Asymptotically Optimal Empirical Bayes Estimation of Parameter for Scale-exponential Family under PA Samples

The Bayes estimator of the parameter is obtained for the scale exponential family in the case of identically distributed and positively associated（PA） samples under weighted square loss function.We construct the empirical Bayes（EB） estimator and prove it is asymptotic optimal.

Cross Validation Based Model Averaging for Varying-Coefficient Models with Response Missing at Random

In this paper, a model averaging method is proposed for varying-coefficient models with response missing at random by establishing a weight selection criterion based on cross-validation. Under certain regularity conditions, it is proved that the proposed method is asymptotically optimal in the sense of achieving the minimum squared error.

Asymptotically Optimal and Admissible Empirical Bayes Estimation of Normal Parameter

Under square loss, this paper constructs the empirical Bayes（EB） estimation for the parameter of normal distribution which has both asymptotic optimality and admissibility. Moreover, the convergence rate of the EB estimation obtained is proved to be O（n^-1）.

ASYMPTOTICALLY OPTIMAL EMPIRICAL BAYES ESTIMATION FOR THE PARAMETERS OF MULTI－PARAMETER DISCRETE EXPONENTIAL FAMILY

For the multi-parameter discrete exponential family,we construct an empirical Bayes(EB)estimator of the vector-valued parameterθ.under some conditions,this estimator is proved to be asymptotically optimal.

Relevant Region sampling strategy with adaptive heuristic for asymptotically optimal path planning

Sampling-based planning algorithm is a powerful tool for solving planning problems in highdimensional state spaces.In this article,we present a novel approach to sampling in the most promising regions,which significantly reduces planning time-consumption.The RRT#algorithm defines the Relevant Region based on the cost-to-come provided by the optimal forward-searching tree.However,it uses the cumulative cost of a direct connection between the current state and the goal state as the cost-to-go.To improve the path planning efficiency,we propose a batch sampling method that samples in a refined Relevant Region with a direct sampling strategy,which is defined according to the optimal cost-to-come and the adaptive cost-to-go,taking advantage of various sources of heuristic information.The proposed sampling approach allows the algorithm to build the search tree in the direction of the most promising area,resulting in a superior initial solution quality and reducing the overall computation time compared to related work.To validate the effectiveness of our method,we conducted several simulations in both SE(2)and SE(3)state spaces.And the simulation results demonstrate the superiorities of proposed algorithm.

Self-tuning weighted measurement fusion Kalman filter and its convergence

For multisensor systems,when the model parameters and the noise variances are unknown,the consistent fused estimators of the model parameters and noise variances are obtained,based on the system identification algorithm,correlation method and least squares fusion criterion.Substituting these consistent estimators into the optimal weighted measurement fusion Kalman filter,a self-tuning weighted measurement fusion Kalman filter is presented.Using the dynamic error system analysis （DESA） method,the convergence of the self-tuning weighted measurement fusion Kalman filter is proved,i.e.,the self-tuning Kalman filter converges to the corresponding optimal Kalman filter in a realization.Therefore,the self-tuning weighted measurement fusion Kalman filter has asymptotic global optimality.One simulation example for a 4-sensor target tracking system verifies its effectiveness.

One-sided empirical Bayes test for location parameter in Gamma distribution

In this paper, we devote to constructing the one-sided empirical Bayes(EB) test for the location parameter in the Gamma distribution by nonparametric method. Under some mild conditions, we prove that the EB test is asymptotically optimal with the rate of the order O(n^(-δs/(2s+1))), where 1/2 ≤ δ < 1 and s > 1 is a given natural number. An example is also given to illustrate that the conditions of the main theorems are easily satisfied.

Empirical Bayes Test for the Parameter of Rayleigh Distribution with Error of Measurement

For the data with error of measurement in historical samples, the empirical Bayes test rule for the parameter of Rayleigh distribution is constructed, and the asymptotically optimal property is obtained. It is shown that the convergence rate of the proposed EB test rule can be arbitrarily close to O（n-1/2） under suitable conditions.

Theoretical investigation of micropolar fluid flow between two porous disks

The steady, laminar, incompressible and two dimensional micropolar flow between two porous disks was investigated using optimal homotopy asymptotic method(OHAM) and fourth order Runge–Kutta numerical method. Comparison between OHAM and numerical method shows that OHAM is an exact and high efficient method for solving these kinds of problems. The results are presented to study the velocity and rotation profiles for different physical parameters such as Reynolds number, vortex viscosity parameter, spin gradient viscosity and microinertia density parameter. As an important outcome, the magnitude of the microrotation increases with an increase in the values of injection velocity while it decreases by increasing the values of suction velocity.

NEW HMM ALGORITHM FOR TOPOLOGY OPTIMIZATION

A new hybrid MMA-MGCMMA （HMM） algorithm for solving topology optimization problems is presented. This algorithm combines the method of moving asymptotes （MMA） algorithm and the modified globally convergent version of the method of moving asymptotes （MGCMMA） algorithm in the optimization process. This algorithm preserves the advantages of both MMA and MGCMMA. The optimizer is switched from MMA to MGCMMA automatically, depending on the numerical oscillation value existing in the calculation. This algorithm can improve calculation efficiency and accelerate convergence compared with simplex MMA or MGCMMA algorithms, which is proven with an example.

Self-tuning measurement fusion white noise deconvolution estimator with correlated noises

For the multisensor linear discrete time-invariant stochastic systems with correlated noises and unknown noise statistics,an on-line noise statistics estimator is presented by using the correlation method.Substituting it into the steady-state Riccati equation,the self-tuning Riccati equation is obtained.Using the Kalman filtering method,based on the self-tuning Riccati equation,a self-tuning weighted measurement fusion white noise deconvolution estimator is presented.By the dynamic error system analysis（DESA） method,it is proved that the self-tuning fusion white noise deconvolution estimator converges to the optimal fusion steadystate white noise deconvolution estimator in a realization,so that it has the asymptotic global optimality.A simulation example for Bernoulli-Gaussian input white noise shows its effectiveness.

Empirical Bayes Test for Two-parameter Exponential Distribution under Type-Ⅱ Censored Samples

The empirical Bayes test problem is considered for scale parameter of twoparameter exponential distribution under type-II censored data.By using wavelets estimation method,the EB test function is constructed,of which the asymptotic optimality and convergence rates are obtained.Finally,an example concerning the main result is given.

THE EXISTENCE AND GLOBAL OPTIMAL ASYMPTOTIC BEHAVIOUR OF LARGE SOLUTIONS FOR A SEMILINEAR ELLIPTIC PROBLEM

By Karamata regular variation theory and constructing comparison functions, the author shows the existence and global optimal asymptotic behaviour of solutions for a semilinear elliptic problem Δu = k（x）g（u）, u 〉 0, x ∈ Ω, u｜δΩ =＋∞, where Ω is a bounded domain with smooth boundary in R^N; g ∈ C^1[0, ∞）, g（0） = g＇（0） = 0, and there exists p 〉 1, such that lim g（sξ）/g（s）=ξ^p, ↓Aξ 〉 0, and k ∈ Cloc^α（Ω） is non-negative non-trivial in D which may be singular on the boundary.

Convergence Rate of Empirical Bayes for Two-parameter Exponential Distribution with Replicated Data

In this paper, empirical Bayes test for a parameter θ of two-parameter exponential distribution is investigated with replicated past data. Under some conditions, the asymptotically optimal property is obtained. It is indicated that the rate of convergence can be very close to O（N-2^-1） in this case that a parameter μ is known.

Performance Analysis of Magnetic Nanoparticles during Targeted Drug Delivery:Application of OHAM

In recent years,the emergence of nanotechnology experienced incredible development in the field of medical sciences.During the past decade,investigating the characteristics of nanoparticles during fluid flow has been one of the intriguing issues.Nanoparticle distribution and uniformity have emerged as substantial criteria in both medical and engineering applications.Adverse effects of chemotherapy on healthy tissues are known to be a significant concern during cancer therapy.A novel treatment method of magnetic drug targeting(MDT)has emerged as a promising topical cancer treatment along with some attractive advantages of improving efficacy,fewer side effects,and reduce drug dose.During magnetic drug targeting,the appropriate movement of nanoparticles(magnetic)as carriers is essential for the therapeutic process in the blood clot removal,infection treatment,and tumor cell treatment.In this study,we have numerically investigated the behavior of an unsteady blood flowinfused with magnetic nanoparticles during MDT under the influence of a uniform external magnetic field in a microtube.An optimal homotopy asymptotic method(OHAM)is employed to compute the governing equation for unsteady electromagnetohydrodynamics flow.The influence of Hartmann number(Ha),particle mass parameter(G),particle concentration parameter(R),and electro-osmotic parameter(k)is investigated on the velocity of magnetic nanoparticles and blood flow.Results obtained show that the electro-osmotic parameter,along with Hartmann’s number,dramatically affects the velocity of magnetic nanoparticles,blood flow velocity,and flow rate.Moreover,results also reveal that at a higher Hartman number,homogeneity in nanoparticles distribution improved considerably.The particle concentration andmass parameters effectively influence the capturing effect on nanoparticles in the blood flow using a micro-tube for magnetic drug targeting.Lastly,investigation also indicates that the OHAM analysis is efficient and quick to handle the system of nonlinear equations.

Application of OHAM-DJ to the System of Burgers’ Equations

In this paper, the system of Burgers’ equations is solved by the optimal homotopy asymptotic method with Daftardar-Jafari polynomials OHAM-DJ. Two numerical examples are illustrated the efficient of this methods for solving the system of Burgers’ equations.

Partial Linear Model Averaging Prediction for Longitudinal Data

Prediction plays an important role in data analysis.Model averaging method generally provides better prediction than using any of its components.Even though model averaging has been extensively investigated under independent errors,few authors have considered model averaging for semiparametric models with correlated errors.In this paper,the authors offer an optimal model averaging method to improve the prediction in partially linear model for longitudinal data.The model averaging weights are obtained by minimizing criterion,which is an unbiased estimator of the expected in-sample squared error loss plus a constant.Asymptotic properties,including asymptotic optimality and consistency of averaging weights,are established under two scenarios:(i)All candidate models are misspecified;(ii)Correct models are available in the candidate set.Simulation studies and an empirical example show that the promise of the proposed procedure over other competitive methods.

Kriging Model Averaging Based on Leave-One-Out Cross-Validation Method

In recent years,Kriging model has gained wide popularity in various fields such as space geology,econometrics,and computer experiments.As a result,research on this model has proliferated.In this paper,the authors propose a model averaging estimation based on the best linear unbiased prediction of Kriging model and the leave-one-out cross-validation method,with consideration for the model uncertainty.The authors present a weight selection criterion for the model averaging estimation and provide two theoretical justifications for the proposed method.First,the estimated weight based on the proposed criterion is asymptotically optimal in achieving the lowest possible prediction risk.Second,the proposed method asymptotically assigns all weights to the correctly specified models when the candidate model set includes these models.The effectiveness of the proposed method is verified through numerical analyses.

Analyzing the Dissemination of News by Model Averaging and Subsampling

The dissemination of news is a vital topic in management science,social science and data science.With the development of technology,the sample sizes and dimensions of digital news data increase remarkably.To alleviate the computational burden in big data,this paper proposes a method to deal with massive and moderate-dimensional data for linear regression models via combing model averaging and subsampling methodologies.The author first samples a subsample from the full data according to some special probabilities and split covariates into several groups to construct candidate models.Then,the author solves each candidate model and calculates the model-averaging weights to combine these estimators based on this subsample.Additionally,the asymptotic optimality in subsampling form is proved and the way to calculate optimal subsampling probabilities is provided.The author also illustrates the proposed method via simulations,which shows it takes less running time than that of the full data and generates more accurate estimations than uniform subsampling.Finally,the author applies the proposed method to analyze and predict the sharing number of news,and finds the topic,vocabulary and dissemination time are the determinants.

Jackknife Model Averaging for Composite Quantile Regression

In this paper,the authors propose a frequentist model averaging method for composite quantile regression with diverging number of parameters.Different from the traditional model averaging for quantile regression which considers only a single quantile,the proposed model averaging estimator is based on multiple quantiles.The well-known delete-one cross-validation or jackknife approach is applied to estimate the model weights.The resultant jackknife model averaging estimator is shown to be asymptotically optimal in terms of minimizing the out-of-sample composite final prediction error.Simulation studies are conducted to demonstrate the finite sample performance of the new model averaging estimator.The proposed method is also applied to the analysis of the stock returns data and the wage data.