The M-estimate of Local Linear Regression with Variable Window Breadth

In this paper, by using the Brouwer fixed point theorem, we consider the existence and uniqueness of the solution for local linear regression with variable window breadth.

Local Linear Regression for Data with AR Errors

In many statistical applications, data are collected over time, and they are likely correlated. In this paper, we investigate how to incorporate the correlation information into the local linear regression. Under the assumption that the error process is an auto-regressive process, a new estimation procedure is proposed for the nonparametric regression by using local linear regression method and the profile least squares techniques. We further propose the SCAD penalized profile least squares method to determine the order of auto-regressive process. Extensive Monte Carlo simulation studies are conducted to examine the finite sample performance of the proposed procedure, and to compare the performance of the proposed procedures with the existing one. From our empirical studies, the newly proposed procedures can dramatically improve the accuracy of naive local linear regression with working-independent error structure. We illustrate the proposed methodology by an analysis of real data set.

Adaptive Local Linear Quantile Regression

In this paper we propose a new method of local linear adaptive smoothing for nonparametric conditional quantile regression. Some theoretical properties of the procedure are investigated. Then we demonstrate the performance of the method on a simulated example and compare it with other methods. The simulation results demonstrate a reasonable performance of our method proposed especially in situations when the underlying image is piecewise linear or can be approximated by such images. Generally speaking, our method outperforms most other existing methods in the sense of the mean square estimation （MSE） and mean absolute estimation （MAE） criteria. The procedure is very stable with respect to increasing noise level and the algorithm can be easily applied to higher dimensional situations.

Prediction of flyrock induced by mine blasting using a novel kernel-based extreme learning machine

Blasting is a common method of breaking rock in surface mines.Although the fragmentation with proper size is the main purpose,other undesirable effects such as flyrock are inevitable.This study is carried out to evaluate the capability of a novel kernel-based extreme learning machine algorithm,called kernel extreme learning machine(KELM),by which the flyrock distance(FRD) is predicted.Furthermore,the other three data-driven models including local weighted linear regression(LWLR),response surface methodology(RSM) and boosted regression tree(BRT) are also developed to validate the main model.A database gathered from three quarry sites in Malaysia is employed to construct the proposed models using 73 sets of spacing,burden,stemming length and powder factor data as inputs and FRD as target.Afterwards,the validity of the models is evaluated by comparing the corresponding values of some statistical metrics and validation tools.Finally,the results verify that the proposed KELM model on account of highest correlation coefficient(R) and lowest root mean square error(RMSE) is more computationally efficient,leading to better predictive capability compared to LWLR,RSM and BRT models for all data sets.

Novel algorithm for pose-invariant face recognition

By combining the AdaBoost modular locality preserving projection （AMLPP） algorithm and the locally linear regression （LLR） algorithm, a novel pose-invariant algorithm is proposed to realize high-accuracy face recognition under different poses. In the training stage of this algorithm, the AMLPP is employed to select the crucial frontal blocks and construct effective strong classifier. According to the selected frontal blocks and the corresponding non-frontal blocks, LLR is then applied to learn the linear mappings which will be used to convert the non-frontal blocks to visual frontal blocks. During the testing of the learned linear mappings, when a non-frontal face image is inputted, the non-frontal blocks corresponding to the selected frontal blocks are extracted and converted to the visual frontal blocks. The generated virtual frontal blocks are finally fed into the strong classifier constructed by AMLPP to realize accurate and efficient face recognition. Our algorithm is experimentally compared with other pose-invariant face recognition algorithms based on the Bosphorus database. The results show a significant improvement with our proposed algorithm.

TESTING SERIAL CORRELATION IN SEMIPARAMETRIC VARYING COEFFICIENT PARTIALLY LINEAR ERRORS-IN-VARIABLES MODEL

The authors propose a V_(N,p) test statistic for testing finite-order serial correlation in asemiparametric varying coefficient partially linear errors-in-variables model.The test statistic is shownto have asymptotic normal distribution under the null hypothesis of no serial correlation.Some MonteCarlo experiments are conducted to examine the finite sample performance of the proposed V_(N,p) teststatistic.Simulation results confirm that the proposed test performs satisfactorily in estimated sizeand power.

Partially Linear Single-Index Model in the Presence of Measurement Error

The partially linear single-index model(PLSIM) is a flexible and powerful model for analyzing the relationship between the response and the multivariate covariates. This paper considers the PLSIM with measurement error possibly in all the variables. The authors propose a new efficient estimation procedure based on the local linear smoothing and the simulation-extrapolation method,and further establish the asymptotic normality of the proposed estimators for both the index parameter and nonparametric link function. The authors also carry out extensive Monte Carlo simulation studies to evaluate the finite sample performance of the new method, and apply it to analyze the osteoporosis prevention data.

Testing for Change Points in Partially Linear Models

In this paper we provide a method to test the existence of the change points in the nonparametric regression function of partially linear models with conditional heteroscedastic variance. We propose the test statistic and establish its asymptotic properties under some regular conditions. Some simulation studies are given to investigate the performance of the proposed method in finite samples. Finally, the proposed method is applied to a real data for illustration.

A systematic framework of constructing surrogate model for slider track peeling strength prediction

Peeling strength can comprehensively reflect slider track safety and is crucial in car seat safety assessments.Current methods for determining slider peeling strength are primarily physical testing and numerical simulation.However,these methods encounter the potential challenges of high costs and overlong time consumption which have not been adequately addressed.Therefore,the efficient and low-cost surrogate model emerges as a promising solution.Nevertheless,currently used surrogate models suffer from inefficiencies and complexity in data sampling,lack of robustness in local model predictions,and isolation between data sampling and model prediction.To overcome these challenges,this paper aims to set up a systematic framework for slider track peeling strength prediction,including sensitivity analysis,dataset sampling,and model prediction.Specifically,the interpretable linear regression is performed to identify the sensitivity of various geometric variables to peeling strength.Based on the variable sensitivity,a distance metric is constructed to measure the disparity of different variable groups.Then,the sparsity-targeted sampling(STS)is proposed to formulate a representative dataset.Finally,the sequentially selected local weighted linear regression(SLWLR)is designed to achieve accurate track peeling strength prediction.Additionally,a quantitative cost assessment of the supplementary dataset is proposed by utilizing the minimum adjacent sample distance as a mediator.Experimental results validate the efficacy of sequential selection and the weighting mechanism in enhancing localization robustness.Furthermore,the proposed SLWLR method surpasses similar approaches and other common surrogate methods in terms of prediction performance and data quantity requirements,achieving an average absolute error of 3.3 kN in the simulated test dataset.

Joint semiparametric mean-covariance model in longitudinal study

Semiparametric regression models and estimating covariance functions are very useful for longitudinal study. To heed the positive-definiteness constraint, we adopt the modified Cholesky decomposition approach to decompose the covariance structure. Then the covariance structure is fitted by a semiparametric model by imposing parametric within-subject correlation while allowing the nonparametric variation function. We estimate regression functions by using the local linear technique and propose generalized estimating equations for the mean and correlation parameter. Kernel estimators are developed for the estimation of the nonparametric variation function. Asymptotic normality of the the resulting estimators is established. Finally, the simulation study and the real data analysis are used to illustrate the proposed approach.

The nonparametric estimation of long memory spatio-temporal random field models

This paper considers the local linear estimation of a multivariate regression function and its derivatives for a stationary long memory(long range dependent) nonparametric spatio-temporal regression model.Under some mild regularity assumptions, the pointwise strong convergence, the uniform weak consistency with convergence rates and the joint asymptotic distribution of the estimators are established. A simulation study is carried out to illustrate the performance of the proposed estimators.

Approximating Conditional Density Functions Using Dimension Reduction

We propose to approximate the conditional density function of a random variable Y given a dependent random d-vector X by that of Y given θ^τX, where the unit vector θ is selected such that the average Kullback-Leibler discrepancy distance between the two conditional density functions obtains the minimum. Our approach is nonparametric as far as the estimation of the conditional density functions is concerned. We have shown that this nonparametric estimator is asymptotically adaptive to the unknown index θ in the sense that the first order asymptotic mean squared error of the estimator is the same as that when θ was known. The proposed method is illustrated using both simulated and real-data examples.