Strong Consistency of Estimators of a Semiparametric Regression Model under Fixed Design

In this paper, we consider the following semipaxametric regression model under fixed design： yi = xi′β＋g（xi）＋ei. The estimators of β, g（·） and σ^2 axe obtained by using the least squares and usual nonparametric weight function method and their strong consistency is proved under the suitable conditions.

Financial development during COVID‑19 pandemic:the role of coronavirus testing and functional labs

The outbreak of the SARS-CoV-2 virus in early 2020,known as COVID-19,spread to more than 200 countries and negatively affected the global economic output.Financial activities were primarily depressed,and investors were reluctant to start new financial investments while ongoing projects further declined due to the global lockdown to curb the disease.This study analyzes the money supply reaction to the COVID-19 pandemic using a cross-sectional panel of 115 countries.The study used robust least square regression and innovation accounting techniques to get sound parameter estimates.The results show that COVID-19 infected cases are the main contributing factor that obstructs financial activities and decrease money supply.In contrast,an increasing number of recovered cases and COVID-19 testing capabilities gave investors confidence to increase stock trade across countries.The overall forecast trend shows that COVID-19 infected cases and recovered cases followed the U-shaped trend,while COVID-19 critical cases and reported deaths showed a decreasing trend.Finally,the money supply and testing capacity show a positive trend over a period.The study concludes that financial development can be expanded by increasing the testing capacity and functional labs to identify suspected coronavirus cases globally.

Estimation for nearly unit root processes with GARCH errors

In this paper the limiting distribution of the least square estimate for the autoregressive coefficient of a nearly unit root model with GARCH errors is derived. Since the limiting distribution depends on the unknown variance of the errors, an empirical likelihood ratio statistic is proposed from which confidence intervals can be constructed for the nearly unit root model without knowing the variance. To gain an intuitive sense for the empirical likelihood ratio, a small simulation for the asymptotic distribution is given.

A Multilayer Recurrent Fuzzy Neural Network for Accurate Dynamic System Modeling

A multilayer recurrent fuzzy neural network(MRFNN)is proposed for accurate dynamic system modeling.The proposed MRFNN has six layers combined with T-S fuzzy model.The recurrent structures are formed by local feedback connections in the membership layer and the rule layer.With these feedbacks,the fuzzy sets are time-varying and the temporal problem of dynamic system can be solved well.The parameters of MRFNN are learned by chaotic search(CS)and least square estimation(LSE)simultaneously,where CS is for tuning the premise parameters and LSE is for updating the consequent coefficients accordingly.Results of simulations show the proposed approach is effective for dynamic system modeling with high accuracy.

Pattern synthesis optimization of 3-D ODAR based on improved GA using LSFE method

Pattern synthesis in 3-D opportunistic digital array radar(ODAR) becomes complex when a multitude of antennas are considered to be randomly distributed in a three dimensional space.In order to obtain an optimal pattern,several freedoms must be constrained.A new pattern synthesis approach based on the improved genetic algorithm(GA) using the least square fitness estimation(LSFE) method is proposed.Parameters optimized by this method include antenna locations,stimulus states and phase weights.The new algorithm demonstrates that the fitness variation tendency of GA can be effectively predicted after several "eras" by the LSFE method.It is shown that by comparing the variation of LSFE curve slope,the GA operator can be adaptively modified to avoid premature convergence of the algorithm.The validity of the algorithm is verified using computer implementation.

Predictive Models for Cumulative Confirmed COVID-19 Cases by Day in Southeast Asia

Coronavirus disease 2019 outbreak has spread as a pandemic since the end of year 2019.This situation has been causing a lot of problems of human beings such as economic problems,health problems.The forecasting of the number of infectious people is required by the authorities of all countries including Southeast Asian countries to make a decision and control the outbreak.This research is to investigate the suitable forecasting model for the number of infectious people in Southeast Asian countries.A comparison of forecasting models between logistic growth curve which is symmetric and Gompertz growth curve which is asymmetric based on the maximumof Coefficient of Determination and theminimumof RootMean Squared Percentage Error is also proposed.The estimation of parameters of the forecasting models is evaluated by the least square method.In addition,spreading of the outbreak is estimated by the derivative of the number of cumulative cases.The findings show that Gompertz growth curve is a suitable forecasting model for Indonesia,Philippines,andMalaysia and logistic growth curve suits the other countries in South Asia.

Neuro-fuzzy system modeling based on automatic fuzzy clustering

A neuro-fuzzy system model based on automatic fuzzy dustering is proposed. A hybrid model identification algorithm is also developed to decide the model structure and model parameters. The algorithm mainly includes three parts：1） Automatic fuzzy C-means （AFCM）, which is applied to generate fuzzy rttles automatically, and then fix on the size of the neuro-fuzzy network, by which the complexity of system design is reducesd greatly at the price of the fitting capability; 2） R.ecursive least square estimation （RLSE）. It is used to update the parameters of Takagi-Sugeno model, which is employed to describe the behavior of the system;3） Gradient descent algorithm is also proposed for the fuzzy values according to the back propagation algorithm of neural network. Finally,modeling the dynamical equation of the two-link manipulator with the proposed approach is illustrated to validate the feasibility of the method.

TWO-DIMENSIONAL VISUALIZATION OF THE PROPAGATION SPEED OF CORTICAL SPREADING DEPRESSION IN RAT CORTEX

Cortical spreading depression(CSD),which is a significant pathological phenomenon that correlates with migraines and cerebral ischemia,has been characterized by a wave of depolarization among neuronal cells and propagates across the cortex at a rate of 2–5mm/min.Although the propagation pattern of CSD was well-investigated using high-resolution optical imaging technique,the variation of propagation speed of CSD across different regions of cortex was not well-concerned,partially because of the lack of ideal approach to visualize two-dimensional distribution of propagation speed of CSD over the whole imaged cortex.Here,we have presented a method to compute automatically the propagation speed of CSD throughout every spots in the imaged cortex.In this method,temporal clustering analysis(TCA)and least square estimation(LSE)were first used to detect origin site where CSD was induced.Taking the origin site of CSD as the origin of coordinates,the data matrix of each image was transformed into the corresponding points based on the polar-coordinate representation.Then,two fixed-distance regions of interest(ROIs)are sliding along with the radial coordinate at each polar angle within the image for calculating the time lag with correlating algorithm.Finally,we could draw a twodimensional image,in which the value of each pixel represented the velocity of CSD when it spread through the corresponding area of the imaged cortex.The results demonstrated that the method can reveal the heterogeneity of propagation speed of CSD in the imaged cortex with high fidelity and intuition.

Dynamic Load Identification for Structures with Variable Stiffness Based on Extended Kalman Filter

We introduce the extended Kalman filter(EKF)method combined with the least square estimation to identify the unknown load acting on the time-varying structure and realize the tracking of the structural parameters of the time-varying system.Firstly,we propose the dynamic load identification method when the unknown parameters are stiffness coefficients.Then,a five-degree-of-freedom slowly-varying-stiffness structure is introduced to verify the effectiveness and the accuracy of the EKF method.The results show that the EKF method can accurately identify unknown loads and structural parameters simultaneously even considering noises in the input data.

THE COMPRESSION LS ESTIMATE OF REGRESSION COEFFICIENT IN MULTIVARIATE LINEAR MODEL

In this paper, compression LS estimate (k) of the regression coefficient B isconsidered when the design matrix present ill-condition in multivariate linear model.The MSE (mean square error)of the estimate(k)=Vec( (k))is less than theMSE of LS estimate β￣* of the regression coefficient β= Vec(B) by choosing the pa-rameter k. Admissibility , numerical stability and relative efficiency of (k)are proved. The method of determining k value for practical use is also suggested

Combined forecast method of HMM and LS-SVM about electronic equipment state based on MAGA

For the deficiency that the traditional single forecast methods could not forecast electronic equipment states, a combined forecast method based on the hidden Markov model（HMM） and least square support vector machine（LS-SVM） is presented. The multi-agent genetic algorithm（MAGA） is used to estimate parameters of HMM to overcome the problem that the Baum-Welch algorithm is easy to fall into local optimal solution. The state condition probability is introduced into the HMM modeling process to reduce the effect of uncertain factors. MAGA is used to estimate parameters of LS-SVM. Moreover, pruning algorithms are used to estimate parameters to get the sparse approximation of LS-SVM so as to increase the ranging performance. On the basis of these, the combined forecast model of electronic equipment states is established. The example results show the superiority of the combined forecast model in terms of forecast precision,calculation speed and stability.

Parameter Estimation for the NEAR(p) Model

As to the acronym NEAR（p）, it means “New Exponential Autoregressive Process of order p”. The NEAR（p） model is defined by

GENERALIZED MULTIVARIATE RIDGE REGRESSION ESTIMATE AND CRITERIA Q(c) FOR CHOOSING MATRIX K

When multicollinearity is present in a set of the regression variables,the least square estimate of the regression coefficient tends to be unstable and it may lead to erroneous inference.In this paper,generalized ridge estimate(K)of the regression coefficient=vec(B)is considered in multivaiale linear regression model.The MSE of the above estimate is less than the MSE of the least square estimate by choosing the ridge parameter matrix K.Moreover,it is pointed out that the Criterion MSE for choosing matrix K of generalized ridge estimate has several weaknesses.In order to overcome these weaknesses,a new family of criteria Q(c)is adpoted which includes the criterion MSE and criterion LS as its special case.The good properties of the criteria Q(c)are proved and discussed from theoretical point of view.The statistical meaning of the scale c is explained and the methods of determining c are also given.

The Superiorities of Bayes Linear Unbiased Estimator in Multivariate Linear Models

In this article, the Bayes linear unbiased estimator （BALUE） of parameters is derived for the multivariate linear models. The superiorities of the BALUE over the least square estimator （LSE） is studied in terms of the mean square error matrix （MSEM） criterion and Bayesian Pitman closeness （PC） criterion.

Mixed Sub-fractional Brownian Motion and Drift Estimation of Related Ornstein-Uhlenbeck Process

In this paper,wewill first give the numerical simulation of the sub-fractional Brownian motion through the relation of fractional Brownian motion instead of its representation of random walk.In order to verify the rationality of this simulation,we propose a practical estimator associated with the LSE of the drift parameter of mixed sub-fractional Ornstein-Uhlenbeck process,and illustrate the asymptotical properties according to our method of simulation when the Hurst parameter H>1/2.

RANDOM WEIGHTING APPROXIMATION IN LINEAR REGRESSION MODELS

In this paper, we give an one-term Edgeworth expansion for the standardized least square estimator (LSE) in a linear regression model and its random weighting approximation. So we have not only improved the expansion result but also given a practical approximating method.

Partial Dynamic Dimension Reduction for Conditional Mean in Regression

In many regression analysis,the authors are interested in regression mean of response variate given predictors,not its the conditional distribution.This paper is concerned with dimension reduction of predictors in sense of mean function of response conditioning on predictors.The authors introduce the notion of partial dynamic central mean dimension reduction subspace,different from central mean dimension reduction subspace,it has varying subspace in the domain of predictors,and its structural dimensionality may not be the same point by point.The authors study the property of partial dynamic central mean dimension reduction subspace,and develop estimated methods called dynamic ordinary least squares and dynamic principal Hessian directions,which are extension of ordinary least squares and principal Hessian directions based on central mean dimension reduction subspace.The kernel estimate methods for dynamic ordinary least squares and dynamic Principal Hessian Directions are employed,and large sample properties of estimators are given under the regular conditions.Simulations and real data analysis demonstrate that they are effective.

Local Linear Estimation by TSLS with Variable Bandwidth for Semi-parametric Simultaneous Equation Models in Econometrics

Econometric simultaneous equation models play an important role in making economic policies, analyzing economic structure and economic forecasting. This paper presents local linear estimators by TSLS with variable bandwidth for every structural equation in semi-parametric simultaneous equation models in econometrics. The properties under large sample size were studied by using the asymptotic theory when all variables were random. The results show that the estimators of the parameters have consistency and asymptotic normality, and their convergence rates are equal to n^-1/2. And the estimator of the nonparametric function has the consistency and asymptotic normality in interior points and its rate of convergence is equal to the optimal convergence rate of the nonparametric function estimation.