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

参数的 Bayes 评估者为规模被获得在情况中的指数的家庭相等分布式、确实联系(PA ) 在加权的方形的损失 function.We 下面的样品构造实验 Bayes (EB ) 评估者并且证明它是 asymptotic 最佳。

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 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.

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.

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.

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.

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.

Optimal Model Average Prediction in Orthogonal Kriging Models

The main objective of this paper is to consider model averaging methods for kriging models.This paper proposes a Mallows model averaging procedure for the orthogonal kriging model and demonstrate the asymptotic optimality of the model averaging estimators in terms of mean square error.Simulation studies are conducted to evaluate the performance of the proposed method and compare it with the competitors to demonstrate its superiority.The authors also analyse a real dataset for an illustration.

Asymptotic Optimality of the Nonnegative Garrote Estimator Under Heteroscedastic Errors

This paper proposes the Nonnegative Garrote(NG)estimator for linear model with heteroscedastic errors.On the other hand,under some regularity conditions,the authors show the asymptotic optimality of the NG estimator by referring to the idea of the asymptotic optimality of the model average estimator.Simulation results and a real data analysis are reported for testing the results obtained previously.These results provide a stronger theoretical basis for the use of NG estimator by strengthening existing findings.

Asymptotic optimality for consensus-type stochastic approximation algorithms using iterate averaging

This paper introduces a post-iteration averaging algorithm to achieve asymptotic optimality in convergence rates of stochastic approximation algorithms for consensus control with structural constraints. The algorithm involves two stages. The first stage is a coarse approximation obtained using a sequence of large stepsizes. Then, the second stage provides a refinement by averaging the iterates from the first stage. We show that the new algorithm is asymptotically efficient and gives the optimal convergence rates in the sense of the best scaling factor and ＇smallest＇ possible asymptotic variance.

Asymptotically Optimal Dividend Policy for Regime-Switching Compound Poisson Models

This work develops asymptotically optimal dividend policies to maximize the expected present value of dividends until ruin.Compound Poisson processes with regime switching are used to model the surplus and the switching（a continuous-time controlled Markov chain） represents random environment and other economic conditions.Assuming the switching to be fast varying together with suitable conditions,it is shown that the system has a limit that is an average with respect to the invariant measure of a related Markov chain.Under simple conditions,the optimal policy of the limit dividend strategy is a threshold policy.Using the optimal policy of the limit system as a guide,feedback control for the original surplus is then developed.It is demonstrated that the constructed dividend policy is asymptotically optimal.

Least Squares Model Averaging for Two Non-Nested Linear Models

This paper studies the least squares model averaging methods for two non-nested linear models.It is proved that the Mallows model averaging weight of the true model is root-n consistent.Then the authors develop a penalized Mallows criterion which ensures that the weight of the true model equals 1 with probability tending to 1 and thus the averaging estimator is asymptotically normal.If neither candidate model is true,the penalized Mallows averaging estimator is asymptotically optimal.Simulation results show the selection consistency of the penalized Mallows method and the superiority of the model averaging approach compared with the model selection estimation.