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 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。

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.

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.

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.

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.

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.

Robust Model Averaging Method Based on LOF Algorithm

Model averaging is a good alternative to model selection,which can deal with the uncertainty from model selection process and make full use of the information from various candidate models.However,most of the existing model averaging criteria do not consider the influence of outliers on the estimation procedures.The purpose of this paper is to develop a robust model averaging approach based on the local outlier factor(LOF)algorithm which can downweight the outliers in the covariates.Asymptotic optimality of the proposed robust model averaging estimator is derived under some regularity conditions.Further,we prove the consistency of the LOF-based weight estimator tending to the theoretically optimal weight vector.Numerical studies including Monte Carlo simulations and a real data example are provided to illustrate our proposed methodology.

Average Estimation of Semiparametric Models for High-Dimensional Longitudinal Data

Model average receives much attention in recent years.This paper considers the semiparametric model averaging for high-dimensional longitudinal data.To minimize the prediction error,the authors estimate the model weights using a leave-subject-out cross-validation procedure.Asymptotic optimality of the proposed method is proved in the sense that leave-subject-out cross-validation achieves the lowest possible prediction loss asymptotically.Simulation studies show that the performance of the proposed model average method is much better than that of some commonly used model selection and averaging methods.

Least Squares Model Averaging Based on Generalized Cross Validation

Frequentist model averaging has received much attention from econometricians and statisticians in recent years.A key problem with frequentist model average estimators is the choice of weights.This paper develops a new approach of choosing weights based on an approximation of generalized cross validation.The resultant least squares model average estimators are proved to be asymptotically optimal in the sense of achieving the lowest possible squared errors.Especially,the optimality is built under both discrete and continuous weigh sets.Compared with the existing approach based on Mallows criterion,the conditions required for the asymptotic optimality of the proposed method are more reasonable.Simulation studies and real data application show good performance of the proposed estimators.

SINGULARLY PERTURBED MARKOV DECISION PROCESSES WITH INCLUSION OF TRANSIENT STATES

This paper is concerned with the continuous-time Markov decision processes (MDP) having weak and strong interactions. Using a hierarchical approach, the state space of the underlying Markov chain can be decomposed into several groups of recurrent states and a group of transient states resulting in a singularly perturbed MDP formulation. Instead of solving the original problem directly, a limit problem that is much simpler to handle is derived. On the basis of the optical solution of the limit problem, nearly optimal decisions are constructed for the original problem. The asymptotic optimality of the constructed control is obtained; the rate of convergence is ascertained.

Analysis of various semi-numerical schemes for magnetohydrodynamic(MHD)squeezing fluid flow in porous medium

In this article comparative analysis of various semi-numerical schemes has beenmade for the case of squeezing flow of an incompressible viscous fluid between two largeparallel plates having no-slip at the boundaries.The medium of flow contains magnetohy-drodynamic(MHD)effect and having small pores.Modeled boundary value problem is solvedanalytically using Optimal homotopy asymptotic method(OHAM),homotopy perturbationmethod(HPM),differential transform method(DTM),Daftardar Jafari method(DIM)andAdomian decomposition method(ADM).For comparison purpose,residuals of these schemeshave been found and analyzed for accuracy.Analytical study indicates that DTM and DJM arequite good in tem of accuracy near the center of domain[—1,1]but the accuracy reducesconsiderably near the start and end of the given interval.HPM and OHAM residuals indicatethat OHAM surpasses HPM in terms of accuracy in the present case.

Non-Newtonian fluid flow in an axisymmetric channel with porous wall

In the present article Optimal Homotopy Asymptotic Method(OHAM)is used to obtain the solutions of momentum and heat transfer equations of non-Newtonian fluid flow in an axisymmetric channel with porous wall for turbine cooling applications.Numerical method is used for validity of this analytical method and excellent agreement is observed between the solutions obtained from OHAM and numerical results.Trusting to this validity,effects of some other parameters are discussed.The results show that Nusselt number increases with increase of Reynolds number,Prandtl number and power law index.

Model Averaging Estimation for Varying-Coefficient Single-Index Models

The varying-coefficient single-index model(VCSIM)is widely used in economics,statistics and biology.A model averaging method for VCSIM based on a Mallows-type criterion is proposed to improve prodictive capacity,which allows the number of candidate models to diverge with sample size.Under model misspecification,the asymptotic optimality is derived in the sense of achieving the lowest possible squared errors.The authors compare the proposed model averaging method with several other classical model selection methods by simulations and the corresponding results show that the model averaging estimation has a outstanding performance.The authors also apply the method to a real dataset.

Model Averaging Multistep Prediction in an Infinite Order Autoregressive Process

The key issue in the frequentist model averaging is the choice of weights.In this paper,the authors advocate an asymptotic framework of mean-squared prediction error(MSPE)and develop a model averaging criterion for multistep prediction in an infinite order autoregressive(AR(∞))process.Under the assumption that the order of the candidate model is bounded,this criterion is proved to be asymptotically optimal,in the sense of achieving the lowest out of sample MSPE for the samerealization prediction.Simulations and real data analysis further demonstrate the effectiveness and the efficiency of the theoretical results.

Mallows Model Averaging Estimation for Linear Regression Model with Right Censored Data

This paper is concerned with an optimal model averaging estimation for linear regression model with right censored data. The weights for model averaging are picked up via minimizing the Mallows criterion. Under some mild conditions, it is shown that the identified weights possess the property of asymptotic optimality, that is,the model averaging estimator corresponding to these weights achieves the lowest squared error asymptotically.Some numerical studies are conducted to evaluate the finite-sample performance of our method and make comparisons with its intuitive competitors, while an application to the PBC dataset is provided to serve as an illustration.

Two-Sided Empirical Bayes Test for the Exponential Family with Contaminated Data

In this study, the two-sided Empirical Bayes test(EBT) rules for the parameter of continuous one-parameter exponential family with contaminated data(errors in variables) are constructed by a deconvolution kernel method. The asymptotically optimal uniformly over a class of prior distributions and uniform rates of convergence, which depends on two types of the error distributions for the proposed EBT rules, are obtained under suitable conditions. Finally, an example about the main results of this paper is given.

Optimal model averaging estimator for multinomial logit models

In this paper,we study optimal model averaging estimators of regression coefficients in a multinomial logit model,which is commonly used in many scientific fields.A Kullback-Leibler(KL)loss-based weight choice criterion is developed to determine averaging weights.Under some regularity conditions,we prove that the resulting model averaging estimators are asymptotically optimal.When the true model is one of the candidate models,the averaged estimators are consistent.Simulation studies suggest the superiority of the proposed method over commonly used model selection criterions,model averaging methods,as well as some other related methods in terms of the KL loss and mean squared forecast error.Finally,the website phishing data is used to illustrate the proposed method.