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In this paper, we have introduced a functional approach for approximating nonparametric functions and coefficients in the presence of multivariate and functional predictors. By utilizing the Fisher scoring algorithm and the cross-validation technique, we derived the necessary components that allow us to explain scalar responses, including the functional index, the nonlinear regression operator, the single-index component, and the systematic component. This approach effectively addresses the curse of dimensionality and can be applied to the analysis of multivariate and functional random variables in a separable Hilbert space. We employed an iterative Fisher scoring procedure with normalized B-splines to estimate the parameters, and both the theoretical and practical evaluations demonstrated its favorable performance. The results indicate that the nonparametric functions, the coefficients, and the regression operators can be estimated accurately, and our method exhibits strong predictive capabilities when applied to real or simulated data. [ABSTRACT FROM AUTHOR]

The paper is devoted to the formal description of the running time of the user task on some virtual nodes in the computing network. Based on the probability theory framework, this time represents a random value with a finite mean and variance. For any class of user task, these moments are the functions of the node resources, task numerical characteristics, and the parameters of the current node state. These functions of the vector arguments can be treated as some surfaces in the multidimensional Euclidean spaces, so the proposed models are called the stochastic time complexity surfaces. The paper also presents a class of functions suitable for the description of both the mean and variance. They contain unknown parameters which should be estimated. The article includes the statement of the parameter identification problem given the statistical results of the node stress testing, recommendations concerning the test planning, and preprocessing of the raw experiment data. To illustrate the performance of the proposed model, the authors design it for an actual database application—the prototype of the passengers' personal data anonymization system. Its application functions are classified into two user task classes: the data anonymization procedures and fulfillment of the statistical queries. The authors identify the stochastic time complexity surfaces for both task types. The additional testing experiments confirm the high performance of the suggested model and its applicability to the solution of the practical providers' problems. [ABSTRACT FROM AUTHOR]

The use of a 3D range scanning device for autonomous object description or unknown environment mapping leads to the necessity of improving computer methods based on identical point pairs from different point clouds (so-called registration problem). The registration problem and three-dimensional transformation of coordinates still require further research. The paper attempts to guide the reader through the vast field of existing registration methods so that he can choose the appropriate approach for his particular problem. Furthermore, the article contains a regression method that enables the estimation of the covariance matrix of the transformation parameters and the calculation of the uncertainty of the estimated points. This makes it possible to extend existing registration methods with uncertainty estimates and to improve knowledge about the performed registration. The paper's primary purpose is to present a survey of known methods and basic estimation theory concepts for the point cloud registration problem. The focus will be on the guiding principles of the estimation theory: ICP algorithm; Normal Distribution Transform; Feature-based registration; Iterative dual correspondences; Probabilistic iterative correspondence method; Point-based registration; Quadratic patches; Likelihood-field matching; Conditional random fields; Branch-and-bound registration; PointReg. The secondary purpose of this article is to show an innovative statistical model for this transformation problem. The new theory needs known covariance matrices of identical point coordinates. An unknown rotation matrix and shift vector have been estimated using a nonlinear regression model with nonlinear constraints. The paper ends with a relevant numerical example. [ABSTRACT FROM AUTHOR]

Global Navigation Satellite Systems (GNSS) are used to provide accurate position, navigation, and time (PNT) information to users in various sectors of our society including transportation. Augmentation systems such as differential GNSS (DGNSS), real-time kinematics (RTK), and Precise Point Positioning (PPP) improve the GNSS performance, and providing reliable measurements from its reference station is very crucial. To ensure safe and accurate PNT solutions, code and carrier measurements must be monitored for potential faults or a performance degrade. Although there exist numerous methods to model and monitor the measurements, research on the carrier phase measurements is not as extensive as the code measurements. This paper introduces a split of residuals into receiver noise and multipath components to customize their estimation according to their respective statistical properties. This study also proposes a method to use machine learning-based non-linear regression to effectively model and monitor potential faults in the GNSS measurements including the carrier phase. A training dataset is used to model the nominal quantities of GNSS measurement residuals, and inflation factors are applied to over-bound the fault-free residuals. These inflated residuals are coupled with uncertainty factors to compute thresholds for monitoring carrier phase residuals, and the effectiveness of the thresholds is validated with a test dataset by achieving the false alarm rate of 6.61 × 10 − 6 , slightly lower than the desired level of 10 − 5 . [ABSTRACT FROM AUTHOR]

As more genetic information becomes available, such as DNA methylation levels, it becomes increasingly important to have techniques to analyze such data in the context of cancers such as anal and cervical carcinomas. In this paper, we present an algorithm that differentiates between healthy control patients and individuals with anal and cervical carcinoma, using as an input DNA methylation data. The algorithm used a combination of ridge regression and neural networks for the classification task, achieving high accuracy, sensitivity and specificity. The relationship between methylation levels and carcinoma could in principle be rather complex, particularly given that a large number of CpGs could be involved. Therefore, nonlinear techniques (machine learning) were used. Machine learning techniques (nonlinear) can be used to model linear processes, but the opposite (linear techniques simulating nonlinear models) would not likely generate accurate forecasts. The feature selection process is carried out using a combination of prefiltering, ridge regression and nonlinear modeling (artificial neural networks). The model selected 13 CpGs from a total of 450,000 CpGs available per patient with 171 patients in total. The model was also tested for robustness and compared to other more complex models that generated less precise classifications. The model obtained (testing dataset) an accuracy, sensitivity and specificity of 97.69%, 95.02% and 98.26%, respectively. The reduction of the dimensionality of the data, from 450,000 to 13 CpGs per patient, likely also reduced the likelihood of overfitting, which is a very substantial risk in this type of modelling. All 13 CpGs individually generated classification forecasts less accurate than the proposed model. [ABSTRACT FROM AUTHOR]

Forecasting future values of Colombian companies traded on the New York Stock Exchange is a daily challenge for investors, due to these stocks' high volatility. There are several forecasting models for forecasting time series data, such as the autoregressive integrated moving average (ARIMA) model, which has been considered the most-used regression model in time series prediction for the last four decades, although the ARIMA model cannot estimate non-linear regression behavior caused by high volatility in the time series. In addition, the support vector regression (SVR) model is a pioneering machine learning approach for solving nonlinear regression estimation procedures. For this reason, this paper proposes using a hybrid model benefiting from ARIMA and support vector regression (SVR) models to forecast daily and cumulative returns of selected Colombian companies. For testing purposes, close prices of Bancolombia, Ecopetrol, Tecnoglass, and Grupo Aval were used; these are relevant Colombian organizations quoted on the New York Stock Exchange (NYSE). [ABSTRACT FROM AUTHOR]

The paper is devoted to the guaranteeing estimation of parameters in the uncertain stochastic nonlinear regression. The loss function is the conditional mean square of the estimation error given the available observations. The distribution of regression parameters is partially unknown, and the uncertainty is described by a subset of probability distributions with a known compact domain. The essential feature is the usage of some additional constraints describing the conformity of the uncertain distribution to the realized observation sample. The paper contains various examples of the conformity indices. The estimation task is formulated as the minimax optimization problem, which, in turn, is solved in terms of saddle points. The paper presents the characterization of both the optimal estimator and the set of least favorable distributions. The saddle points are found via the solution to a dual finite-dimensional optimization problem, which is simpler than the initial minimax problem. The paper proposes a numerical mesh procedure of the solution to the dual optimization problem. The interconnection between the least favorable distributions under the conformity constraint, and their Pareto efficiency in the sense of a vector criterion is also indicated. The influence of various conformity constraints on the estimation performance is demonstrated by the illustrative numerical examples. [ABSTRACT FROM AUTHOR]

The current standard for evaluating road conditions worldwide relies primarily on the Pavement Condition Index (PCI) and the International Roughness Index (IRI). The IRI can be further calculated to obtain the Riding Quality Index (RQI). To assess pavement damage, various imaging equipment is commonly utilized, providing consistent results that align with actual road conditions. For roughness detection, the Laser Profilometer offers excellent results but may not be suitable for rural roads with poor conditions due to its high inspection cost and the need for a stable environmental setting. Therefore, there is a pressing need to develop cost-effective, rapid, and accurate roughness inspection methods for these roads, which constitute a significant portion of the road network. This study examined the relationship between PCI and RQI using nonlinear regression on 30,088 valid pavement inspection records from various regions in China (totaling 24,624.222 km). Our objective was to estimate RQI solely from PCI data, capitalizing on its broad coverage and superior accuracy. Additionally, we explored how PCI levels impact RQI decay rates. The models in this study were compared to several models published in previous studies at last. Our findings indicate that the model performs best for low-grade roads with low PCI scores, achieving over 90% accuracy for both cement concrete and asphalt concrete pavements. Furthermore, different levels of pavement damage have distinct effects on RQI decay rates, with the most significant impact observed when the pavement is severely damaged. The models in this study outperformed all the other available models in the literature. Consequently, under limited inspection conditions in rural areas, pavement damage inspection results can effectively predict riding quality or roughness, thereby reducing inspection costs. Overall, this study offers valuable insights but has limitations, including limited global generalizability and the model's applicability to high-grade roads. Future research is needed to address these issues and enhance practical applications. [ABSTRACT FROM AUTHOR]

This paper uses the median-of-means (MOM) method to estimate the parameters of the nonlinear regression models and proves the consistency and asymptotic normality of the MOM estimator. Especially when there are outliers, the MOM estimator is more robust than nonlinear least squares (NLS) estimator and empirical likelihood (EL) estimator. On this basis, we propose hypothesis testing Statistics for the parameters of the nonlinear regression models using empirical likelihood method, and the simulation performance shows the superiority of MOM estimator. We apply the MOM method to analyze the top 50 data of GDP of China in 2019. The result shows that MOM method is more feasible than NLS estimator and EL estimator. [ABSTRACT FROM AUTHOR]

There exist many topological indices that are calculated on saturated hydrocarbons since they can be easily modelled by simple graphs. On the other hand, it is more challenging to investigate topological indices for hydrocarbons with multiple bonds. The purpose of this paper is to introduce a simple model that gives good results for predicting physico-chemical properties of alkenes and alkadienes. In particular, we are interested in predicting boiling points of these molecules by using the well known Wiener index and its weighted versions. By performing the non-linear regression analysis we predict boiling points of alkenes and alkadienes. [ABSTRACT FROM AUTHOR]

The growth and yield modeling of a forest stand has progressed rapidly, starting from the generalized nonlinear regression models of uneven/even-aged stands, and continuing to stochastic differential equation (SDE) models. We focus on the adaptation of the SDEs for the modeling of forest stand dynamics, and relate the tree and stand size variables to the age dimension (time). Two different types of diffusion processes are incorporated into a hybrid model in which the shortcomings of each variable types can be overcome to some extent. This paper presents the hybrid multivariate SDE regarding stand basal area and volume models in a forest stand. We estimate the fixed- and mixed-effect parameters for the multivariate hybrid stochastic differential equation using a maximum likelihood procedure. The results are illustrated using a dataset of measurements from Mountain pine tree (Pinus mugo Turra). [ABSTRACT FROM AUTHOR]

We study a joint model where logistic regression is applied to binary longitudinal data with a mismeasured time-varying covariate that is modeled using a mechanistic nonlinear model. Multiple random effects are necessary to characterize the trajectories of the covariate and the response variable, leading to a high dimensional integral in the likelihood. To account for the computational challenge, we propose a stochastic expectation-maximization (StEM) algorithm with a Gibbs sampler coupled with Metropolis–Hastings sampling for the inference. In contrast with previous developments, this algorithm uses single imputation of the missing data during the Monte Carlo procedure, substantially increasing the computing speed. Through simulation, we assess the algorithm's convergence and compare the algorithm with more classical approaches for handling measurement errors. We also conduct a real-world data analysis to gain insights into the association between CD4 count and viral load during HIV treatment. [ABSTRACT FROM AUTHOR]

The identification of partially observed continuous nonlinear systems from noisy and incomplete data series is an actual problem in many branches of science, for example, biology, chemistry, physics, and others. Two stages are needed to reconstruct a partially observed dynamical system. First, one should reconstruct the entire phase space to restore unobserved state variables. For this purpose, the integration or differentiation of the observed data series can be performed. Then, a fast-algebraic method can be used to obtain a nonlinear system in the form of a polynomial dynamical system. In this paper, we extend the algebraic method proposed by Kera and Hasegawa to Laurent polynomials which contain negative powers of variables, unlike ordinary polynomials. We provide a theoretical basis and experimental evidence that the integration of a data series can give more accurate results than the widely used differentiation. With this technique, we reconstruct Lorenz attractor from a one-dimensional data series and B. Muthuswamy's circuit equations from a three-dimensional data series. [ABSTRACT FROM AUTHOR]

The article is aimed at the mathematical and optimization modeling of technological processes of surface treatments, specifically the zincing process. In surface engineering, it is necessary to eliminate the risk that the resulting product quality will not be in line with the reliability requirements or needs of customers. To date, a number of research studies deal with the applications of mathematical modeling and optimization methods to control technological processes and eliminate uncertainties in the technological response variables. The situation is somewhat different with the acid zinc plating process, and we perceive their lack more. This article reacts to the specific requirements from practice for the prescribed thickness and quality of the zinc layer deposited in the acid electrolyte, which stimulated our interest in creating a statistical nonlinear model predicting the thickness of the resulting zinc coating (ZC). The determination of optimal process conditions for acid galvanizing is a complex problem; therefore, we propose an effective solving strategy based on the (i) experiment performed by using the design of experiments (DOE) approach; (ii) exploratory and confirmatory statistical analysis of experimentally obtained data; (iii) nonlinear regression model development; (iv) implementation of nonlinear programming (NLP) methods by the usage of MATLAB toolboxes. The main goal is achieved—regression model for eight input variables, including their interactions, is developed (the coefficient of determination reaches the value of R2 = 0.959403); the optimal values of the factors acting during the zincing process to achieve the maximum thickness of the resulting protective zinc layer (the achieved optimum value th* = 12.7036 μm), are determined. [ABSTRACT FROM AUTHOR]

Legalization of the proceeds of crime represents a worldwide problem with serious economic and social consequences. Information technologies in conjunction with advanced computer techniques are important tools in the fight against money laundering (ML), financial crime (FC) and terrorism financing (TF). Nowadays, the applied literature on ML/FC/TF uses much more mathematical modelling as a solving strategy to estimate illicit money flows. However, we perceive that there is preference of linear models of economical dependences and sometimes lack of acceptance of nonlinearity of such investigated economic systems. To characterize the risk of legalization of crime proceeds in a certain country, the scientific researchers use the Basel anti-money laundering (AML) index. To better understand how the global indicators (WCI, CPI, EFI, GII, SEDA, DBI, GSCI, HDI, VATGAP, GDP per capita) affect the level of risk of ML/TF in the countries of EU, the authors use a unique data set of 24 destination countries of EU over the period 2012–2019. The article deals with two main research goals: to develop a nonlinear model and optimize the ML/TF risk by implementation of nonlinear optimization methods. The authors contribute: (i) providing the cross-country statistical analysis; (ii) creating the new nonlinear mathematical-statistical computational model (MSCM); and (iii) describing the observed dependent variable (Basel AML index). This study deepens previous knowledge in this research field and, in addition to the panel regression analysis, also applies nonlinear regression analysis to model the behavior of the investigated system (with nonlinearity). Our results point out the differences between the estimates of the investigated system behavior when using panel and nonlinear regression analysis. Based on the developed MSC model, the optimization procedure is conducted by applying an interior point method and MATLAB toolboxes and the second goal is achieved: the statement that such values of input variables at which the risk of legalization of income from criminal activity will be minimal. [ABSTRACT FROM AUTHOR]

The solution of the so-called mixed-integer optimization problem is an important challenge for modern life sciences. A wide range of methods has been developed for its solution, including metaheuristics approaches. Here, a modification is proposed of the differential evolution entirely parallel (DEEP) method introduced recently that was successfully applied to mixed-integer optimization problems. The triangulation recombination rule was implemented and the recombination coefficients were included in the evolution process in order to increase the robustness of the optimization. The deduplication step included in the procedure ensures the uniqueness of individual integer-valued parameters in the solution vectors. The developed algorithms were implemented in the DEEP software package and applied to three bioinformatic problems. The application of the method to the optimization of predictors set in the genomic selection model in wheat resulted in dimensionality reduction such that the phenotype can be predicted with acceptable accuracy using a selected subset of SNP markers. The method was also successfully used to optimize the training set of samples for such a genomic selection model. According to the obtained results, the developed algorithm was capable of constructing a non-linear phenomenological regression model of gene expression in developing a Drosophila eye with almost the same average accuracy but significantly less standard deviation than the linear models obtained earlier. [ABSTRACT FROM AUTHOR]

We developed two models for real-time monitoring and forecasting of the evolution of the COVID-19 pandemic: a non-linear regression model and an error correction model. Our strategy allows us to detect pandemic peaks and make short- and long-term forecasts of the number of infected, deaths and people requiring hospitalization and intensive care. The non-linear regression model is implemented in an expert system that automatically allows the user to fit and forecast through a graphical interface. This system is equipped with a control procedure to detect trend changes and define the end of one wave and the beginning of another. Moreover, it depends on only four parameters per series that are easy to interpret and monitor along time for each variable. This feature enables us to study the effect of interventions over time in order to advise how to proceed in future outbreaks. The error correction model developed works with cointegration between series and has a great forecast capacity. Our system is prepared to work in parallel in all the Autonomous Communities of Spain. Moreover, our models are compared with a SIR model extension (SCIR) and several models of artificial intelligence. [ABSTRACT FROM AUTHOR]

SPSS model syntax was defined and used to evaluate the individual performance of 49 linear and non-linear models to fit the lactation curve of 159 Murciano-Granadina goats selected for genotyping analyses. Lactation curve shape, peak and persistence were evaluated for each model using 3107 milk yield controls with an average of 3.78 ± 2.05 lactations per goat. Best fit (Adjusted R2) values (0.47) were reached by the five-parameter logarithmic model of Ali and Schaeffer. Three main possibilities were detected: non-fitting (did not converge), standard (Adjusted R2 over 75%) and atypical curves (Adjusted R2 below 75%). All the goats fitted for 38 models. The ability to fit different possible functional forms for each goat, which progressively increased with the number of parameters comprised in each model, translated into a higher sensitivity to explaining curve shape individual variability. However, for models for which all goats fitted, only moderate increases in explanatory and predictive potential (AIC, AICc or BIC) were found. The Ali and Schaeffer model reported the best fitting results to study the genetic variability behind goat milk yield and perhaps enhance the evaluation of curve parameters as trustable future selection criteria to face the future challenges offered by the goat dairy industry. [ABSTRACT FROM AUTHOR]

Time series data for decision problems such as energy demand forecasting are often derived from uncertain assessments, and do not meet any statistical assumptions. The interval grey number becomes an appropriate representation for an uncertain and imprecise observation. In order to obtain nonlinear interval grey numbers with better forecasting accuracy, this study proposes a combined model by fusing interval grey numbers estimated by neural networks (NNs) and the grey prediction models. The proposed model first uses interval regression analysis using NNs to estimate interval grey numbers for a real valued sequence; and then a grey residual modification model is constructed using the upper and lower wrapping sequences obtained by NNs. It turns out that two different kinds of interval grey numbers can be estimated by nonlinear interval regression analysis. Forecasting accuracy on real data sequences was then examined by the best non-fuzzy performance values of the combined model. The proposed combined model performed well compared with the other interval grey prediction models considered. [ABSTRACT FROM AUTHOR]