A Geometric Approach to Support Vector Regression and Its Application to Fermentation Process Fast Modeling

Support vector machine(SVM) has shown great potential in pattern recognition and regressive estima-tion.Due to the industrial development demands,such as the fermentation process modeling,improving the training performance on increasingly large sample sets is an important problem.However,solving a large optimization problem is computationally intensive and memory intensive.In this paper,a geometric interpretation of SVM re-gression(SVR) is derived,and μ-SVM is extended for both L1-norm and L2-norm penalty SVR.Further,Gilbert al-gorithm,a well-known geometric algorithm,is modified to solve SVR problems.Theoretical analysis indicates that the presented SVR training geometric algorithms have the same convergence and almost identical cost of computa-tion as their corresponding algorithms for SVM classification.Experimental results show that the geometric meth-ods are more efficient than conventional methods using quadratic programming and require much less memory.

Small-area estimation of forest stand structure in Jalisco, Mexico

Natural resource statistics are often unavailable for small ecological or economic regions and policymakers have to rely on state-level datasets to evaluate the status of their resources （i.e., forests, rangelands, grasslands, agriculture, etc.） at the regional or local level. These resources can be evaluated using small-area estimation techniques. However, it is unknown which small area technique produces the most valid and precise results. The reliability and accuracy of two methods, synthetic and regression estimators, used in smallarea analyses, were examined in this study. The two small-area analysis methods were applied to data from Jalisco＇s state-wide natural resource inventory to examine how well each technique predicted selected characteristics of forest stand structure. The regression method produced the most valid and precise estimates of forest stand characteristics at multiple geographical scales. Therefore, state and local resource managers should utilize the regression method unless appropriate auxiliary information is not available.

A LARGE SAMPLE ESTIMATE IN MEDIAN LINEAR REGRESSION MODEL Ⅰ: NONTRUNCATED CASE

This paper uses a grouping-adjusting procedure to the data from a median linear regression model, and estimtes the regression coefficients by the method of weighted least squares. This method simplifies computation and in the meantime, preserves the same asymptotic normal distribution for the estimator, as in the ordinary minimum L_1-norm estimates.

Improvement of Channel Estimation with 16QAM Modulation over Fading Channel for DS-CDMA

The application of low complexity and low order robust regression algorithm in channel estimation with 16QAM over fading channel for DS-CDMA is presented in this paper After initial channel estimation with classical methods, channel gains estimated are filtered by linear or conic regression algorithm within a given regression length Simulation results show that this method offers up to 0,3 dB gain in a DS-CDMA system. The length and order of regression algorithm are two key parameters, which affect the system performance significantly and the optimal values of which depend on the speed of mobile station. It is demonstrated that this improved method can track fading channel accurately and outperforms over classical methods substantially by selecting appropriate parameters of regression algorithm under a certain channel environment.

Nonlinear wavelet estimation of regression function with random desigm

The nonlinear wavelet estimator of regression function with random design is constructed. The optimal uniform convergence rate of the estimator in a ball of Besov spaceB 3 p,q is proved under quite general assumpations. The adaptive nonlinear wavelet estimator with near-optimal convergence rate in a wide range of smoothness function classes is also constructed. The properties of the nonlinear wavelet estimator given for random design regression and only with bounded third order moment of the error can be compared with those of nonlinear wavelet estimator given in literature for equal-spaced fixed design regression with i.i.d. Gauss error.

TYRE DYNAMICS MODELLING OF VEHICLE BASED ON SUPPORT VECTOR MACHINES

Various methods of tyre modelling are implemented from pure theoretical to empirical or semi-empirical models based on experimental results. A new way of representing tyre data obtained from measurements is presented via support vector machines （SVMs）. The feasibility of applying SVMs to steady-state tyre modelling is investigated by comparison with three-layer backpropagation （BP） neural network at pure slip and combined slip. The results indicate SVMs outperform the BP neural network in modelling the tyre characteristics with better generalization performance. The SVMsqyre is implemented in 8-DOF vehicle model for vehicle dynamics simulation by means of the PAC 2002 Magic Formula as reference. The SVMs-tyre can be a competitive and accurate method to model a tyre for vehicle dynamics simuLation.

Multi-view space object recognition and pose estimation based on kernel regression

The application of high-performance imaging sensors in space-based space surveillance systems makes it possible to recognize space objects and estimate their poses using vision-based methods. In this paper, we proposed a kernel regression-based method for joint multi-view space object recognition and pose estimation. We built a new simulated satellite image dataset named BUAA-SID 1.5 to test our method using different image representations. We evaluated our method for recognition-only tasks, pose estimation-only tasks, and joint recognition and pose estimation tasks. Experimental results show that our method outperforms the state-of-the-arts in space object recognition, and can recognize space objects and estimate their poses effectively and robustly against noise and lighting conditions.

Robust U-type test for high dimensional regression coefficients using refitted cross-validation variance estimation

This paper aims to develop a new robust U-type test for high dimensional regression coefficients using the estimated U-statistic of order two and refitted cross-validation error variance estimation. It is proved that the limiting null distribution of the proposed new test is normal under two kinds of ordinary models.We further study the local power of the proposed test and compare with other competitive tests for high dimensional data. The idea of refitted cross-validation approach is utilized to reduce the bias of sample variance in the estimation of the test statistic. Our theoretical results indicate that the proposed test can have even more substantial power gain than the test by Zhong and Chen(2011) when testing a hypothesis with outlying observations and heavy tailed distributions. We assess the finite-sample performance of the proposed test by examining its size and power via Monte Carlo studies. We also illustrate the application of the proposed test by an empirical analysis of a real data example.

Generalized Class of Mean Estimators with Known Measures for Outliers Treatment

In estimation theory,the researchers have put their efforts to develop some estimators of population mean which may give more precise results when adopting ordinary least squares(OLS)method or robust regression techniques for estimating regression coefficients.But when the correlation is negative and the outliers are presented,the results can be distorted and the OLS-type estimators may give misleading estimates or highly biased estimates.Hence,this paper mainly focuses on such issues through the use of non-conventional measures of dispersion and a robust estimation method.Precisely,we have proposed generalized estimators by using the ancillary information of non-conventional measures of dispersion(Gini’s mean difference,Downton’s method and probabilityweighted moment)using ordinary least squares and then finally adopting the Huber M-estimation technique on the suggested estimators.The proposed estimators are investigated in the presence of outliers in both situations of negative and positive correlation between study and auxiliary variables.Theoretical comparisons and real data application are provided to show the strength of the proposed generalized estimators.It is found that the proposed generalized Huber-M-type estimators are more efficient than the suggested generalized estimators under the OLS estimation method considered in this study.The new proposed estimators will be useful in the future for data analysis and making decisions.

Adaptive Fuzzy Controller Using Nearest Neighborhood Clustering and Its Application

A novel control method for the nonlinear and complex plants with environmental uncertainties and variable parameters has been proposed by use of the nearest neighborhood clustering algorithm, the fuzzy control and the variable regressive estimation (VRE) technology. It overcomes the defects of the other adaptive methods such as the strong dependence to the system and the difficulty of the acquirement of the professional knowledge during the modifying period of the rules. The application of new algorithm to the electrical heating furnace with multiple zones demonstrates the advantages of the proposed method.

ESTIMATION OF THE NUISANCE PARAMETER FOR A SEMIMARTINGALE REGRESSION MODEL

A nuisance parameter is introduced to the semimartingale regression model proposed by Aalen(1980), and we construct two estimators for this nuisance parameter based on the results ofparametric estimation which were given by Mckeague (1986) using the method of sieves. Theconsistency of the estimators is also provided.

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.

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.

ADMISSIBILITY OF LINEAR ESTIMATORS OF REGRESSION COEFFICIENTS UNDER QUADRATIC LOSS

For the general fixed effects linear model: Y = X_T+ε, ε～N(0, V), V≥0, weobtain the necessary and sufficient conditions for LY +a to be admissible for a linear estimablefunction S_r in the class of all estimators under the loss function (d -- Sr)'D(d --Sr), whereD≥0 is known. For the general random effects linear model: Y = Xβ+ε,(βε)～N((Aα 0), (V_(11)V_(12)V_(21)V_(22))), ∧= XV_(11)X'+XV_(12)+ V_(21)X+V_(22)≥0, we also get the necessaryand sufficient conditions for LY+a to be admissible for a linear estimable function Sα+Qβin the class of all estimators under the loss function (d-Sα-Qβ)'D(d-Sα-Qβ).whereD≥0 is known.

Existence of the Uniformly Minimum Risk Unbiased Estimator in Seemingly Unrelated Regression System

For a seemingly Unrelated regression system with the assumption of normality,a necessary and sufficient condition for the existence of the Uniformly Minimum Risk Unbiased (UMRU)estimator of regression coefficients under strictly convex loss is obtained;it is proved that any unbiased estimator can not improve the least squares estimator;it is also shown that no UMRU estimator exists under missing observations.

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.

A Regression Analysis Model Based on Wavelet Networks

In this paper, an approach is proposed to combine wavelet networks and techniques of regression analysis. The resulting wavelet regression estimator is well suited for regression estimation of moderately large dimension, in particular for regressions with localized irregularities.

Estimating traffic volume on Wyoming low volume roads using linear and logistic regression methods

Traffic volume is an important parameter in most transportation planning applications. Low volume roads make up about 69% of road miles in the United States. Estimating traffic on the low volume roads is a cost-effective alternative to taking traffic counts. This is because traditional traffic counts are expensive and impractical for low priority roads. The purpose of this paper is to present the development of two alternative means of cost- effectively estimating traffic volumes for low volume roads in Wyoming and to make recommendations for their implementation. The study methodology involves reviewing existing studies, identifying data sources, and carrying out the model development. The utility of the models developed were then verified by comparing actual traffic volumes to those predicted by the model. The study resulted in two regression models that are inexpensive and easy to implement. The first regression model was a linear regression model that utilized pavement type, access to highways, predominant land use types, and population to estimate traffic volume. In verifying the model, an R^2 value of 0.64 and a root mean square error of 73.4% were obtained. The second model was a logistic regression model that identified the level of traffic on roads using five thresholds or levels. The logistic regression model was verified by estimating traffic volume thresholds and determining the percentage of roads that were accurately classified as belonging to the given thresholds. For the five thresholds, the percentage of roads classified correctly ranged from 79% to 88%. In conclusion, the verification of the models indicated both model types to be useful for accurate and cost-effective estimation of traffic volumes for low volume Wyoming roads. The models developed were recommended for use in traffic volume estimations for low volume roads in pavement management and environmental impact assessment studies.

Asymptotics of the“Minimum L_1-Norm”Estimates in Nonparametric Regression Models

Consider the nonparametric regression model Y=go（T）+u,where Y is real-valued, u is a random error,T ranges over a nondegenerate compact interval,say[0,1],and go（·）is an unknown regression function,which is m（m≥0）times continuously differentiable and its ruth derivative,g0（m）,satisfies a H■lder condition of order γ（m +γ】1/2）.A piecewise polynomial L1- norm estimator of go is proposed.Under some regularity conditions including that the random errors are independent but not necessarily have a common distribution,it is proved that the rates of convergence of the piecewise polynomial L1-norm estimator are o(n-2（m+γ）+1/m+γ-1/δalmost surely and o(n-2（m+γ）+1/m+γ-δ)in probability,which can arbitrarily approach the optimal rates of convergence for nonparametric regression,where δ is any number in （0, min（（m+γ-1/2）/3,γ））.