Asymptotic for LS estimators in the EV regression model for dependent errors

Filomat ◽  
2017 ◽  
Vol 31 (15) ◽  
pp. 4845-4856
Author(s):  
Konrad Furmańczyk
Keyword(s):  
Regression Model ◽  
Functional Dependence ◽  
Dependent Data ◽  
Errors In Variables ◽  
Mixing Conditions ◽  
Asymptotic Results ◽  
Dependence Measure ◽  
Wide Range ◽  
Ev Regression Model ◽  
Linear And Nonlinear

We study consistency and asymptotic normality of LS estimators in the EV (errors in variables) regression model under weak dependent errors that involve a wide range of linear and nonlinear time series. In our investigations we use a functional dependence measure of Wu [16]. Our results without mixing conditions complete the known asymptotic results for independent and dependent data obtained by Miao et al. [7]-[10].

scholarly journals ITERATIONS OF DEPENDENT RANDOM MAPS AND EXOGENEITY IN NONLINEAR DYNAMICS

2021 ◽  
pp. 1-38
Author(s):  
Zinsou Max Debaly ◽  
Lionel Truquet
Keyword(s):  
Time Series ◽  
Nonlinear Models ◽  
Functional Dependence ◽  
National Academy Of Sciences ◽  
Random Maps ◽  
Dependence Measure ◽  
Binary Choice Models ◽  
Wide Range ◽  
Categorical Time Series ◽  
Academy Of Sciences

Abstract We discuss the existence and uniqueness of stationary and ergodic nonlinear autoregressive processes when exogenous regressors are incorporated into the dynamic. To this end, we consider the convergence of the backward iterations of dependent random maps. In particular, we give a new result when the classical condition of contraction on average is replaced with a contraction in conditional expectation. Under some conditions, we also discuss the dependence properties of these processes using the functional dependence measure of Wu (2005, Proceedings of the National Academy of Sciences 102, 14150–14154) that delivers a central limit theorem giving a wide range of applications. Our results are illustrated with conditional heteroscedastic autoregressive nonlinear models, Generalized AutoRegressive Conditional Heteroskedasticity (GARCH) processes, count time series, binary choice models, and categorical time series for which we provide many extensions of existing results.

scholarly journals Asymptotic normality of a simple linear EV regression model with martingale difference errors

Filomat ◽  
2014 ◽  
Vol 28 (9) ◽  
pp. 1817-1825
Author(s):  
Guo-Liang Fan ◽  
Tian-Heng Chen
Keyword(s):  
Regression Model ◽  
Least Squares ◽  
Measurement Errors ◽  
Least Squares Method ◽  
Error Variance ◽  
Martingale Difference ◽  
Errors In Variables ◽  
Ev Regression Model ◽  
Biased Estimators ◽  
Better Than

This paper considers the estimation of a linear EV (errors-in-variables) regression model under martingale difference errors. The usual least squares estimations lead to biased estimators of the unknown parametric when measurement errors are ignored. By correcting the attenuation we propose a modified least squares estimator for a parametric component and construct the estimators of another parameter component and error variance. The asymptotic normalities are also obtained for these estimators. The simulation study indicates that the modified least squares method performs better than the usual least squares method.

Evaluation of the accuracy indicators in determination of the coating thickness by crater grinding method

2020 ◽  
Vol 86 (7) ◽  
pp. 39-44
Author(s):  
K. V. Gogolinsky ◽  
A. E. Ivkin ◽  
V. V. Alekhnovich ◽  
A. Yu. Vasiliev ◽  
A. E. Tyurnina ◽  
...  
Keyword(s):  
Coating Thickness ◽  
Functional Dependence ◽  
Measurement Procedure ◽  
Metrological Certification ◽  
Measuring Instruments ◽  
Properties Of Coatings ◽  
Special Equipment ◽  
Grinding Method ◽  
Accuracy Of Measurements ◽  
Wide Range

Thickness is one of the key indicators characterizing the quality and functional properties of coatings. Various indirect methods (electromagnetic, radiation, optical) most often used in practice to measure thickness are based on the functional dependence of a particular physical parameter of the system «base – coating» on the coating thickness. The sensitivity of these procedures to the certain properties of coatings imposes the main restriction to the accuracy of measurements. Therefore, the development and implementation of the approaches based on direct measurements of geometric parameters of the coating appears expedient. These methods often belong to the class of «destructive» and, in addition to measuring instruments, require the use of special equipment. To ensure the uniformity of measurements in the laboratory or technological control, these methods are isolated as a separate procedure (method) and must undergo metrological certification in accordance with GOST R 8.563–2009. We present implementation, metrological certification and practical application of the method for measuring thickness of coatings by crater-grinding method. The principles of technical implementation of test equipment, measurement procedure and calculation formulas are described. The results of evaluating the accuracy indicators of the proposed procedure by calculation and experimental methods are presented. In both cases, the relative error did not exceed 6%. The applicability of the developed technique is shown for a wide range of coating materials (from soft metals to superhard ceramics) of different thickness (with from units to hundreds of micrometers). Apart from the goals of process control and outgoing inspection, the method can be recommended as a reference measurement procedure for calibration of measures and adjusting samples for various types of thickness gauges.

scholarly journals Towards the Dependence on Parameters for the Solution of the Thermostatted Kinetic Framework

Axioms ◽  
2021 ◽  
Vol 10 (2) ◽  
pp. 59
Author(s):  
Bruno Carbonaro ◽  
Marco Menale
Keyword(s):  
Complex System ◽  
Continuous Dependence ◽  
Social Role ◽  
Probability Distributions ◽  
Functional Dependence ◽  
Transition Probability ◽  
Classical Mechanics ◽  
Human Society ◽  
Wide Range ◽  
Probability Densities

A complex system is a system involving particles whose pairwise interactions cannot be composed in the same way as in classical Mechanics, i.e., the result of interaction of each particle with all the remaining ones cannot be expressed as a sum of its interactions with each of them (we cannot even know the functional dependence of the total interaction on the single interactions). Moreover, in view of the wide range of its applications to biologic, social, and economic problems, the variables describing the state of the system (i.e., the states of all of its particles) are not always (only) the usual mechanical variables (position and velocity), but (also) many additional variables describing e.g., health, wealth, social condition, social rôle ⋯, and so on. Thus, in order to achieve a mathematical description of the problems of everyday’s life of any human society, either at a microscopic or at a macroscpoic scale, a new mathematical theory (or, more precisely, a scheme of mathematical models), called KTAP, has been devised, which provides an equation which is a generalized version of the Boltzmann equation, to describe in terms of probability distributions the evolution of a non-mechanical complex system. In connection with applications, the classical problems about existence, uniqueness, continuous dependence, and stability of its solutions turn out to be particularly relevant. As far as we are aware, however, the problem of continuous dependence and stability of solutions with respect to perturbations of the parameters expressing the interaction rates of particles and the transition probability densities (see Section The Basic Equations has not been tackled yet). Accordingly, the present paper aims to give some initial results concerning these two basic problems. In particular, Theorem 2 reveals to be stable with respect to small perturbations of parameters, and, as far as instability of solutions with respect to perturbations of parameters is concerned, Theorem 3 shows that solutions are unstable with respect to “large” perturbations of interaction rates; these hints are illustrated by numerical simulations that point out how much solutions corresponding to different values of parameters stay away from each other as t→+∞.

scholarly journals Automated System for Kinetic Analysis of Particle Size Distributions for Pharmaceutically Relevant Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
John-Bruce D. Green ◽  
Phillip W. Carter ◽  
Yingqing Zhang ◽  
Dipa Patel ◽  
Priyanka Kotha ◽  
...  
Keyword(s):  
Particle Size ◽  
Clinical Importance ◽  
Automated System ◽  
Size Distributions ◽  
Mixing Conditions ◽  
Particle Size Distributions ◽  
Complex Formulation ◽  
Wide Range ◽  
Key Variables ◽  
Kinetics Of

Detailing the kinetics of particle formation for pharmaceutically relevant solutions is challenging, especially when considering the combination of formulations, containers, and timescales of clinical importance. This paper describes a method for using commercial software Automate with a stream-selector valve capable of sampling container solutions from within an environmental chamber. The tool was built to monitor changes in particle size distributions via instrumental particle counters but can be adapted to other solution-based sensors. The tool and methodology were demonstrated to be highly effective for measuring dynamic changes in emulsion globule distributions as a function of storage and mixing conditions important for parenteral nutrition. Higher levels of agitation induced the fastest growth of large globules (≥5 μm) while the gentler conditions actually showed a decrease in the number of these large globules. The same methodology recorded calcium phosphate precipitation kinetics as a function of [Ca2+] and pH. This automated system is readily adaptable to a wide range of pharmaceutically relevant systems where the particle size is expected to vary with time. This instrumentation can dramatically reduce the time and resources needed to probe complex formulation issues while providing new insights for monitoring the kinetics as a function of key variables.

scholarly journals COMPARATIVE ANALYSIS OF DIFFERENT CRITERIA OF SITE STRUCTURAL STABILITY IN THE TIME SERIES

2019 ◽  
pp. 119-128
Author(s):  
Liliya Andreevna Landman ◽  
Andrei Vladimirovich Faddeenkov
Keyword(s):  
Time Series ◽  
Regression Model ◽  
Structural Changes ◽  
Least Squares Method ◽  
Complex Structure ◽  
Standard Normal Distribution ◽  
Regression Equations ◽  
Unknown Parameters ◽  
Chow Test ◽  
Wide Range

The concept of structure is used to describe a set of stable relations between the main parts of the object, which describe its integrity and identity, i.e, preserving the basic properties for a wide range of internal and external changes. This concept usually relates to the concepts of system and organization. The structure expresses a stable part of the system that is slightly changed during different reforms. Over the years structural changes take place because of active economic policy or as a result of spontaneous, uncontrollable processes. Therefore, it seems to be quite natural to find out whether there have been structural changes in the observation period, and to find them reflected in the specification of the model. The basic ideas of methods for determining structural changes in the time series dynamics have been considered, such as Chow test, Gujarati test and Poirier method. The power study was conducted for the three possible cases of change in time series trends. The random error was modeled according to the standard normal distribution. A linear multiple regression model with three independent variables was used as a time series model. Estimation of the vector of unknown parameters of the model was conducted using least squares method. For each of the three criteria the of test the null hypothesis about time series instability was carried out using the F -criterion, which involves finding the residual sum of squares of a regression model and analysis of correlation between its decline and the loss of degrees of freedom. It can be noted that Gujarati and Poirier equations have a more complex structure than equation of Chow test; however, using Chow test assumes estimation of the parameters of the three regression equations.

Empirical analysis of time series using feature selection algorithms

2021 ◽  
Author(s):  
Mikhail Kanevski
Keyword(s):  
Machine Learning ◽  
Time Series ◽  
Feature Selection ◽  
Dimensional Space ◽  
Multivariate Time Series ◽  
Feature Space ◽  
Real Data ◽  
Theoretical Concepts ◽  
Wide Range ◽  
Linear And Nonlinear

<p>Nowadays a wide range of methods and tools to study and forecast time series is available. An important problem in forecasting concerns embedding of time series, i.e. construction of a high dimensional space where forecasting problem is considered as a regression task. There are several basic linear and nonlinear approaches of constructing such space by defining an optimal delay vector using different theoretical concepts. Another way is to consider this space as an input feature space – IFS, and to apply machine learning feature selection (FS) algorithms to optimize IFS according to the problem under study (analysis, modelling or forecasting). Such approach is an empirical one: it is based on data and depends on the FS algorithms applied. In machine learning features are generally classified as relevant, redundant and irrelevant. It gives a reach possibility to perform advanced multivariate time series exploration and development of interpretable predictive models.</p><p>Therefore, in the present research different FS algorithms are used to analyze fundamental properties of time series from empirical point of view. Linear and nonlinear simulated time series are studied in detail to understand the advantages and drawbacks of the proposed approach. Real data case studies deal with air pollution and wind speed times series. Preliminary results are quite promising and more research is in progress.</p>

scholarly journals Adverse drug reactions associated with treatment in patients with chronic rheumatic diseases in childhood: a retrospective real life review of a single center cohort

2020 ◽  
Vol 60 (1) ◽  
Author(s):  
Manar Amanouil Said ◽  
Liana Soido Teixeira e Silva ◽  
Aline Maria de Oliveira Rocha ◽  
Gustavo Guimarães Barreto Alves ◽  
Daniela Gerent Petry Piotto ◽  
...  
Keyword(s):  
Risk Factors ◽  
Regression Model ◽  
Children And Adolescents ◽  
Adverse Drug Reactions ◽  
Rheumatic Diseases ◽  
Real Life ◽  
Drug Reactions ◽  
Wide Range ◽  
Disease Modifying ◽  
Chronic Rheumatic Diseases

Abstract Background Adverse drug reactions (ADRs) are the sixth leading causes of death worldwide; monitoring them is fundamental, especially in patients with disorders like chronic rheumatic diseases (CRDs). The study aimed to describe the ADRs investigating their severity and associated factors and resulting interventions in pediatric patients with CRDs. Methods A retrospective, descriptive and analytical study was conducted on a cohort of children and adolescents with juvenile idiopathic arthritis (JIA), juvenile systemic lupus erythematosus (JSLE) and juvenile dermatomyositis (JDM). The study evaluated medical records of the patients to determine the causality and the management of ADRs. In order to investigate the risk factors that would increase the risk of ADRs, a logistic regression model was carried out on a group of patients treated with the main used drug. Results We observed 949 ADRs in 547 patients studied. Methotrexate (MTX) was the most frequently used medication and also the cause of the most ADRs, which occurred in 63.3% of patients, followed by glucocorticoids (GCs). Comparing synthetic disease-modifying anti-rheumatic drugs (sDMARDs) vs biologic disease-modifying anti-rheumatic drugs (bDMARDs), the ADRs attributed to the former were by far higher than the latter. In general, the severity of ADRs was moderate and manageable. Drug withdrawal occurred in almost a quarter of the cases. In terms of risk factors, most patients who experienced ADRs due to MTX, were 16 years old or younger and received MTX in doses equal or higher than 0.6 mg/kg/week. Patients with JIA and JDM had a lower risk of ADRs than patients with JSLE. In the multiple regression model, the use of GCs for over 6 months led to an increase of 0.5% in the number of ADRs. Conclusions Although the ADRs highly likely affect a wide range of children and adolescents with CRDs they were considered moderate and manageable cases mostly. However, triggers of ADRs need further investigations.

scholarly journals Robust Support Vector Regression Model in the Presence of Outliers and Leverage Points

2017 ◽  
Vol 11 (8) ◽  
pp. 92
Author(s):  
Waleed Dhhan ◽  
Habshah Midi ◽  
Thaera Alameer
Keyword(s):  
Regression Model ◽  
Support Vector Regression ◽  
Support Vector ◽  
Data Set ◽  
Support Vector Regression Model ◽  
Leverage Points ◽  
Linear Relationships ◽  
Linear And Nonlinear ◽  
Abnormal Points ◽  
Robust Support Vector Regression

Support vector regression is used to evaluate the linear and non-linear relationships among variables. Although it is non-parametric technique, it is still affected by outliers, because the possibility to select them as support vectors. In this article, we proposed a robust support vector regression for linear and nonlinear target functions. In order to carry out this goal, the support vector regression model with fixed parameters is used to detect and minimize the effects of abnormal points in the data set. The efficiency of the proposed method is investigated by using real and simulation examples.

Reflection of Conductive Plane Covered by Double Inhomogeneous Plasma Slab

2012 ◽  
Vol 229-231 ◽  
pp. 941-944
Author(s):  
Fei Yan ◽  
Zhong Cai Yuan ◽  
Yong Wang ◽  
Shi Lian Gong ◽  
Zheng Li
Keyword(s):  
Functional Dependence ◽  
Inhomogeneous Plasma ◽  
Plasma Electron ◽  
Reflection Coefficients ◽  
Frequency Range ◽  
Wide Range ◽  
Plasma Slab ◽  
Electromagnetic Signals ◽  
Set Up ◽  
Plasma Electron Density

This paper presents numerical results in the form of graphs of the power reflection coefficients for electromagnetic signals normally incident upon a conductive plane covered with two layers of inhomogeneous plasma slabs. The plasma electron density varies only in the direction perpendicular to the plane. Parameters considered in the computation cover a relatively wide range and the functional dependence of the power reflection coefficients on these parameters is studied. The results indicate that in a rather broad frequency range, the electromagnetic attenuations by the double slabs obviously excel the sum of attenuations resulted from two plasma layers when each layer exits respectively. The structure presented is easy to set up, which is instructive for plasma stealth.

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