Strong Convergence of Partitioning Estimation for Nonparametric Regression Function under Dependence Samples

In this paper, we study the strong consistency for partitioning estimation of regression function under samples that axe φ-mixing sequences with identically distribution.Key words: nonparametric regression function; partitioning estimation; strong convergence;φ-mixing sequences.

Strong Convergence and Its Rate of Modified Partitioning Estimation for Nonparametric Regression Function under Dependence Samples

In this paper, we study the strong consistency and convergence rate for modified partitioning estimation of regression function under samples that are ψ-mixing with identically distribution.

ASYMPTOTIC NORMALITY OF WAVELET ESTIMATOR IN HETEROSCEDASTIC REGRESSION MODEL

The following heteroscedastic regression model Yi = g（xi） ＋σiei （1 ≤i ≤ n） is 2 considered, where it is assumed that σi^2 = f（ui）, the design points （xi,ui） are known and nonrandom, g and f are unknown functions. Under the unobservable disturbance ei form martingale differences, the asymptotic normality of wavelet estimators of g with f being known or unknown function is studied.

On the L_p Convergence Rate of Kernel Estimates for the Nonparametric Regression Function

Let (X,Y) be an R^d×R^1 valued random vector (X_1,Y_1),…, (X_n,Y_n) be a random sample drawn from (X,Y), and let E|Y|<∞. The regression function m(x)=E(Y|X=x) for x∈R^d is estimated by where, and h_n is a positive number depending upon n only, nad K is a given nonnegative function on R^d. In the paper, we study the L_p convergence rate of kernel estimate m_n(x) of m(x) in suitable condition, and improve and extend the results of Wei Lansheng.

Developing Weibull-based diameter distributions for the major coniferous species in Heilongjiang Province,China

Diameter distribution models play an important role in forest inventories,growth prediction,and management.The Weibull probability density function is widely used in forestry.Although a number of methods have been proposed to predict or recover the Weibull distribution,their applicability and predictive performance for the major tree species of China remain to be determined.Trees in sample plots of three even-aged coniferous species(Larix olgensis,Pinus sylvestris and Pinus koraiensis)were measured both in un-thinned and thinned stands to develop parameter prediction models for the Weibull probability density function.Ordinary least squares(OLS)and maximum likelihood regression(MLER),as well as cumulative distribution function regression(CDFR)were used,and their performance compared.The results show that MLER and CDFR were better than OLS in predicting diameter distributions of tree plantations.CDFR produced the best results in terms of fitting statistics.Based on the error statistics calculated for different age groups,CDFR was considered the most suitable method for developing prediction models for Weibull parameters in coniferous plantations.

Real-time and wearable functional electrical stimulation system for volitional hand motor function control using the electromyography bridge method

Voluntary participation of hemiplegic patients is crucial for functional electrical stimulation therapy.A wearable functional electrical stimulation system has been proposed for real-time volitional hand motor function control using the electromyography bridge method.Through a series of novel design concepts,including the integration of a detecting circuit and an analog-to-digital converter,a miniaturized functional electrical stimulation circuit technique,a low-power super-regeneration chip for wireless receiving,and two wearable armbands,a prototype system has been established with reduced size,power,and overall cost.Based on wrist joint torque reproduction and classification experiments performed on six healthy subjects,the optimized surface electromyography thresholds and trained logistic regression classifier parameters were statistically chosen to establish wrist and hand motion control with high accuracy.Test results showed that wrist flexion/extension,hand grasp,and finger extension could be reproduced with high accuracy and low latency.This system can build a bridge of information transmission between healthy limbs and paralyzed limbs,effectively improve voluntary participation of hemiplegic patients,and elevate efficiency of rehabilitation training.

Real-Time Hand Motion Parameter Estimation with Feature Point Detection Using Kinect

This paper presents a real-time Kinect- based hand pose estimation method. Different from model-based and appearance-based approaches, our approach retrieves continuous hand motion parameters in real time. First, the hand region is segmented from the depth image. Then, some specific feature points on the hand are located by the random forest classifier, and the relative displacements of these feature points are transformed to a rotation invariant feature vector. Finally, the system retrieves the hand joint parameters by applying the regression functions on the feature vectors. Experimental results are compared with the ground truth dataset obtained by a data glove to show the effectiveness of our approach. The effects of different distances and different rotation angles for the estimation accuracy are also evaluated.

DISTRIBUTION FREE LAWS OF THEITERATED LOGARITHM FOR KERNELESTIMATOR OF REGRESSION FUNCTIONBASED ON DIRECTIONAL DATADISTRIBUTION FREE LAWS OF THEITERATED LOGARITHM FOR KERNELESTIMATOR OF REGRESSION FUNCTIONBASED ON DIRECTIONAL DATA

The authors derive laws of the iterated logarithm for kernel estimator of regression function based on directional data. The results are distribution free in the sense that they are true for all distributions of design variable.

Partial functional linear quantile regression

This paper studies estimation in partial functional linear quantile regression in which the dependent variable is related to both a vector of finite length and a function-valued random variable as predictor variables. The slope function is estimated by the functional principal component basis. The asymptotic distribution of the estimator of the vector of slope parameters is derived and the global convergence rate of the quantile estimator of unknown slope function is established under suitable norm. It is showed that this rate is optirnal in a minimax sense under some smoothness assumptions on the covariance kernel of the covariate and the slope function. The convergence rate of the mean squared prediction error for the proposed estimators is also established. Finite sample properties of our procedures are studied through Monte Carlo simulations. A real data example about Berkeley growth data is used to illustrate our proposed methodology.

Nonparametric Regression with Interval-Censored Data

In many medical studies,the prevalence of interval censored data is increasing due to periodic monitoring of the progression status of a disease.In nonparametric regression model,when the response variable is subjected to interval-censoring,the regression function could not be estimated by traditional methods directly.With the censored data,we construct a new response variable which has the same conditional expectation as the original one.Based on the new variable,we get a nearest neighbor estimator of the regression function.It is established that the estimator has strong consistency and asymptotic normality.The relevant simulation reports are given.

Weighted quantile regression for longitudinal data using empirical likelihood

This paper proposes a new weighted quantile regression model for longitudinal data with weights chosen by empirical likelihood(EL). This approach efficiently incorporates the information from the conditional quantile restrictions to account for within-subject correlations. The resulted estimate is computationally simple and has good performance under modest or high within-subject correlation. The efficiency gain is quantified theoretically and illustrated via simulation and a real data application.

Regression Function Comparison for Paired Data

In this paper,the regression function comparison for paired data is studied.The proposed test statistic is based on the weighted integral of characteristic function marked by the difference of responses.There are several merits of the proposed statistic.For instance,it takes a simple V-statistic form.No bandwidth is needed.No moment conditions are required for covariates.It can be applied to covariates of any fixed dimension.The asymptotic results are also developed.It is proven that n times the proposed test statistic converges to a finite limit under the null hypothesis and the test is consistent against any fixed alternatives.Local alternative hypotheses which converge to the null hypothesis at the rate of n-1/2 are also detected.A suitable Bootstrap algorithm is also proposed for the implementation of the proposed test statistic.Simulation studies are carried out to illustrate the merits of the proposed method.A real data example is also used to illustrate the proposed testing procedures.

Strong Consistency and Convergence Rate of Modified Partitioning Estimate of Non.p.arametric Regression Function under α-Mixing Sample

In this paper, we study the strong consistency and convergence partitioning estimate of nonparametric regression function under the sample that is α sequence taking values in R^d × R^1 with identical distribution. rate of modified （（Xi,Yi）,i 〉 1} .

Dynamically integrated regression model for online auction data

We propose a dynamically integrated regression model to predict the price of online auctions,including the final price.Different from existing models,the proposed method uses not only the historical price but also the information from bidding time.Consequently,the prediction accuracy is improved compared with the existing methods.An estimation method based on B-spline approximation is proposed for the estimation and the inference of parameters and nonparametric functions in this model.The minimax rate of convergence for the prediction risk and large-sample results including the consistency and the asymptotic normality are established.Simulation studies verify the finite sample performance and the appealing prediction accuracy and robustness.Finally,when we apply our method to a 7-day auction of iPhone 6s during December 2015 and March 2016,the proposed method predicts the ending price with a much smaller error than the existing models.

THE WAVELET DETECTION OF THE JUMP AND CUSP POINTS OF A REGRESSION FUNCTION

Wavelets are applied to a regression model with an additive stationary noise. By checking the empirical wavelet coefficients with significantly large absolute values across fine scale levels, the jump points are detected first. Then the cusp points are identified by checking the wavelet coefficients with significantly large absolute values which are secondly large only to the previous wavelet coefficient across fine scale levels. All estimators are shown to be consistent.

A Gradient Iteration Method for Functional Linear Regression in Reproducing Kernel Hilbert Spaces

We consider a gradient iteration algorithm for prediction of functional linear regression under the framework of reproducing kernel Hilbert spaces.In the algorithm,we use an early stopping technique,instead of the classical Tikhonov regularization,to prevent the iteration from an overfitting function.Under mild conditions,we obtain upper bounds,essentially matching the known minimax lower bounds,for excess prediction risk.An almost sure convergence is also established for the proposed algorithm.

Heteroscedasticity Detection and Estimation with Quantile Difference Method

When dealing with regression analysis,heteroscedasticity is a problem that the authors have to face with.Especially if little information can be got in advance,detection of heteroscedasticity as well as estimation of statistical models could be even more difficult.To this end,this paper proposes a quantile difference method(QDM) that can effectively estimate the heteroscedastic function.This method,being completely free from the estimation of mean regression function,is simple,robust and easy to implement.Moreover,the QDM method enables the detection of heteroscedasticity without any restrictions on error terms,consequently being widely applied.What is worth mentioning is that based on the proposed approach estimators of both mean regression function and heteroscedastic function can be obtained.In the end,the authors conduct some simulations to examine the performance of the proposed methods and use a real data to make an illustration.

Model-Assisted Estimators with Auxiliary Functional Data

Few studies focus on the application of functional data to the field of design-based survey sampling.In this paper,the scalar-onunction regression model-assisted method is proposed to estimate the finite population means with auxiliary functional data information.The functional principal component method is used for the estimation of functional linear regression model.Our proposed functional linear regression model-assisted(FLR-assisted)estimator is asymptotically design-unbiased,consistent under mild conditions.Simulation experiments and real data analysis show that the FLR-assisted estimators are more efficient than the Horvitz-Thompson estimators under different sampling designs.