Search

Finite mixtures with different regression models for different mixture components naturally arise in statistical analysis of biological and sociological data. In this paper a model of mixtures with varying concentrations is considered in which the mixing probabilities are different for different observations. A modified local linear estimation (mLLE) technique is developed to estimate the regression functions of the mixture component nonparametrically. Consistency of the mLLE is demonstrated. Performance of mLLE and a modified Nadaraya–Watson estimator (mNWE) is assessed via simulations. The results confirm that the mLLE technique overcomes the boundary effect typical to the NWE.

In business process management, business process change analysis is the key link to ensure the flexibility and adaptability of the system. The existing methods mostly focus on the change analysis of a single business process from the perspective of control flow, ignoring the influence of data changes on collaborative processes with information interaction. In order to compensate for this deficiency, this paper proposes a rule-driven consistency analysis method for data changes in collaborative processes. Firstly, it analyzes the influence of data changes on other elements (such as activities, data, roles, and guards) in collaborative processes, and gives the definition of data influence. Secondly, the optimal alignment technology is used to explore how data changes interfere with the expected behavior of deviation activities, and decision rules are integrated into the Petri net model to accurately evaluate and screen out the effective expected behavior that conforms to business logic and established rules. Finally, the initial optimal alignment is repaired according to the screened effective expected behavior, and the consistency of business processes is recalculated. The experimental results show that the introduced rule constraint mechanism can effectively avoid the misjudgment of abnormal behavior. Compared with the traditional method, the average accuracy, recall rate, and F1-score of effective expected behavior are improved by 4%, 4.7%, and 4.3%, respectively. In addition, the repaired optimal alignment significantly enhances the system’s ability to respond quickly and self-adjust to data changes, providing a strong support for the intelligent and automated transformation of business process management.

The aim of this manuscript is to introduce and analyze a stochastic finite difference scheme for Ito stochastic partial differential equations. We also discuss the consistency, stability, and convergence for the stochastic finite difference scheme. The numerical simulations obtained from the proposed stochastic finite difference scheme show the efficiency of the suggested stochastic finite difference scheme.

Addressing current challenges in music aesthetic education at colleges and universities, this study introduces an evaluation system rooted in hierarchical analysis to advance goal management in teaching. Expert consensus guided the selection and weighting of evaluation indices across a province’s higher education landscape. Implementing this system through information technology and data analysis software, our research analyzed teaching examples to gauge effectiveness. Results demonstrated improved teaching quality, with experimental and control groups showing average score increases of 1.24 and 1.03 points, respectively. This underscores the system’s potential to elevate the management and organization of music aesthetic education, contributing valuable insights to its evaluation theory and enhancing educational quality in Chinese colleges and universities.

This paper deals with least squares estimation for the Cox–Ingersoll–Ross model with fractional Lévy noise from discrete observations. The contrast function is given to obtain the least squares estimators. The consistency and asymptotic distribution of estimators are derived when a small dispersion coefficient $\varepsilon \to 0$, $n \to \infty $, $\varepsilon {n^{\frac{1}{2} - d}} \to 0$, and $n\varepsilon \to \infty $ simultaneously.

In this paper, the enhanced higher-order unconditionally positive finite difference method is developed to solve the linear, non-linear and system advection diffusion reaction equations. Investigation into the effectiveness and efficiency of the proposed method is carried out by calculating the convergence rate, error and computational time. A comparison of the solutions obtained by the enhanced higher-order unconditionally positive finite difference and exact solution is conducted for validation purposes. The numerical results show that the developed method reduced the time taken to solve the linear and non-linear advection diffusion reaction equations as compared to the results obtained by the higher-order unconditionally positive finite difference method.

Consistency checking is one of the reasons for the Analytic Hierarchy Process (AHP) leadership in publications on multiple criteria decision-making (MCDM). Consistency is a measure of the quality of data input in the AHP. The theory of AHP provides indicators for the consistency of data. When an indicator is out of the desired interval, the data must be reviewed. This article presents a method for improving the consistency of reviewing the data input in an AHP application. First, a conventional literature review is presented on the theme. Then, an innovative tool of artificial intelligence is shown to confirm the main result of the conventional review: this topic is still attracting interest from AHP and MCDM researchers. Finally, a simple technique for consistency improvement is presented and illustrated with a practical case of MCDM: supplier selection by a company.

The transformation method between the linguistic judgement matrix and other four forms of preference information is researched in this paper. The four forms of preference information are preference ordering, utility value, reciprocal judgement matrices and complementary judgement matrices. First, based on the definition of preference information, the mutual transformation methods of linguistic judgement matrix and other four forms of preference information are given. Then new transformation equations are obtained. Next, it is proved that when the linguistic judgement matrix has complete consistency, the other four forms of preference information will have complete consistency too. Finally, a numerical analysis is offered to show that these methods are feasible and effective.

This paper is concerned with $ L_{\infty} $-norm minimum distance estimation for stochastic differential equations driven by small fractional Lévy noise. By applying the Gronwall-Bellman lemma, Chebyshev's inequality and Taylor's formula, the minimum distance estimator is established and the consistency and asymptotic distribution of the estimator are derived when a small dispersion coefficient $ \varepsilon\rightarrow 0 $.

New energy vehicles (NEVs) are the main direction for the development of the global automobile industry. Evaluating and analyzing the competitiveness of new energy vehicle enterprises (NEVEs) is of great significance for promoting their development. In order to explore the current situation of NEVEs in Henan Province, this paper firstly constructs a competitiveness evaluation index system for NEVEs, comprising both quantitative and qualitative indexes. Then, a new definition of consistency, the consistency measure level, and corresponding improvement methods for interval multiplicative preference relations (IMPRs) are proposed. On this basis, fuzzy group decision-making models with IMPRs are constructed to deal with the ambiguity and uncertainty of the decision information, where consistency and consensus are both considered. In our case study, decision results are derived using Lingo 11.0 software. The results of this paper show that the degree of specialization has the greatest impact on the competitiveness of NEVEs, and some NEVEs are deficient in this regard. Related suggestions based on expert evaluation results are also provided. In addition, a comparison with other consistency improvement methods of IMPRs reveals that the methods proposed utilize the original information provided to decision-makers to the utmost degree.

This study seeks to investigate the performance as well as the performance consistency of Iranian mutual funds during the current and subsequent periods. To this end, the Capital Asset Pricing Model along with CARHART’s four-factor model have been utilized to analyze the performance and performance consistency of investment funds. In order to examine persistency, all models are divided into 10 portfolios (10 distributions) based on the performance of the past one year. Then we considered succeeding 12 months later. Our results revealed that mutual funds in Iran have not outperformed the market, but there is performance consistency. This means mutual funds with the best performance (worst performance) will perform the same (better or worse) in the upcoming years. However, the extent of the best and worst performance of mutual funds is not significantly different. The historical performance of mutual funds can, to some extent, explain future performance. Therefore, investors' reliance on the backgrounds of investment funds as a recourse for investment is well justified. In other words, if investors spend on mutual funds with a past outperformance, there is a reasonable assurance to be repeated the past and will be among the winning funds in future periods. The opposite is also true

In this paper, several bootstrap properties of m-generalized order statistics (m-GOSs) with variable rank (central and intermediate) are revealed. We study the inconsistency, weak consistency and strong consistency of bootstrapping central and intermediate m-GOSs when the normalizing constants are assumed to be known or estimated from the re-sampled data using a proper re-sample size. Furthermore, sufficient conditions for the weak and strong consistencies of the bootstrapping distributions of central and intermediate m-GOSs based on the normalizing constant estimators are given. Finally, a simulation study is conducted to determine the optimal bootstrap re-sample size corresponding to the best fitting of the bootstrapping distribution.

For decades, understanding the dynamics of infectious diseases and halting their spread has been a major focus of mathematical modelling and epidemiology. The stochastic SIRS (susceptible–infectious–recovered–susceptible) reaction–diffusion model is a complicated but crucial computational scheme due to the combination of partial immunity and an incidence rate. Considering the randomness of individual interactions and the spread of illnesses via space, this model is a powerful instrument for studying the spread and evolution of infectious diseases in populations with different immunity levels. A stochastic explicit finite difference scheme is proposed for solving stochastic partial differential equations. The scheme is comprised of predictor–corrector stages. The stability and consistency in the mean square sense are also provided. The scheme is applied to diffusive epidemic models with incidence rates and partial immunity. The proposed scheme with space’s second-order central difference formula solves deterministic and stochastic models. The effect of transmission rate and coefficient of partial immunity on susceptible, infected, and recovered people are also deliberated. The deterministic model is also solved by the existing Euler and non-standard finite difference methods, and it is found that the proposed scheme forms better than the existing non-standard finite difference method. Providing insights into disease dynamics, control tactics, and the influence of immunity, the computational framework for the stochastic SIRS reaction–diffusion model with partial immunity and an incidence rate has broad applications in epidemiology. Public health and disease control ultimately benefit from its application to the study and management of infectious illnesses in various settings.

In this paper, we study the problem of simultaneous variable selection and estimation for longitudinal ordinal data with high-dimensional covariates. Using the penalized generalized estimation equation (GEE) method, we obtain some asymptotic properties for these types of data in the case that the dimension of the covariates pn tends to infinity as the number of cluster n approaches to infinity. More precisely, under appropriate regular conditions, all the covariates with zero coefficients can be examined simultaneously with probability tending to 1, and the estimator of the non-zero coefficients exhibits the asymptotic Oracle properties. Finally, we also perform some Monte Carlo studies to illustrate the theoretical analysis. The main result in this paper extends the elegant work of Wang et al. [1] to the multinomial response variable case.

The varying coefficient model assumes that the regression function depends linearly on some regressors, and that the regression coefficients are smooth functions of other predictor variables. It provides an appreciable flexibility in capturing the underlying dynamics in data and avoids the so-called "curse of dimensionality" in analyzing complex and multivariate nonlinear structures. Existing estimation methods usually assume that the errors for the model are independent; however, they may not be satisfied in practice. In this study, we investigated the estimation for the varying coefficient model with correlated errors via B-spline. The B-spline approach, as a global smoothing method, is computationally efficient. Under suitable conditions, the convergence rates of the proposed estimators were obtained. Furthermore, two simulation examples were employed to demonstrate the performance of the proposed approach and the necessity of considering correlated errors.

In this paper, an efficient artificial neural network is proposed for solving a generalized vertical complementarity problem. Based on the properties of log-exponential function, the generalized vertical complementarity problem is reformulated in terms of the unconstrained minimization problem. The existence and the convergence of the trajectory of the neural network are addressed in detail. In addition, it is also proved that if the neural network problem has an equilibrium point under some initial condition, the equilibrium point is asymptotically stable or exponentially stable under certain conditions. At the end of this paper, the simulation results for the generalized bimatrix game are illustrated to show the efficiency of the neural network.

In the context of some multi-criteria decision-making methods, such as the Analytic Hierarchy Process, an expert is required to compare entities, e.g. alternatives and criteria. However, often, for various reasons, the expert cannot provide judgments on all pairs of entities. For these cases, several completion methods have been proposed in the literature to estimate the missing values of pairwise comparison matrices. In this paper, we study the similarity of eleven completion methods on the basis of numerical simulations and hierarchical clustering. We perform simulations for matrices of different orders considering various numbers of missing comparisons. Finally, the results suggest the existence of a cluster of five extremely similar methods, and a method significantly dissimilar from all the others.

The consistency of the classical Richardson extrapolation (CRE), a simple and robust computational device, is analysed for the case where the underlying method is an explicit one-step numerical method for ordinary differential equations with order of consistency one or two. It is shown in the classical framework that the CRE increases the order of consistency by one. The convergence of the method is proved by the assumption that the time-stepping operator of the base method has the Lipschitz property in its second argument.

Recent debate about the error theory has taken a 'formal turn'. On the one hand, there are those who argue that the error theory should be rejected because of its difficulties in providing a convincing formal account of the logic and semantics of moral claims. On the other hand, there are those who claim that such formal objections fail, maintaining that arguments against the error theory must be of a substantive rather than a formal kind. In this paper, we argue that formal objections to the error theory cannot be eschewed but must be met head-on. [ABSTRACT FROM AUTHOR]

Abstract In this paper, we construct a method with eight steps that belongs to the family of Obrechkoff methods. Due to the explicit nature of the new method, not only does it not require another method as predictor, but it can also be considered as a suitable predictive technique to be used with implicit methods. Periodicity and error terms are studied when applied to solve the radial Schrödinger equation, considering different energy levels. We show its advantages in terms of accuracy, consistency, and convergence in comparison with other methods of the same order appearing in the literature.

In this paper, we consider the regression model with fixed design: Yi=g(xi)+εi{Y}_{i}=g\left({x}_{i})+{\varepsilon }_{i}, 1≤i≤n1\le i\le n, where {xi}\left\{{x}_{i}\right\} are the nonrandom design points, and {εi}\left\{{\varepsilon }_{i}\right\} is a sequence of martingale, and gg is an unknown function. Nonparametric estimator gn(x){g}_{n}\left(x) of g(x)g\left(x) will be introduced and its strong convergence properties are established.

In this article, one standard and four nonstandard finite difference methods are used to solve a cross-diffusion malignant invasion model. The model consists of a system of nonlinear coupled partial differential equations (PDEs) subject to specified initial and boundary conditions, and no exact solution is known for this problem. It is difficult to obtain theoretically the stability region of the classical finite difference scheme to solve the set of nonlinear coupled PDEs, this is one of the challenges of this class of method in this work. Three nonstandard methods abbreviated as NSFD1, NSFD2, and NSFD3 are considered from the study of Chapwanya et al., and these methods have been constructed by the use of a more general function replacing the denominator of the discrete derivative and nonlocal approximations of nonlocal terms. It is shown that NSFD1, which preserves positivity when used to solve classical reaction-diffusion equations, does not inherit this property when used for the cross-diffusion system of PDEs. NSFD2 and NSFD3 are obtained by appropriate modifications of NSFD1. NSFD2 is positivity-preserving when the functional relationship [ψ(h)]2=2ϕ(k){\left[\psi \left(h)]}^{2}=2\phi \left(k) holds, while NSFD3 is unconditionally dynamically consistent with respect to positivity. First, we show that NSFD2 and NSFD3 are not consistent methods. Second, we tried to modify NSFD2 in order to make it consistent but we were not successful. Third, we extend NSFD3 so that it becomes consistent and still preserves positivity. We denote the extended version of NSFD3 as NSFD5. Finally, we compute the numerical rate of convergence in time for NSFD5 and show that it is close to the theoretical value. NSFD5 is consistent under certain conditions on the step sizes and is unconditionally positivity-preserving.

This paper is presented in the context of sensitivity analysis (SA) of large-scale data assimilation (DA) models. We studied consistency, convergence, stability and roundoff error propagation of the reduced-space optimization technique arising in parallel 4D Variational DA problems. The results are helpful to understand the reliability of DA, to assess what confidence one can have that the simulation results are correct and to determine its configuration in any application. The main contributions of the present work are as follows. By using forward error analysis, we derived the number of conditions of the parallel approach. We found that the parallel approach reduces the number of conditions, revealing that it is more appropriate than the standard approach usually implemented in most operative software. As the background values are used as initial conditions of local PDE models, we analyzed stability with respect to time direction. Finally, we proved consistency of the proposed approach by analyzing local truncation errors of each computational kernel.

This paper presents a new class of fractional order Runge–Kutta (FORK) methods for numerically approximating the solution of fractional differential equations (FDEs). We construct explicit and implicit FORK methods for FDEs by using the Caputo generalized Taylor series formula. Due to the dependence of fractional derivatives on a fixed base point, in the proposed method, we had to modify the right-hand side of the given equation in all steps of the FORK methods. Some coefficients for explicit and implicit FORK schemes are presented. The convergence analysis of the proposed method is also discussed. Numerical experiments are presented to clarify the effectiveness and robustness of the method.

Regression analysis is a huge part of mathematical and applied statistics. Nonlinear regression analysis is a significant extension and complication of classical linear regression analysis, due to the use of nonlinear or partially nonlinear in parameters models that describe more adequately than linear model phenomena requiring statistical analysis. A large number of applied problems in the numerical scientific, technical, and humanitarian fields of knowledge give impetus to the development of nonlinear regression analysis. The task of estimation the vector signal parameter in the «signal + noise» observation models is a well-known problem of statistics of stochastic processes, and in the case of a nonlinear signal parameter is the problem of nonlinear regression analysis. Among the variety of nonlinear regression analysis problems the problem of estimating amplitudes and angular frequencies of the sum of harmonic oscillations that are observed against the background of a random noise, takes significant place due to its numerous applications. Statistical model of such a type is said to be trigonometric regression, and the problem of statistical estimation is called the problem of detecting hidden periodicities. The paper is devoted to the study of time continuous trigonometric regression model where the random noise is a linear L´evy driven stationary of the fourth order stochastic process with zero mean, integrable and square integrable impulse transmission function. This assumption leads to the integrability of the noise covariance function and cumulant function of the fourth order. To estimate unknown amplitudes and angular frequencies of such a trigonometric model we use the least squares estimators in the Walker sense, that is special parametric set are considered to distinguish properly different angular frequencies in the sum of harmonic oscillations. Theorem on strong consistency of the least squares estimators is proved in the paper under the assumption on the random noise described above. To obtain such a result a very important lemma was proved on the uniform tending to zero almost surely of the average value of L´evy-driven linear stochastic process Fourier transform. This Lemma is the main tool of the strong consistency Theorem proof. To prove the Theorem we, firstly, find some expressions for the least squares estimates of amplitudes via corresponding estimates of angular frequencies. Secondly, we substitute these formulas into the functional of the least squares method. The last step of the proof consists of the L2- norm transformation of the difference between empirical trigonometric regression function and true regression function such that this norm tends to zero almost surely if and on if the estimators are strongly consistent.

GARCH(1, 1) model is used for analysis and forecasting of financial and economic time series. In the classical version, the maximum likelihood method is used to estimate the model parameters. However, this method is not convenient for analysis of models with residuals distribution different from normal. In this paper, we consider M-estimator for the GARCH(1, 1) model parameters, which is a generalization of the maximum likelihood method. An algorithm for constructing an M-estimator is described and its asymptotic properties are studied. A set of conditions is formulated under which the estimator is strictly consistent and has an asymptotically normal distribution. This method allows to analyze models with different residuals distributions; in particular, models with stable and tempered stable distributions that allow to take into account the features of real financial data: volatility clustering, heavy tails, asymmetry.

This paper provides a useful supplement note for implementing the Kalman filters. The material presented in this work points out several significant highlights with emphasis on performance evaluation and consistency validation between the discrete Kalman filter (DKF) and the continuous Kalman filter (CKF). Several important issues are delivered through comprehensive exposition accompanied by supporting examples, both qualitatively and quantitatively for implementing the Kalman filter algorithms. The lesson learned assists the readers to capture the basic principles of the topic and enables the readers to better interpret the theory, understand the algorithms, and correctly implement the computer codes for further study on the theory and applications of the topic. A wide spectrum of content is covered from theoretical to implementation aspects, where the DKF and CKF along with the theoretical error covariance check based on Riccati and Lyapunov equations are involved. Consistency check of performance between discrete and continuous Kalman filters enables readers to assure correctness on implementing and coding for the algorithm. The tutorial-based exposition presented in this article involves the materials from a practical usage perspective that can provide profound insights into the topic with an appropriate understanding of the stochastic process and system theory.

We propose introducing fairness constraints to one of the most famous multi-criteria decision-making methods, the analytic hierarchy process (AHP). We offer a solution that guarantees consistency while respecting legally binding fairness constraints in AHP pairwise comparison matrices. Through a synthetic experiment, we generate the comparison matrices of different sizes and ranges/levels of the initial parameters (i.e., consistency ratio and disparate impact). We optimize disparate impact for various combinations of these initial parameters and observed matrix sizes while respecting an acceptable level of consistency and minimizing deviations of pairwise comparison matrices (or their upper triangles) before and after the optimization. We use a metaheuristic genetic algorithm to set the dually motivating problem and operate a discrete optimization procedure (in connection with Saaty’s 9-point scale). The results confirm the initial hypothesis (with 99.5% validity concerning 2800 optimization runs) that achieving fair ranking while respecting consistency in AHP pairwise comparison matrices (when comparing alternatives regarding given criterium) is possible, thus meeting two challenging goals simultaneously. This research contributes to the initiatives directed toward unbiased decision-making, either automated or algorithm-assisted (which is the case covered by this research).

Abstract Consider the heteroscedastic semiparametric regression model yi=xiβ+g(ti)+εi $y_{i}=x_{i}\beta+g(t_{i})+\varepsilon_{i}$, i=1,2,…,n $i=1, 2, \ldots, n$, where β is an unknown slope parameter, εi=σiei $\varepsilon_{i}=\sigma_{i}e_{i}$, σi2=f(ui) $\sigma^{2}_{i}=f(u_{i})$, (xi,ti,ui) $(x_{i},t_{i},u_{i})$ are nonrandom design points, yi $y_{i}$ are the response variables, f and g are unknown functions defined on the closed interval [0,1] $[0,1]$, random errors {ei} $\{e_{i} \}$ are negatively associated (NA) random variables with zero means. Whereas kernel estimators of β, g, and f have attracted a lot of attention in the literature, in this paper, we investigate their wavelet estimators and derive the strong consistency of these estimators under NA error assumption. At the same time, we also obtain the Berry–Esséen type bounds of the wavelet estimators of β and g.

In this paper, we propose a new consistency measurement for classification rule sets that is based on the similarity of their classification abilities. The similarity of the classification abilities of the two rule sets is evaluated though the similarity of the corresponding partitions of the feature space using the different rule sets. The proposed consistency measure can be used to measure the equivalent symmetry of subsystems decomposed from a large, complex cyber–physical system (CPS). It can be used to verify whether the same knowledge is obtained by the sensing data in the different subsystems. In the experiments, five decision tree algorithms and eighteen datasets from the UCI machine learning repository are employed to extract the classification rules, and the consistency between the corresponding rule sets is investigated. The classification rule sets extracted from the use of the C4.5 algorithm on the electrical grid stability dataset have a consistency of 0.88, which implies that the different subsystems contain almost equivalent knowledge about the network stability.

The main goal of this paper is to propose a two-step method for the estimation of parameters in non-linear mixed-effects models. A first-step estimate θ˜ of the vector θ of parameters is obtained by solving estimation equations, with a working covariance matrix as the identity matrix. It is shown that θ˜ is consistent. If, furthermore, we have an estimated covariance matrix, V^, by θ˜, a second-step estimator θ^ can be obtained by solving the optimal estimation equations. It is shown that θ^ maintains asymptotic optimality. We establish the consistency and asymptotic normality of the proposed estimators. Simulation results show the improvement of θ^ over θ˜. Furthermore, we provide a method to estimate the variance σ2 using the method of moments; we also assess the empirical performance. Finally, three real-data examples are considered.

Fractional differential equations describe nature adequately because of the symmetry properties that describe physical and biological processes. In this paper, a new approximation is found for the variable-order (VO) Riemann–Liouville fractional derivative (RLFD) operator; on that basis, an efficient numerical approach is formulated for VO time-fractional modified subdiffusion equations (TFMSDE). Complete theoretical analysis is performed, such as stability by the Fourier series, consistency, and convergence, and the feasibility of the proposed approach is also discussed. A numerical example illustrates that the proposed scheme demonstrates high accuracy, and that the obtained results are more feasible and accurate.

In statistical analyses, especially those using a multiresponse regression model approach, a mathematical model that describes a functional relationship between more than one response variables and one or more predictor variables is often involved. The relationship between these variables is expressed by a regression function. In the multiresponse nonparametric regression (MNR) model that is part of the multiresponse regression model, estimating the regression function becomes the main problem, as there is a correlation between the responses such that it is necessary to include a symmetric weight matrix into a penalized weighted least square (PWLS) optimization during the estimation process. This is, of course, very complicated mathematically. In this study, to estimate the regression function of the MNR model, we developed a PWLS optimization method for the MNR model proposed by a previous researcher, and used a reproducing kernel Hilbert space (RKHS) approach based on a smoothing spline to obtain the solution to the developed PWLS optimization. Additionally, we determined the symmetric weight matrix and optimal smoothing parameter, and investigated the consistency of the regression function estimator. We provide an illustration of the effects of the smoothing parameters for the estimation results using simulation data. In the future, the theory generated from this study can be developed within the scope of statistical inference, especially for the purpose of testing hypotheses involving multiresponse nonparametric regression models and multiresponse semiparametric regression models, and can be used to estimate the nonparametric component of a multiresponse semiparametric regression model used to model Indonesian toddlers’ standard growth charts.

Least absolute deviation is proposed as a robust estimator to solve the problem when the error has an asymmetric heavy-tailed distribution or outliers. In order to be insensitive to the above situation and select the truly important variables from a large number of predictors in the linear regression, this paper introduces a two-stage variable selection method named relaxed lad lasso, which enables the model to obtain robust sparse solutions in the presence of outliers or heavy-tailed errors by combining least absolute deviation with relaxed lasso. Compared with lasso, this method is not only immune to the rapid growth of noise variables but also maintains a better convergence rate, which is Opn−1/2. In addition, we prove that the relaxed lad lasso estimator has the property of consistency at large samples; that is, the model selects the number of important variables with a high probability of convergence to one. Through the simulation and empirical results, we further verify the outstanding performance of relaxed lad lasso in terms of prediction accuracy and the correct selection of informative variables under the heavy-tailed distribution.

In practice, measurement results are sometimes described by an estimate, which is not the best one as defined in the GUM. Such alternative estimates arise when the result of a measurement is not corrected for all systematic effects. No recommendation exists in the GUM for associating an uncertainty with an uncorrected estimate.

Abstract This paper is concerned with the estimation problem for incomplete information stochastic systems from discrete observations. The suboptimal estimation of the state is obtained by constructing the extended Kalman filtering equation. The approximate likelihood function is given by using a Riemann sum and an Itô sum to approximate the integrals in the continuous-time likelihood function. The consistency of the maximum likelihood estimator and the asymptotic normality of the error of estimation are proved by applying the martingale moment inequality, Hölder’s inequality, the Chebyshev inequality, the Burkholder–Davis–Gundy inequality and the uniform ergodic theorem. An example is provided to verify the effectiveness of the estimation methods.

This article introduces a novel two-stage variable selection method to solve the common asymmetry problem between the response variable and its influencing factors. In practical applications, we cannot correctly extract important factors from a large amount of complex and redundant data. However, the proposed method based on the relaxed lasso and the adaptive lasso, namely, the relaxed adaptive lasso, can achieve information symmetry because the variables it selects contain all the important information about the response variables. The goal of this paper is to preserve the relaxed lasso’s superior variable selection speed while imposing varying penalties on different coefficients. Additionally, the proposed method enjoys favorable asymptotic properties, that is, consistency with a fast rate of convergence with Opn−1. The simulation demonstrates that the proper variable recovery, i.e., the number of significant variables selected, and prediction accuracy of the relaxed adaptive lasso in a limited sample is superior to the regular lasso, relaxed lasso and adaptive lasso estimators.

We consider the preservation under products, finite powers, and forcing of a selection-principle-based covering property of T0 topological groups. Though the paper is partly a survey, it contributes some new information: (1) The product of a strictly o-bounded group with an o-bounded group is an o-bounded group—Corollary 1. (2) In the generic extension by a finite support iteration of ℵ1 Hechler reals the product of any o-bounded group with a ground model ℵ0 bounded group is an o-bounded group—Theorem 11. (3) In the generic extension by a countable support iteration of Mathias reals the product of any o-bounded group with a ground model ℵ0 bounded group is an o-bounded group—Theorem 12.

This article makes use of simultaneous decomposition of four quaternion matrixes to investigate some Sylvester-like quaternion matrix equation systems. We present some useful necessary and sufficient conditions for the consistency of the system of quaternion matrix equations in terms of the equivalence form and block matrixes. We also derive the general solution to the system according to the partition of the coefficient matrixes. As an application of the system, we present some practical necessary and sufficient conditions for the consistency of a ϕ-Hermitian solution to the system of quaternion matrix equations in terms of the equivalence form and block matrixes. We also provide the general ϕ-Hermitian solution to the system when the equation system is consistent. Moreover, we present some numerical examples to illustrate the availability of the results of this paper.

Abstract We study the minimum Skorohod distance estimation θε∗ $\theta _{\varepsilon}^{\ast }$ and minimum L1 $L_{1}$-norm estimation θε˜ $\widetilde {\theta _{\varepsilon}}$ of the drift parameter θ of a stochastic differential equation dXt=θXtdt+εdLtd $dX_{t}=\theta X_{t}\,dt+\varepsilon \,dL^{d}_{t}$, X0=x0 $X_{0}=x_{0}$, where {Ltd,0≤t≤T} $\{L^{d}_{t},0\leq t\leq T\}$ is a fractional Lévy process, ε∈(0,1] $\varepsilon \in (0,1]$. We obtain their consistency and limit distribution for fixed T, when ε→0 $\varepsilon \rightarrow 0$. Moreover, we also study the asymptotic laws of their limit distributions for T→∞ $T\rightarrow \infty $.

When examinees are classified into groups based on scores from educational assessment, two indices are widely used to gauge the psychometric quality of the classifications: accuracy and consistency. The two indices take correct classifications into consideration while overlooking incorrect ones, where unbalanced class distribution threatens the validity of results from the accuracy and consistency indices. The single values produced from the two indices also fail to address the inconsistent accuracy of the classifier across different cut score locations. The current study proposed the concept of classification quality, which utilizes the receiver operating characteristics (ROC) graph to comprehensively evaluate the performance of classifiers. The ROC graph illustrates the tradeoff between benefits (true positive rate) and costs (false positive rate) in classification. In this article, a simulation study was conducted to demonstrate how to generate and interpret ROC graphs in educational assessment and the benefits of using ROC graphs to interpret classification quality. The results show that ROC graphs provide an efficient approach to (a) visualize the fluctuating performance of scoring classifiers, (b) address the unbalanced class distribution issue inherent in the accuracy and consistency indices, and (c) produce more accurate estimation of the classification results.

The strength of a person’s beliefs can be measured by the buying and selling prices they offer on contingent promissory notes. Consider a promissory note contingent on a proposition; it pays off one unit of money if the proposition is true and nothing otherwise. The more strongly a person believes the proposition, the higher the minimum price would be at which they would sell it. The same would apply to the maximum purchase price. The well-known Dutch Book Argument claims that, if the person’s beliefs are rational, their buying/selling prices should combine additively, meaning that the price of a promissory note contingent on the disjunction of two incompatible propositions should be the sum of the prices of the promissory notes contingent on the individual incompatible propositions. This paper shows that the essence of the Dutch Book Argument is that rational belief is additive because money is additive. It is proved that, if the structure of the Dutch Book Argument is kept, but a nonadditive resource is substituted for money, then rational belief will follow a nonadditive combining rule. It is also shown how rational buying/selling prices behave when the pay-off amount of a contingent note changes.

This article introduces a new variant of the inventory routing problem related to real-world businesses. Specifically, in the beverage industry, business customers such as restaurants and bars, demand consistent delivery times, have different opening times and delivery time windows, and occasionally, due to special events, exhibit demands that exceed single-vehicle capacity leading to the need of splitting demands between several vehicles. We present two variants of a mathematical formulation that include all the characteristics of this inventory routing problem. In the first, we apply the maximum level policy, whereas in the second variant, we apply an order-up-to-level policy. As a solution technique, we propose a matheuristic based on an adaptive large neighborhood search algorithm for which we developed several destroy and repair operators specifically designed to address the special problem features. Extensive computational tests based on artificial and real-world instances affirm the efficiency of the solution approach. Furthermore, we analyze the solution quality, the impact of the characteristics and policies applied, and the practicability for the real world.

A multiresponse multipredictor semiparametric regression (MMSR) model is a combination of parametric and nonparametric regressions models with more than one predictor and response variables where there is correlation between responses. Due to this correlation we need to construct a symmetric weight matrix. This is one of the things that distinguishes it from the classical method, which uses a parametric regression approach. In this study, we theoretically developed a method of determining a confidence interval for parameters in a MMSR model based on a truncated spline, and investigating asymptotic properties of estimator for parameters in a MMSR model, especially consistency and asymptotic normality. The weighted least squares method was used to estimate the MMSR model. Next, we applied a pivotal quantity method, a Cramer–Wold theorem, and a Slutsky theorem to determine the confidence interval, investigate consistency, and asymptotic normality properties of estimator for parameters in a MMSR model. The obtained results were that the estimated regression function is linear to observation. We also obtained a 1001−α% confidence interval for parameters in the MMSR model, and the estimator for parameters in MMSR model was consistent and asymptotically normally distributed. In the future, these obtained results can be used as a theoretical basis in designing a standard toddlers growth chart to assess nutritional status.

Non-manipulable factors, such as gender or race have posed conceptual and practical challenges to causal analysts. On the one hand these factors do have consequences, and on the other hand, they do not fit into the experimentalist conception of causation. This paper addresses this challenge in the context of public debates over the health cost of obesity, and offers a new perspective, based on the theory of Structural Causal Models (SCM).

Abstract The method of robust approach is applied to estimate drift function and diffusion function of diffusion processes with discrete-time observations. The proposed method combines the ideas of local linear regression technique and maximum likelihood type estimation technique, so the advantages of local linear estimators persist and overcome the disadvantages of least-squares estimator. Moreover, a variable bandwidth instead of a constant bandwidth is considered in the local maximum likelihood type estimators. The consistency and asymptotic normality of the local maximum likelihood type estimators for drift and diffusion functions are developed under some given conditions. We perform a simulation study to evaluate the robust performances of the proposed estimators.

In this paper, we investigate the nonparametric regression model based on extended negatively dependent errors. Some consistency results for the estimator of the regression function g(x) are presented, including the rates of strong consistency and complete consistency, and the mean convergence. The results obtained in this paper improve and extend the corresponding ones of Yang and Wang (Acta Math Appl Sin 22(4):522–530, 1999) and Priestley and Chao (J R Stat Soc B 34:385–392, 1972). Finally, we present a numerical simulation study to verify the validity of the results established here. [ABSTRACT FROM AUTHOR]

Stationary processes have been extensively studied in the literature. Their applications include modeling and forecasting numerous real life phenomena such as natural disasters, sales and market movements. When stationary processes are considered, modeling is traditionally based on fitting an autoregressive moving average (ARMA) process. However, we challenge this conventional approach. Instead of fitting an ARMA model, we apply an AR(1) characterization in modeling any strictly stationary processes. Moreover, we derive consistent and asymptotically normal estimators of the corresponding model parameter.

The answers to extreme phenomena both in nature and in business sectors are the constructions of the distribution of random variables with extreme values. Another area in which appropriate theoretical research is conducted regarding the influence of suppressor (third) variables in categorical data. When examining dependencies in PivotTables, we often find it necessary to merge data into larger sets (e.g., due to a greater number of theoretical frequencies lower than their critical value). A phenomenon many exist wherein the partial relation is stronger than the zero relation. For example, in such a combination, instability may occur, which indicates contingent subgroups with the merged group. The dependence of dependencies is practically manifested because the data of contingent subgroups indicate inconsistent (inverted) conclusions compared to the associated group. For this reason, this paper aimed to find the critical ratios of partial probabilities in the contingency table of subgroups of the original variables, and to determine the conditions of result consistency and contingency stability, including the proof. For practical use and for the ease of repeating the proposed procedure, the solution is based on a case study that compares the effectiveness of vaccination.