The known works on the generalization of functional linear regression are usually based on the assumption of independently and identically distributed (i.i.d.) sample and this i.i.d. assumption does not hold in many machine learning applications. In this paper, we want to understand the generalization ability of functional regularized least squares regression (FRLSR) and functional Huber linear regression (FHLR) from non-i.i.d. sample perspective. We first establish the generalization bounds of the FRLSR based on exponentially strongly mixing sequence (e.s.m.s.) and uniformly ergodic Markov chain (u.e.M.c.) samples, respectively. Since the solution of FRLSR may suffer from lack of robustness and be spoiled by outliers, fHLR can enhance the robustness of the squared error loss function to outliers, we then research the generalization bounds of FHLR based on e.s.m.s. and u.e.M.c. samples, respectively. These established results show that FRLSR and FHLR based on non-i.i.d. samples are consistent and the corresponding learning rates are same as that of i.i.d. sample.

Spatial databases are the main means to manage geo-big data, and learned spatial indices are a novel approach to improve the spatial retrieval performance of spatial databases by modeling the data distribution. However, the complex hierarchical structures in current learning models pose significant limitations, including prolonged construction times, slow data updates, and suboptimal dynamic query performance. Consequently, improving the efficiency of both index construction and updates is essential. We addressed these challenges by introducing a new method, the Spatial Uniform Partition Learned Index (SUPLI). SUPLI utilizes an iterative uniform partitioning algorithm that simplifies data distribution by uniformly segmenting space and applies a linear regression function—instead of a neural network model—to enable efficient index construction. Additionally, SUPLI incorporates query load optimization and historical query learning strategies, which dynamically adjust the spatial query algorithm to enhance query efficiency. Furthermore, a buffer structure is employed to store change information, facilitating efficient updates. Comparative evaluations conducted on three synthetic datasets and two real-world datasets show that SUPLI outperforms the classic R-tree by an order of magnitude in construction, query, and update performance, and demonstrates additional advantages over similar spatial learned indices, such as SPRIG and LISA.

Testing Exogeneity in the Functional Linear Regression Model

Functional Adaptive Double-Sparsity Estimator for Functional Linear Regression Model with Multiple Functional Covariates

Enhancing spatial functional linear regression with robust dimension reduction methods

Older patients who are evaluated for kidney transplantation (KT) experience an earlier onset of cognitive impairment due to dialysis, comorbidities, and inactivity. Ambient fine particulate matter (PM2.5) is a modifiable risk factor for dementia among community-dwelling older adults. Inflammatory responses and oxidative stress caused by inactivity in older patients evaluated for KT may heighten vulnerability to PM2.5. Thus, the impact of PM2.5 on dementia may be more severe in this population. We leveraged a prospective cohort (2009-2019) of older (age ≥50) patients evaluated for KT (n=2073) with Modified Mini-Mental State Examination (3MS). We derived annual PM2.5 from residential ZIP codes (high: PM2.5>9µg/m3), quantifying its association with global cognitive function (linear regression), impairment (logistic regression), and risk of dementia (Cox proportional hazards model). We tested the interaction between PM2.5 and dementia risk factors using a Wald test. Models were adjusted for confounders, including social determinants of health. High PM2.5 was associated with worse global cognitive function (difference=-3.00 points [3MS score], 95% CI: -3.93 to -2.07), with a stronger association among patients with low physical activity (p [interaction] <0.001). High PM2.5 was associated with 1.90-fold higher odds of global cognitive impairment (95% CI: 1.48-2.46), and 3.29-fold higher risk of dementia (95% CI: 1.14-9.55). High PM2.5 was associated with worse cognitive function among older patients evaluated for KT, particularly those with low physical activity. The association was stronger than prior findings among community-dwelling older adults. Clinicians may counsel patients to monitor air quality. Patients in high PM2.5 neighborhoods should discuss cognitive assessments and ways to increase physical activity with providers.

The area of behavioral finance integrates economic and psychological concepts to comprehend and elucidate the decision­making process involved in personal finance. The purpose of this paper is to determine the impact of anchoring, herding, and loss aversion on influencing working women investors’ investment decision-making. The sample size consists of 196 working women investors who are trading in the Indian Stock Market from Uttar Pradesh, India. A structured questionnaire is used for the collection of data, which is based on a five-point Likert scale. The SPSS (Version 22) software is used to analyze data employing the linear regression function. The result of this study confirmed that anchoring, herding, and loss aversion bias have a significant positive impact on working women investors’ investment decision-making. Based on the data obtained, this paper concludes that anchoring has the most influence on working women investors’ investment decisions, followed by herding, while loss aversion has the least influence on working women investors’ investment decision-making. The findings of this study have significant implications for working women investors, researchers, policymakers, and financial advisors. Awareness of these behavioral biases is vital for empowering working women to make informed and rational investment choices. It is important for financial advisors and policymakers to acknowledge these behavioral biases in order to offer customized counselling and support for working women investors. Even though these biases affect people of both genders equally, this research concentrates on how they particularly affect working women since they frequently deal with particular socio-cultural settings and expectations.

Within the field of organizational behavior research, workplace politics has acquired a new dimension and significance. The phenomena of workplace politics were rendered significantly essential and evident during the analysis of organizational behavior as a result of the extensive effort and research on contemporary intellectuals. The majority of research focuses on workplace politics in relation to employee loyalty, work satisfaction, and organizational culture. Organizational scientists have described workplace politics in a variety of ways, which has resulted in divergent perspectives and has complicated the process of reaching a consensus among experts regarding terminology. As a result, the concept of transmitted phenomena can be classified in a variety of ways. The studies exclusively clarify the political aspect, leaving the genuine divination unexplained. The sample size for this investigation was 38. This includes personnel at every level of the organization. Simple random sampling functions as a sampling methodology, while linear regression functions as a statistical instrument. Workplace politics and job performance exhibit a substantial correlation, according to the analysis. This relationship is significant, despite its fragility. The conclusion is that organizational dynamics influence job performance, as one variable influence another. As a result, employees are not primarily interested in their work, and they lack personal engagement in their roles.

Photodiode sensors are widely used in various applications such as light intensity measurement, optoelectronic devices, and automation. In improving the quality of measurement and automation systems, more sophisticated technology is needed such as photodiode sensor arrays, which allow more accurate data collection from multiple sensors simultaneously. This research aims to design a photodiode sensor array with high sensitivity. The system design consists of six photodiode sensors combined with a summing amplifier circuit and a non-inverting amplifier as a signal conditioner which is then processed by a microcontroller. After that, the linear regression function is determined through the calibration process and experiments carried out. Two linear regression functions are obtained and implemented in two operating modes: normal mode and sensitive mode. Experimental results yield two linear regression functions applied to a photodiode sensor array in normal and sensitive modes. Normal mode shows 82.50% accuracy with a 36.69% coefficient of variation, while sensitive mode boasts 94.05% accuracy and 49.81% coefficient of variation. Both modes cater to different light conditions, with sensitive mode excelling in detecting light intensity. Linear regression implementation proves precise and accurate for light detection.

This study introduces two innovative methods—Three-frequency pseudorange combination (TFPC) and Three-frequency carrier phase combination (TFCPC)—for estimating soil moisture using GNSS-IR technology. Unlike traditional methods that require separating direct and reflected signals, these approaches leverage carrier phase and pseudorange multipath errors to improve accuracy. The new methods eliminate the impact of geometrical factors and atmospheric delays. By applying minimum covariance determinant (MCD) and moving average filter (MAF), the study effectively detects and corrects outliers in delay phases, enhancing the quality of the data. Using data from the Plate Boundary Observatory (PBO) H2O project, the study finds that combining corrected delay phases from multiple satellites improves correlations between estimated and actual soil moisture values. The TFPC method achieves correlation coefficients of 0.82 and 0.87 with multivariate linear regression (MLR) and radial basis function neural network (RBFNN) models, while the TFCPC method yields even better results at 0.85 and 0.91, respectively. These findings represent a significant advancement in high-precision soil moisture estimation, offering valuable implications for applications in agriculture, weather forecasting, and environmental monitoring.

In this paper, we study a flexible functional linear regression model where the dependency of a scalar response on a functional predictor is function-valued process rather than conventional one-way processes. Additionally, we provide an intuitively appealing estimation approach to estimate the bivariate functional regression coefficient. We first represent the bivariate functional coefficient by using the data-driven bases function to achieve the dimension reduction, and then introduce an iterative least square procedure to estimate the coefficients after dimension reduction in the framework of low-rank structure. Theoretically, we investigate the convergence rate of bivariate functional coefficient estimator under mild conditions. Simulation studies indicate that the proposed methods perform well in finite samples and an empirical example is presented to illustrate its usefulness.

Contribution of informal sector to the economy remains substantial in developed countries such as Tanzania. In order to promote sustainable industrialization through manufacturing enterprises in the informal sector, this study was conducted to analyze their technical efficiency and profitability. The study employed data from the 2019 Informal Sector Survey conducted in Dar es Salaam, Tanzania. Variables involved in this study were output, maximum possible output, technical efficiency level, value added, net income, return on assets, total asset value, capital investment in equipment and machinery, number of workers, labor costs, worker productivity, intermediate consumption, age of enterprise, and sex and education level of enterprise operators. The study employed multiple linear regression and stochastic frontier production function for analysis. Results from multiple linear regression showed that output increased significantly with labor costs (p &lt; 0.1) and with intermediate consumption (p &lt; 0.01). Also, results showed that technical efficiency ranged between 0.00 and 70.15, with an average of 17.77 percent. Additionally, profitability increased significantly with worker productivity (p &lt; 0.01) and with sex of the enterprise operator being female compared to a male (p &lt; 0.05). The study recommends enhancing resource optimization and strengthening workforce capacity to support profitable manufacturing practices.

Canonical components of the canonical analysis of two random vectors are collinear with principal components of a PCA of the multidimensional linear regression function of one vector with respect to the other or projected PCA. In the context of streaming data, we define processes to estimate online in parallel this regression function and components of the canonical analysis, possibly taking into account at each step all the data up to this step to have a faster convergence and using an extended Oja process. We deal with the cases of canonical correlation analysis, factorial correspondence analysis and factorial discriminant analysis.

Partially functional linear expectile regression model with missing observations

ABSTRACTWe propose a new class of high‐dimensional multiresponse partially functional linear regressions (MR‐PFLRs) to investigate the relationship between scalar responses and a set of explanatory variables, which include both functional and scalar types. In this framework, both the dimensionality of the responses and the number of scalar covariates can diverge to infinity. To account for within‐subject correlation, we develop a functional principal component analysis (FPCA)‐based penalized weighted least squares estimation procedure. In this approach, the precision matrix is estimated using penalized likelihoods, and the regression coefficients are then estimated through the penalized weighted least squares method, with the precision matrix serving as the weight. This method allows for the simultaneous estimation of both functional and scalar regression coefficients, as well as the precision matrix, while identifying significant features. Under mild conditions, we establish the consistency, rates of convergence, and oracle properties of the proposed estimators. Simulation studies demonstrate the finite‐sample performance of our estimation method. Additionally, the practical utility of the MR‐PFLR model is showcased through an application to Alzheimer's disease neuroimaging initiative (ADNI) data.

Functional regression models represent a crucial research area within functional data analysis. To enhance the flexibility of the model, this paper proposes a partial functional linear regression model based on ensemble learning and kernel techniques. On one hand, this method effectively models the relationship between non-linear predictor variables and scalar response variables by employing the Reproducing Kernel Hilbert Space. On the other hand, it utilizes Functional Principal Component Analysis to approximate and estimate functional predictor variables, and addresses the selection of truncation numbers through the stacking framework. In the stacking framework, the meta model takes a model-free form, further increasing the flexibility of the model and effectively balancing the variance and bias of the prediction model. The results of simulation experiments and real-world data analysis demonstrate that the proposed method is more competitive compared to traditional benchmark methods.

Theoretical background: Market indicators are considered to be one of the most important groups of financial metrics used by investors when valuing shares. Among the quotients describing the environment of the listed entities, a security's Price-to-Sales ratio deserves a special attention. Its pattern allows the company's price to be measured in relation to quarterly/annual revenues, not profits. Thus, the C/P ratio indicates the extent to which a given company is underestimated or overestimated by the market in comparison to sales achieved. Purpose of the article: This paper focuses on constructing a model of potential exogenous variables from financial analysis determining the dynamics of changes in the C/Ps of the public companies. Measuring enterprise's value was conducted on a sample of 172 entities listed at the Warsaw Stock Exchange during three phases of the SARS-CoV-2 pandemic, covering its financial statements as per the first quarter of 2021-2023. Research methods: In the example below statistical tools such as linear correlation matrices and multiple regression functions were applied within a given time horizon. Due to the failure to meet the assumptions for random components variances' homogeneity of the individual objects series a generalized least squares (GLS) method was used, comparing the obtained outcomes with its classical counterpart. The statistical significance of the parameters in each equation was verified by means of the Student's t-test at the significance level α = 0.05. Main findings: The study confirmed statistically significant relationships in fluctuations between the C/P ratios and selected financial indicators during waves III and V of the COVID-19 pandemic (the adjusted R2^ coefficients in the generalized regression formulae equalled to 0.92 and 0.89, respectively). In both cases, C/P fluctuations were positively influenced by changes in the debts level, in the sense of the Financial Sustainability Ratio (FSR). On the contrary, negative impacts of C/Ps in the area of profitability, i.e. on Operating Margin (OM) indices and ROS ratios were noticed. Alternatively, the dynamics of the company's value could be described to a limited extent by financial indicators during the wave VII of the COVID-19 diffusion (adjusted R2^ = 0.62), with its maximum traditionally recorded by ROS and FSR ratios. The transformation of the residuals matrices towards the generalized least squares method resulted in decreases in standard errors of coefficients building estimation intervals around the mean.

Statistical methods play an important role in image processing. The most important of these methods are the simple linear regression function and the binary logistic regression function, which are used to study the relationship between the dependent variable and the independent variable. They are also used in the process of predicting the value of the dependent variable at a specific value for the independent variable. In this research, the simple linear regression function and the binary logistic regression function were employed in image processing as a statistical technique whose purpose is not to study the relationship between the dependent variable and the independent variable or in the prediction process, but rather a tool that works to segment images using the threshold technique, considering the sum of the simple linear regression vector and the binary logistic linear regression vector, which were estimated from the image data as the threshold limit for segmenting images. The two techniques were good in the segmentation process in terms of giving the best segmented images containing important areas that have features that are useful for the study, while removing the useless or unimportant areas. The two techniques were compared using the Jaccard scale, which is used to determine which technique was better in the segmentation process. It was found that the simple linear regression technique gave a clearer segmented image of the features, and thus it is better than the segmented image using the binary logistic linear regression technique

The thermal error of the high-power grinding motorized spindle, caused by heating, seriously affects machining accuracy. In this paper, an ensemble learning algorithm is used to predict the thermal error of a high-precision motorized spindle. The subsequent problem of thermal error compensation can be effectively solved by a suitable thermal error model, which is crucial for improving the machining accuracy of the actual machining process. Firstly, the steady-state temperature field of the grinding motorized spindle is analyzed and used to determine the position of the sensors. Then, a signal acquisition instrument is used to monitor real-time temperature data. After that, experimental results are obtained, followed by verification. Finally, based on experimental data and the optimization results of temperature measurement points, temperature data are used as the input variable, and thermal deformation data are used as the output variable. The ensemble learning model is composed of different weak learners, which include multiple linear regression, back-propagation, and radial basis function neural networks. Different weak learners are trained using datasets separately, and the output of the weak learners is used as input to the model. Through integrating strategies, an ensemble learning model is established and compared with a weak learner. The error residual set of the ensemble learning model remains within [-0.2, 0.2], and the prediction performance shows that the ensemble learning model has a better predictive effect and strong robustness.

INTRODUCTION. The median lethal dose (LD50) and the low lethal dose (LD10) are critical parameters for the safety of medicinal products. Sometimes, the pharmacopoeial probit method (PM) fails to calculate the LD10 value, and the calculation result is obviously lower than the true value. In such cases, the use of other computational techniques is warranted.AIM. This study aimed to evaluate the potential of a script in the R environment as a tool for calculating the LD50 and LD10 of medicines.MATERIALS AND METHODS. This study compared the results of determining LD50 and LD10 using the spreadsheet-based pharmacopoeial PM and a modified script in the R environment (MS). The lm() function (linear regression model) was used to establish the relationships between the LD50 and LD10 values obtained using the PM and those calculated using the MS.RESULTS. A script originally developed by S. Young for LD50 calculation was modified and supplemented to simplify its use. The modification reduced the amount of input data required for calculation, added the ability to calculate LD10 values, and improved the visual clarity of the calculation results. Reducing the step size for the seq() function was shown to improve the output smoothness when the MS yielded a jagged mortality curve. The MS-derived LD50 values were within the confidence limits for the values obtained using the PM (P=0.95). The regression analysis confirmed the accuracy of the MS-based LD50 and LD10 calculations, which was demonstrated by a statistically insignificant systematic error, a significant dose dependence at P=0.999, and a high coefficient of determination (R2). If the PM underestimates LD10 values, the analyst should be guided by the LD50 and LD10 values calculated using the MS.CONCLUSIONS. The experimental data demonstrate the applicability of the MS for testing medicines. In some cases presented in the article, the custom R script offers an advantage over the current pharmacopoeial method. A tentative direction for further work may be the automation of the MS-based LD10 calculation.