ON THE POINTWISE ESTIMATIONS OF APPROXIMATION OF FUNCTIONS AND THEIR DERIVATIVES BY HERMITE INTERPOLATION

The object of this paper is to establish the pointwise estimations of approximation of functions in C^1 and their derivatives by Hermite interpolation polynomials. The given orders have been proved to be exact in gen- eral.

Online LS-SVM for function estimation and classification

An online algorithm for training LS-SVM (Least Square Support VectorMachines) was proposed for the application of function estimation and classification. Online LS-SVMmeans that LS-SVM can be trained in an incremental way, and can be pruned to get sparseapproximation in a decremental way. When a SV (Support Vector) is added or removed, the onlinealgorithm avoids computing large-scale matrix inverse. Thus the computation cost is reduced. Onlinealgorithm is especially useful to realistic function estimation problem such as systemidentification. The experiments with benchmark function estimation problem and classificationproblem show the validity of this online algorithm.

EMPIRICAL BAYES ESTIMATION FOR ESTIMABLE FUNCTION OF REGRESSION COEFFICIENT IN A MULTIPLE LINEAR REGRESSION MODEL

In this paper we consider the empirical Bayes (EB) estimation problem for estimable function of regression coefficient in a multiple linear regression model Y=Xβ+e. where e with given β has a multivariate standard normal distribution. We get the EB estimators by using kernel estimation of multivariate density function and its first order partial derivatives. It is shown that the convergence rates of the EB estimators are under the condition where an integer k > 1 . is an arbitrary small number and m is the dimension of the vector Y.

Temporally Consistent Depth Map Estimation for 3D Video Generation and Coding

In this paper, we propose a new algorithm for temporally consistent depth map estimation to generate three-dimensional video. The proposed algorithm adaptively computes the matching cost using a temporal weighting function, which is obtained by block-based moving object detection and motion estimation with variable block sizes. Experimental results show that the proposed algorithm improves the temporal consistency of the depth video and reduces by about 38% both the flickering artefact in the synthesized view and the number of coding bits for depth video coding.

A SHARP ESTIMATE ON THE DEGREE OF APPROXIMATION TO FUNCTIONS OF BOUNDED VARIATION BY CERTAIN OPERATORS

Recently Guo introduced integrated Meyer -Konig and Zeller operators and studied the rate of convergence for function of bounded variation. In this note we give a sharp estimate for these operators.

Generalized Method of Moments and Generalized Estimating Functions Using Characteristic Function

GMM inference procedures based on the square of the modulus of the model characteristic function are developed using sample moments selected using estimating function theory and bypassing the use of empirical characteristic function of other GMM procedures in the literature. The procedures are relatively simple to implement and are less simulation-oriented than simulated methods of inferences yet have the potential of good efficiencies for models with densities without closed form. The procedures also yield better estimators than method of moment estimators for models with more than three parameters as higher order sample moments tend to be unstable.

A LAW OF THE ITERATED LOGARITHM FOR NEAREST NEIGHBOR ESTIMATION OF MULTIVARIATE DENSITY FUNCTION

Let X be a d-dimensional random vector with unknown density function f(z) = f (z1, ..., z(d)), and let f(n) be teh nearest neighbor estimator of f proposed by Loftsgaarden and Quesenberry (1965). In this paper, we established the law of the iterated logarithm of f(n) for general case of d greater-than-or-equal-to 1, which gives the exact pointwise strong convergence rate of f(n).

Estimation of Reliability for Stress-Strength Cascade Model

The study endeavors to provide statistical inference for a (1 + 1) cascade system for exponential distribution under joint effect of stress-strength attenuation factors. Estimators of reliability function are obtained using Maximum Likelihood Estimator (MLE) and Uniformly Minimum Variance Unbiased Estimator (UMVUE) of the parameters. Asymptotic distribution of the parameters is also obtained. Comparison between estimators is made using data obtained through simulation experiment.

DOA estimation method for wideband signals by block sparse reconstruction

For the direction of arrival（DOA） estimation,traditional sparse reconstruction methods for wideband signals usually need many iteration times.For this problem,a new method for two-dimensional wideband signals based on block sparse reconstruction is proposed.First,a prolate spheroidal wave function（PSWF） is used to fit the wideband signals,then the block sparse reconstruction technology is employed for DOA estimation.The proposed method uses orthogonalization to choose the matching atoms,ensuring that the residual components correspond to the minimum absolute value.Meanwhile,the vectors obtained by iteration are back-disposed according to the corresponding atomic matching rules,so the extra atoms are abandoned in the course of iteration,and the residual components of current iteration are reduced.Thus the original sparse signals are reconstructed.The proposed method reduces iteration times comparing with the traditional reconstruction methods,and the estimation precision is better than the classical two-sided correlation transformation（TCT）algorithm when the snapshot is small or the signal-to-noise ratio（SNR） is low.

Boundedness for Multilinear Operators of Pseudo-Differential Operators

In this paper, we establish a sharp function estimate for the multilinear integral operators associated to the pseudo-differential operators. As the application, we obtain the Lp (1 p norm inequalities for the multilinear operators.

Fingerprint Directional Image Partitioning Based on Genetic Algorithm

In this work, we introduce a method of fingerprint directional image partitioning based on GA. According to the fingerprint topology, A set of dynamic partition masks and a cost estimating function are designed to guide the partitioning procedure. Finding best fitted mask application is converted to an functional optimizing problem, and we give out a GA solution to the problem. At last, we discuss the application of the proposed method in Fingerprint Classification.

Comparison of ground truth location of earthquake from InSAR and from ambient seismic noise: A case study of the 1998 Zhangbei earthquake

Because ambient seismic noise provides estimated Green’s function （EGF） between two sites with high accuracy, Rayleigh wave propagation along the path connecting the two sites is well resolved. Therefore, earthquakes which are close to one seismic station can be well located with calibration extracting from EGF. We test two algorithms in locating the 1998 Zhangbei earthquake, one algorithm is waveform-based, and the other is traveltime-based. We first compute EGF between station ZHB （a station about 40 km away from the epicenter） and five IC/IRIS stations. With the waveform-based approach, we calculate 1D synthetic single-force Green’s functions between ZHB and other four stations, and obtain traveltime corrections by correlating synthetic Green’s functions with EGFs in period band of 10–30 s. Then we locate the earthquake by minimizing the differential travel times between observed earthquake waveform and the 1D synthetic earthquake waveforms computed with focal mechanism provided by Global CMT after traveltime correction from EGFs. This waveform-based approach yields a location which error is about 13 km away from the location observed with InSAR. With the traveltime-based approach, we begin with measuring group velocity from EGFs as well as group arrival time on observed earthquake waveforms, and then locate the earthquake by minimizing the difference between observed group arrival time and arrival time measured on EGFs. This traveltime-based approach yields accuracy of 3 km, Therefore it is feasible to achieve GT5 （ground truth location with accuracy 5 km） with ambient seismic noises. The less accuracy of the waveform-based approach was mainly caused by uncertainty of focal mechanism.

Estimated Green's function extracted from superconducting gravimeters and seismometers

Estimated Green’s function （EGF） between stations has been extracted from ambient seismic noise, direct surface wave and coda waves. It is also confirmed by laboratory experiments on ultrasonics and theoretical derivations assuming diffusive wave field, equi-partition of modes or random sources on an enclosed surface. This method provides a new approach to study the crust and mantle structure at regional scale, continental scale and global scale. Following the achievements with seismometer records, the records of infrasonic station, hydrophone and microphone were also used to obtain the EGFs of different wave fields. Since superconducting gravimeter is a better long period instrument than regular seismometer, EGF at longer period is expected to be obtained with the cross correlation of gravity data. In this paper, we will show the EGFs extracted by cross-correlations between the superconducting gravimeters and the seismometers. Both the travel times and dispersion curves obtained from different data types are consistent. The result shows that it is possible to retrieve the deep structure by the cross correlation of gravity data.

A computational model of the human glucose-insulin regulatory system

Objective：A computational model of insulin secretion and glucose metabolism for assisting the diagnosis of diabetes mellitus in clinical research is introduced.The proposed method for the estimation of parameters for a system of ordinary differential equations（ODEs）that represent the time course of plasma glucose and insulin concentrations during glucose tolerance test（GTT）in physiological studies is presented.The aim of this study was to explore how to interpret those laboratory glucose and insulin data as well as enhance the Ackerman mathematical model.Methods：Parameters estimation for a system of ODEs was performed by minimizing the sum of squared residuals（SSR）function,which quantifies the difference between theoretical model predictions and GTT＇s experimental observations.Our proposed perturbation search and multiple-shooting methods were applied during the estimating process.Results：Based on the Ackerman＇s published data,we estimated the key parameters by applying R-based iterative computer programs.As a result,the theoretically simulated curves perfectly matched the experimental data points.Our model showed that the estimated parameters,computed frequency and period values,were proven a good indicator of diabetes.Conclusion：The present paper introduces a computational algorithm to biomedical problems,particularly to endocrinology and metabolism fields,which involves two coupled differential equations with four parameters describing the glucose-insulin regulatory system that Ackerman proposed earlier.The enhanced approach may provide clinicians in endocrinology and metabolism field insight into the transition nature of human metabolic mechanism from normal to impaired glucose tolerance.

ASYMPTOTIC NORMALITY OF KERNEL ESTIMATES OF A DENSITY FUNCTION UNDER ASSOCIATION DEPENDENCE

Let {Xn, n≥1} be a strictly stationary sequence of random variables, which are either associated or negatively associated, f(.) be their common density. In this paper, the author shows a central limit theorem for a kernel estimate of f(.) under certain regular conditions.

An Optimization Technique for PMF Estimation in Approximate Circuits

As an emerging computing technology,approximate computing enables computing systems to utilize hardware resources efficiently.Recently,approximate arithmetic units have received extensive attention and have been employed as hardware modules to build approximate circuit systems,such as approximate accelerators.In order to make the approximate circuit system meet the application requirements,it is imperative to quickly estimate the error quality caused by the approximate unit,especially in the high-level synthesis of the approximate circuit.However,there are few studies in the literature on how to efficiently evaluate the errors in the approximate circuit system.Hence,this paper focuses on error evaluation techniques for circuit systems consisting of approximate adders and approximate multipliers,which are the key hardware components in fault-tolerant applications.In this paper,the characteristics of probability mass function(PMF)based estimation are analyzed initially,and then an optimization technique for PMF-based estimation is proposed with consideration of these features.Finally,experiments prove that the optimization technology can reduce the time required for PMF-based estimation and improve the estimation quality.

Quantitative Green's function estimates for lattice quasi-periodic Schrodinger operators

In this paper,we establish quantitative Green’s function estimates for some higher-dimensional lattice quasi-periodic(QP)Schrodinger operators.The resonances in the estimates can be described via a pair of symmetric zeros of certain functions,and the estimates apply to the sub-exponential-type non-resonance conditions.As the application of quantitative Green’s function estimates,we prove both the arithmetic version of Anderson localization and the finite volume version of(1/2-)-Holder continuity of the integrated density of states(IDS)for such QP Schrodinger operators.This gives an affirmative answer to Bourgain’s problem in Bourgain(2000).

On nonparametric change point estimator based on empirical characteristic functions

We propose a nonparametric change point estimator in the distributions of a sequence of independent observations in terms of the test statistics given by Huˇskov′a and Meintanis(2006) that are based on weighted empirical characteristic functions. The weight function ω(t; a) under consideration includes the two weight functions from Huˇskov′a and Meintanis(2006) plus the weight function used by Matteson and James(2014),where a is a tuning parameter. Under the local alternative hypothesis, we establish the consistency, convergence rate, and asymptotic distribution of this change point estimator which is the maxima of a two-side Brownian motion with a drift. Since the performance of the change point estimator depends on a in use, we thus propose an algorithm for choosing an appropriate value of a, denoted by a_s which is also justified. Our simulation study shows that the change point estimate obtained by using a_s has a satisfactory performance. We also apply our method to a real dataset.

Estimation of maximum inclusion by statistics of extreme values method in bearing steel

A statistic method, statistics of extreme values （SEV）, was described in detail, which can esti mate the size of maximum inclusion in steel. The characteristic size of the maximum inclusion in a high clean bearing steel （GCrl5） was evaluated by this method, and the morphology and corn position of large inclusions found were analyzed by scanning electron microscopy （SEM）. When standard inspection area （S0） is 280 mm2, the characteristic size of the biggest inclusion found in 30 standard inspection area is 23.93 μm, and it has a 99.9% probability of the characteristic size of maximum inclusion predicted being no larger than 36.85μm in the experimental steel. SEM result shows that large inclusions found are mainly composed of CaS, calcium-aluminate and MgO. Compositing widely exists in large inclusions in high clean bearing steel. Compared with traditional evaluation method, SEV method mainly focuses on inclusion size, and the esti- mation result is not affected by inclusion types. SEV method is suitable for the inclusion eval uation of high clean bearing steel.

Measurement and estimation of free field to eardrumtransfer function for virtual acoustic space research

Free field to Eardrum Thansfer Function (FETF) is one of the major factors influencing the identification of the sound source direction. FETF can be employed to generate a Virtual Acoustic Space (VAS) by computer and other equlpment. In this paper the methods to improve the measurement and estimation of FETF are approached. Least-mean-squares (LMS)method is much better than empirical FFT method. This paper also gives a sample description of excitation signals for measuring the impulse response of FETF.