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A novel method for testing skew-normal distribution is proposed, and this method is called the fourth-order moment test (FOMT). It is a statistic constructed based on the fourth-order moment of the standard skew-normal distribution. We compared FOMT with the Kolmogorov-Smirnov test (KS test), the Anderson-Darling test (AD test), AS test, and W test, both of which generate random numbers of skew-normal distribution by stochastic representing and compares the probability of the Type I error for tests. The true distributions of different alternative hypotheses are simulated by Monte Carlo (MC), and the power functions of the tests are calculated. Monte Carlo simulations show that FOMT has a significant advantage in power function. A real data application is analyzed by the proposed methodology. [ABSTRACT FROM AUTHOR]

With the advent of big data, the fields of biomedicine and economics generate massive data with skew characteristics. Numerous methods have been proposed for modeling either skewed or massive data, whereas most existing methods cannot allow a direct handling of massive and skewed data. We first investigate the subsampling algorithms for skew-normal mode regression model, which include uniform subsampling, leverage subsampling, optimal subsampling, and vector mode subsampling. Since the aforementioned algorithms mainly leverage the value of the information module to calculate the sampling probability without accounting for the residuals in the modeling process. This observation motivates us to propose a novel residual subsampling method with applications to massive data. We then employ the signal-to-noise ratio (SNR) to carry out simulation studies to compare the performance of various sampling methods under various information quantities. Finally, a real-data example is provided for illustrative methods. [ABSTRACT FROM AUTHOR]

In this article, we develop a new adaptive event‐triggered asymptotic control scheme for strict‐feedback systems with fast time‐varying parameters. To deal with time‐varying parameters with unknown variation boundaries in the feedback path and the input path, we construct three adaptive laws for parameter estimation, two for the uncertain parameters in the feedback path and one for the uncertain parameters in the input path. In particular, two sets of tuning functions are introduced to avoid over‐parametrization. Additionally, an event‐triggering mechanism is embedded in this adaptive control framework to reduce the data transmission from the controller to the actuator. We also introduce a soft sign function to handle the perturbations caused by sampling errors to achieve asymptotic stability and avoid the so‐called parameter drift. The stability analysis shows that the closed‐loop system is globally uniformly asymptotically stable and the Zeno behavior can be excluded. Simulation results verify the effectiveness and performance of the proposed adaptive scheme. [ABSTRACT FROM AUTHOR]

The mode of a distribution provides a significant summary. A regression model with skew-normal errors provides a useful extension for traditional normal regression models when the data involve asymmetric outcomes. Finite mixture of regression (FMR) models are frequently used to analyze data that arise from a heterogeneous population. This work develops a new data analysis tool called finite mixture of mode regression (FMMoR) in order to explore skewed data from several subpopulations. The main virtue of considering the FMMoR models for skewed data is that this class of models has a nice hierarchical representation which allows easy implementation of inferences. A productive clustering method via mode identification is applied to select the number of components. A modified expectation-maximization algorithm facilitated by the two-point step size gradient descent method (GDEM), simultaneously, is developed for the inference. The proposed methods are evaluated through some simulation studies and illustrated by a real dataset. [ABSTRACT FROM AUTHOR]

A large amount of literature has been developed for the presence of multicollinearity among the explanatory variables that are often performed with the aim of reducing the undesirable effects on the maximum likelihood estimate(MLE). In particular, many authors have discussed ridge estimation (RE) under the framework of the mean regression model, because the RE enjoys the advantage that its mean squared error (MSE) is less than that of MLE. However, most of the existing methods assume or are applicable to symmetrical data. In this paper, we consider the case of skewed (or asymmetrical) data, which often occur in practice and include symmetrical data as a special case, and derive the RE of the skew-mormal mode regression model under multicollinearity problem. A maximum likelihood method via an EM algorithm and the eleven ridge parameter methods are investigated. Monte Carlo simulation results indicate that the suggested estimator performs better than the MLE in terms of MSE. Then proposed methods are illustrated by a real data analysis. [ABSTRACT FROM AUTHOR]

Mixture of regression models are one of the most important statistical data analysis tools in a heterogeneous population. Similar to modeling variance parameter in a homogeneous population, we apply the idea of joint mean and variance models to the mixture of regression models and propose a new class of models: mixture of joint mean and variance models to analyze the heteroscedastic normal data coming from a heterogeneous population in this paper. The problem of variable selection for the proposed models is considered. In particular, a modified Expectation-Maximization (EM) algorithm for estimating the model parameters is developed. The consistency and the oracle property of the penalized estimators are established. Properties of the estimators of the regression coefficients are evaluated through Monte Carlo simulations. Finally, a real data analysis is illustrated by the proposed methodologies. [ABSTRACT FROM AUTHOR]

Variable selection in finite mixture of regression (FMR) models is frequently used in statistical modeling. The majority of applications of variable selection in FMR models use a normal distribution for regression error. Such assumptions are unsuitable for a set of data containing a group or groups of observations with asymmetric behavior. In this paper, we introduce a variable selection procedure for FMR models using the skew-normal distribution. With appropriate choice of the tuning parameters, we establish the theoretical properties of our procedure, including consistency in variable selection and the oracle property in estimation. To estimate the parameters of the model, a modified EM algorithm for numerical computations is developed. The methodology is illustrated through numerical experiments and a real data example. [ABSTRACT FROM AUTHOR]

Assuming that the error terms follow a Pearson type VII distribution, we propose a new estimation in mixture of experts models by adding an l 2 − norm of the regression coefficients of the mixing proportions to the log-likelihood function. This l2-penalized maximum likelihood estimator is a root-n consistent estimator of the true parameter vector, and its finite sample behaviour is better than that of the ordinary maximum likelihood estimator. An efficient EM algorithm is suggested for the inference, and the methodology is illustrated through some simulation and comparison studies. An application of the proposed method to a data set is described. [ABSTRACT FROM AUTHOR]

Variable selection in finite mixture of regression (FMR) models is frequently used in statistical modeling. The majority of applications of variable selection in FMR models use a normal distribution for regression error. Such assumptions are unsuitable for a set of data containing a group or groups of observations with heavy tails and outliers. In this paper, we introduce a robust variable selection procedure for FMR models using the t distribution. With appropriate selection of the tuning parameters, the consistency and the oracle property of the regularized estimators are established. To estimate the parameters of the model, we develop an EM algorithm for numerical computations and a method for selecting tuning parameters adaptively. The parameter estimation performance of the proposed model is evaluated through simulation studies. The application of the proposed model is illustrated by analyzing a real data set. [ABSTRACT FROM AUTHOR]