in agreement with linear regression theory. • Marginal parameter distributions of KG efficiency are approximately Gaussian. The Kling-Gupta efficiency, hereafter referred to as KG efficiency rather than its common abbreviation KGE, proposed by Gupta et al. (2009) has become a widely used metric for evaluating the goodness-of-fit of n -vectors of observations, y ̃ = [ y ̃ 1 y ̃ 2 … y ̃ n ] ⊤ , and corresponding model simulations, y θ = y 1 θ y 2 θ … y n θ ⊤ . This metric rectifies some of the shortcomings of the coefficient of determination, R 2 , also known to hydrologists as the efficiency of Nash and Sutcliffe (1970) , by using a Euclidean-distance based weighting of the correlation, bias and temporal variability of the observed, y ̃ , and simulated, y θ , data. But as the KG efficiency is not borne out of assumptions with respect to the statistical distribution of the residuals, e θ = y ̃ - y θ , we cannot formally characterize its uncertainty. The NS efficiency suffers a similar problem, yet, statistical theory postulates that its confidence intervals should follow a beta distribution in certain special cases. Without a formal description of the confidence intervals of the KG efficiency, we cannot (amongst others) quantify parameter uncertainty, compute confidence and prediction limits on simulated model responses, inform decision makers about critical modeling uncertainties, evaluate model adequacy and assess the information content of calibration data. More fundamentally, without confidence intervals we cannot establish whether the KG efficiency is a consistent, efficient and unbiased estimator. In this paper we present an empirical description of the confidence intervals of the KG efficiency. We relate the unknown probability distribution of the KG efficiency to the measurement errors of the training data record, y ̃ , and use the bootstrap method to carry out statistical inference. We illustrate our method by application to a simple linear regression function for which the least squares parameter confidence regions are exactly known and two hydrologic models of contrasting complexity. The empirical parameter confidence regions and/or intervals of the KG efficiency are compared to those derived from generalized least squares, objective function contouring and Bayesian analysis using Markov chain Monte Carlo simulation. The marginal parameter distributions of the KG efficiency are generally well described by a normal distribution. Results further confirm that the distribution of the KG efficiency is a complex function of data length and the magnitude, distribution and structure of the measurement errors. This prohibits an analytic description of the empirical confidence regions and/or intervals of the KG efficiency and reiterates the need for the bootstrap method.

HIGH-RESOLUTION SPATIAL SOLUTION FOR AIR QUALITY ASSESSMENT IN THE TROPICAL CITY OF HO CHI MINH CITY, VIETNAM

Air pollution is the leading environmental agent that poses a severe threat to human health and is one of the most severe problems in cities. Of the pollutants, particulate matter (PM), especially particles less than 2.5 microns in diameter, has the most profound health impacts. Urbanization and industrialization in cities have made the air quality up there worse and worse. Our study was based on the Aerosol Optical Depth (AOD) feature, a parameter obtained by remote sensing that relates to the presence of airborne particles potentially associated with PM. In this study, the PM2.5 concentration data from the ground monitoring station and the MODIS AOD product of 3 km resolution were correlated to build a suitable regression function to simulate the spatial distribution of PM2.5 concentrations. Next, the AOD was retrieved from the Landsat image based on the characteristics of the decrease in atmospheric clarity caused by the pollution particles. Landsat AOD has a 600m higher resolution than MODIS AOD. Research results on air quality (AQ) were simulated on Landsat AOD image through PM2.5 concentration distribution and air quality index (AQI), in which AQI was determined based on USEPA standards. The analysis shows that the linear regression function between PM2.5 concentration and MODIS AOD correlated best with the correlation coefficient R=0.9. Then PM2.5 distribution was established on Landsat AOD image with higher spatial resolution. Case analysis for March of 2018 reflected that the average concentration of PM2.5 across Ho Chi Minh City (HCMC) was higher than the allowable threshold specified in QCVN05:2013/BTNMT. PM2.5 concentration in central districts tended to be higher than in suburban districts. The study also found that the city average AQI-PM2.5 was around 97.38, peaking at 159, which was in the Unhealthy range, especially for sensitive groups. The result of the study provides potential solutions for AQ monitoring at the city level with a detailed spatial distribution.

Single-index partially functional linear quantile regression

Tecator dataset has been widely used in the content of functional data analysis. As far as we know, this dataset is only considered under mean regression, which is easily affected by outliers. However, there are 8 more fat samples and 17 more protein samples in this dataset, so, in this paper, we explore this dataset by quantile regression, which is a robust method. Single-index partially functional linear quantile regression is proposed, and B-splines are used to estimate the unknown link function in the single-index component and the unknown slope function in the functional linear component. We establish the convergence rates and asymptotic normality of the estimators. Simulation studies and a real data application are presented to illustrate the performance of the proposed methodologies.

Variability in Minimal-Damage Sap Flow Observations and Whole-Tree Transpiration Estimates in a Coniferous Forest

Transpiration is fundamental to the understanding of the ecophysiology of planted forests in arid ecosystems, and it is one of the most uncertain components in the ecosystem water balance. The objective of this study was to quantify differences in whole-tree transpiration estimates obtained with a heat ratio probe in a secondary Qinghai spruce (Picea crassifolia) forest. To do this, we analyzed the sap flux density values obtained with sensors installed in (1) holes drilled in the preceding growing season (treatment) and (2) holes drilled in the current year (control). The study was conducted in a catchment in the Qilian Mountains of western China. The results showed that an incomplete diameter at breast height (DBH) range contributed to 28.5% of the overestimation of the sapwood area when the DBH > 10 cm and 22.6% of the underestimation of the sapwood area when the DBH < 5 cm. At daily scales, there were significant differences in both the quantity and magnitude of the sap flux density between the treatment and control groups. Furthermore, a linear regression function (R2 = 0.96, p < 0.001), which was almost parallel to the 1:1 reference line, was obtained for the sap flux density correction for the treatment group, and the daily sap flux density and whole-tree transpiration were underestimated by 36.8 and 37.5%, respectively, at the half-hour scale. This study illustrates uncertainties and a correction function for sap flow estimations in young Qinghai spruce trees when using heat ratio sensors with minimal damage over multiple growing seasons.

Impact of COVID-19-Related Lockdown Measures on Economic and Social Outcomes in Lithuania

The current world crisis caused by the COVID-19 pandemic has transformed into an economic crisis, becoming a problem and a challenge not only for individual national economies but also for the world economy as a whole. The first global lockdown, which started in mid-March of 2020 and lasted for three months in Lithuania, affected the movement and behavior of the population, and had an impact on the economy. This research presents results on the impact of lockdown measures on the economy using nonparametric methods in combination with parametric ones. The impact on unemployment and salary inequality was estimated. To assess the impact of lockdown on the labor market, the analysis of the dynamics of the unemployment rate was performed using the results of the cluster analysis. The Lithuanian data were analyzed in the context of other countries, where the dynamics of the spread of the virus were similar. The salary inequality was measured by the Gini coefficient and analyzed using change point analysis, functional data analysis and linear regression. The study found that the greatest impact of the closure restrictions on socio-economic indicators was recorded in 2020, with a lower impact in 2021. The proposed multi-step approach could be applied to other countries and to various types of shocks and interventions, not only the COVID-19 crisis, in order to avoid adverse economic and social outcomes.

Functional linear regression with Huber loss

In this paper, we consider the robust regression problem associated with Huber loss in the framework of functional linear model and reproducing kernel Hilbert spaces. We propose an Ivanov regularized empirical risk minimization estimation procedure to approximate the slope function of the linear model in the presence of outliers or heavy-tailed noises. By appropriately tuning the scale parameter of the Huber loss, we establish explicit rates of convergence for our estimates in terms of excess prediction risk under mild assumptions. Our study in the paper justifies the efficiency of Huber regression for functional data from a theoretical viewpoint.

Research on UWB fusion location algorithm

In order to solve the problem that ultra-wideband (ultra-wideband, UWB) positioning is greatly affected by the environment in the indoor environment of mobile robot, an indoor positioning algorithm based on UWB, odometer and inertial measurement unit is proposed. Taking advantage of the high positioning accuracy of UWB in indoor environment and the high accuracy of odometer positioning in a small range, the adaptive parameter equation of error is constructed by using linear regression function. The weight coefficient is obtained by combining the position data solved by UWB and the previous moment fusion algorithm to solve the position difference and the mileage displacement formula, and the weight value of angle increment is given according to the state of the system. Through the calculation, the displacement increment matrix of each measurement of the system is obtained, and the final linear optimal value is obtained by substituting the extended Kalman filter algorithm. Compared with the single UWB positioning method, the results show that the system can maintain good accuracy and robustness, and the mean error of the whole system is less than 8cm, which provides a solution for the single UWB positioning of mobile robot affected by NLOS error.

Local influence of climate on grapevine: an analytical process involving a functional and Bayesian exploration of farm data time series synchronised with an eGDD thermal index

Climate influence on grapevine physiology is prevalent and this influence is expected to increase with climate change. Climate influence on grapevine physiology can vary depending on the terroir. A better understanding of these local terroir variations is likely to be achieved with analyses that use local data; i.e., farm/vineyard data. Thus, the challenge lies in exploiting farm data to enable grape growers to understand their own terroir and consequently adapt their practices to the local conditions. In such a context, this article proposes an analytical process to site-specifically study climate influence on grapevine physiology by focusing on time series of the weather data often contained in farm data sets. This article focuses on temperature and precipitation influence on yield in the form of a case study. The analytical process includes the Extended Growing Degree Days (eGDD) and the Bayesian functional Linear regression with Sparse Steps functions (BLiSS) methods in order to detect site-specific periods of strong climate influence on grapevine yield. It uses data from three commercial vineyards situated in the Bordeaux region (France), California (USA) and Israel. In general, the periods of climate influence on grapevine yield detected for the three vineyards identified the same stages of yield development, which have already been studied in the scientific literature. However, some vineyard differences were observed, including: i) different periods of influence associated with a given stage of yield development between the vineyards, ii) different influential weather variables between the three vineyards for a given period, and iii) differing duration of the period of influence associated with a given stage of yield development between the vineyards. These results show the potential of the proposed analytical process for analysing the time series of farm weather data in order to extract site-specific climate indicators of grapevine yield.

Evaluation of multiple linear regression function and generalized linear model types in estimating natural menopausal age: A cross-sectional study.

BackgroundSince women spend about one-third of their lifespan in menopause, accurate prediction of the age of natural menopause and its effective parameters are crucial to increase women's life expectancy.ObjectiveThis study aimed to compare the performance of generalized linear models (GLM) and the ordinary least squares (OLS) method in predicting the age of natural menopause in a large population of Iranian women.Materials and Methods This cross-sectional study was conducted using data from the recruitment phase of the Shahedieh Cohort Study, Yazd, Iran. In total, 1251 women who had the experience of natural menopause were included. For modeling natural menopause, the multiple linear regression model was employed using the ordinary least squares method and GLMs. With the help of the Akaike information criterion, root-mean-square error (RMSE), and mean absolute error, the performance of regression models was measured.ResultsThe mean age of menopausal women was 49.1 4.7 yr (95% CI: 48.8-49.3) with a median of 50 yr. The analysis showed similar Akaike criterion values for the multiple linear models with the OLS technique and the GLM with the Gaussian family. However, the RMSE and mean absolute error values were much lower in GLM. In all the models, education, history of salpingectomy, diabetes, cardiac ischemic, and depression were significantly associated with menopausal age.Conclusion To predict the age of natural menopause in this study, the GLM with the Gaussian family and the log link function with reduced RMSE and mean absolute error can be a good alternative for modeling menopausal age.

Functional linear regression with truncated signatures

We place ourselves in a functional regression setting and propose a novel methodology for regressing a real output on vector-valued functional covariates. This methodology is based on the notion of signature, which is a representation of a function as an infinite series of its iterated integrals. The signature depends crucially on a truncation parameter for which an estimator is provided, together with theoretical guarantees. An empirical study on both simulated and real-world datasets shows that the resulting methodology is competitive with traditional functional linear models, in particular when the functional covariates take their values in a high dimensional space.

SIGNIFICANT FACTORS ASSOCIATED WITH INSULIN-LIKE GROWTH FACTOR 1 AND ITS BINDING PROTEIN 3 IN COLORECTAL CANCER – MULTIPLE REGRESSION ANALYSIS

Aim: the aim of our study was to investigate the association of insulin-like growth factor-1 and its binding protein 3 levels with CRC risk factors and symptoms by multiple regression analyzes. Methods: The IGF-1 laboratory test was performed using the ECLIA method. Serum insulin and glucose levels were assessed by oral glucose tolerance test (OGTT) in fasting state and after 120 minutes of glucose loading (40 g / 1 m2 of body surface). Multiple regression analysis performed to study the mutual impact of different parameters on outcome (IGF-1 and IGF BP3). Results: Finally, significant variables (factors) were left in the model having mutual effect on the outcome (IGF BP3 value). The linear multiple regression function took the following form: Hence these factors (each factor in parentheses indicates the nature of the correlation - direct or inverse): X1 - Sex (direct); X4 – Code of Surgery (inverse); X7 – other general pains/symptoms (inverse); X13 - Flatulence Gases (inverse); X14 - Diarrhea (direct); X20 – A course of chemotherapy or radiation therapy before surgery (inverse); X27 – HOMA-S (direct); X28 - HOMA-IR (inverse); X31 – creatinine (direct). Conclusion: Based on the results of current study we concluded that CRC is multifactorial and many significant factors are responsible for its development. One of possible mechanisms for its development is the changes insulin/IGF-1 signaling pathway with other significant biological and non-biological factors.

A method for assessing heat losses in developing countries with a focus on operational data of a district heating (DH) system

The goal hereof was to propose a new method to estimate heat loss rates and find out how either the weather conditions of the serviced area or the available operational data affect each of the heat loss rate components. A linear regression function was used to describe the correlation between heat production and outdoor temperatures. Monthly measurements are used to estimate onsite heat loss in pipes in Russia. However, model coefficients can be adjusted to make it applicable to any European city, and the simulated behavior of the system is realistic in terms of the temperature profiles and heat losses for any DH system. The proposed model is more accurate than the conventional method with respect to the heat loss difference attributable to the variance in outdoor, supply, return, and ground soil temperatures. The difference between actual heat losses and heat losses projected by this new method varies from 0.4% to 1.2% with an average error of 0.65%. The results also show how the measurements state-of-the-art DH systems provide can help improve daily operation and maintenance to promote data-driven approaches. Technologies can be combined to further improve the performance.