Application of local polynomial estimation in suppressing strong chaotic noise

In this paper, we propose a new method that combines chaotic series phase space reconstruction and local polynomial estimation to solve the problem of suppressing strong chaotic noise. First, chaotic noise time series are reconstructed to obtain multivariate time series according to Takens delay embedding theorem. Then the chaotic noise is estimated accurately using local polynomial estimation method. After chaotic noise is separated from observation signal, we can get the estimation of the useful signal. This local polynomial estimation method can combine the advantages of local and global law. Finally, it makes the estimation more exactly and we can calculate the formula of mean square error theoretically. The simulation results show that the method is effective for the suppression of strong chaotic noise when the signal to interference ratio is low.

LOCAL MEDIAN ESTIMATION OF VARIANCE FUNCTION

This paper considers local median estimation in fixed design regression problems. The proposed method is employed to estimate the median function and the variance function of a heteroscedastic regression model. Strong convergence rates of the proposed estimators are obtained. Simulation results are given to show the performance of the proposed methods.

Global parameter estimation of the Cochlodinium polykrikoides model using bioassay data

Cochlodinium polykrikoides is a notoriously harmful algal species that inflicts severe damage on the aquacultures of the coastal seas of Korea and Japan. Information on their expected movement tracks and boundaries of influence is very useful and important for the effective establishment of a reduction plan. In general, the information is supported by a red-tide（a.k.a algal bloom） model. The performance of the model is highly dependent on the accuracy of parameters, which are the coefficients of functions approximating the biological growth and loss patterns of the C. polykrikoides. These parameters have been estimated using the bioassay data composed of growth-limiting factor and net growth rate value pairs. In the case of the C. polykrikoides, the parameters are different from each other in accordance with the used data because the bioassay data are sufficient compared to the other algal species. The parameters estimated by one specific dataset can be viewed as locally-optimized because they are adjusted only by that dataset. In cases where the other one data set is used, the estimation error might be considerable. In this study, the parameters are estimated by all available data sets without the use of only one specific data set and thus can be considered globally optimized. The cost function for the optimization is defined as the integrated mean squared estimation error, i.e., the difference between the values of the experimental and estimated rates. Based on quantitative error analysis, the root-mean squared errors of the global parameters show smaller values, approximately 25%–50%, than the values of the local parameters. In addition, bias is removed completely in the case of the globally estimated parameters. The parameter sets can be used as the reference default values of a red-tide model because they are optimal and representative. However, additional tuning of the parameters using the in-situ monitoring data is highly required.As opposed to the bioassay data, it is necessary because the bioassay data have limitations in terms of the in-situ coastal conditions.

Local Hybrid Linear State Estimation for Electric Power Systems Using Stream Processing

The increasing penetration of renewable energy resources with highly fluctuating outputs has placed increasing concern on the accuracy and timeliness of electric power system state estimation(SE).Meanwhile,we note that only a fraction of system states fluctuate at the millisecond level and require to be updated.As such,refreshing only those states with significant variation would enhance the computational efficiency of SE and make fast-continuous update of states possible.However,this is difficult to achieve with conventional SE methods,which generally refresh states of the entire system every 4–5 s.In this context,we propose a local hybrid linear SE framework using stream processing,in which synchronized measurements received from phasor measurement units(PMUs),and trigger/timingmode measurements received from remote terminal units(RTUs)are used to update the associated local states.Moreover,the measurement update process efficiency and timeliness are enhanced by proposing a trigger measurement-based fast dynamic partitioning algorithm for determining the areas of the system with states requiring recalculation.In particular,non-iterative hybrid linear formulations with both RTUs and PMUs are employed to solve the local SE problem.The timeliness,accuracy,and computational efficiency of the proposed method are demonstrated by extensive simulations based on IEEE 118-,300-,and 2383-bus systems.

Target localization and parameters estimation by sonar system with explosions as underwater sound sources

Underwater target localization and parameters(azimuth and range) estimation by the method of utilizing explosions as underwater sound sources are described in this paper.The narrow beam reverberation model of the target echo signal is researched to estimate the target azimuth in reverberation background.Estimation errors of target azimuth and range are studied and proved to approximately meet Gauss distribution.Then the variance formula of target range error is deduced.Simulation experiments are applied to research the target range error and its standard deviation,and a series of measures to improve the estimation accuracy of target range are proposed.It is confirmed by the data processing results of simulations and lake experiments that the proposed method can accurately locate underwater target at a long distance on the condition of a certain underwater explosion range error.

Testing Linearity of Nonparametric Component in Partially Linear Model

In this paper, we propose the test statistic to check whether the nonparametric function in partially linear models is linear or not. We estimate the nonparametric function in alternative by using the local linear method, and then estimate the parameters by the two stage method. The test statistic under the null hypothesis is calculated, and it is shown to be asymptotically normal.

LOCAL ERROR ESTIMATES FOR METHODS OF CHARACTERISTICS INCORPORATING STREAMLINE DIFFUSION

Allen and Liu (1995) introduced a new method for a time-dependent convection dominated diffusion problem, which combines the modified method of characteristics and method of streamline diffusion. But they ignored the fact that the accuracy of time discretization decays at half an order when the characteristic line goes out of the domain. In present paper, the author shows that, as a remedy, a simple lumped scheme yields a full accuracy approximation. Forthermore, some local error bounds independent of the small viscosity axe derived for this scheme outside the boundary layers.

RELATIVE STABILITY FOR LOCAL MEDIAN ESTIMATE

Consider the nonparametric median regression model Y-ni = g(x(ni)) + epsilon(ni), 1 less than or equal to i less than or equal to n, where Y-ni's are the observations at the fixed design points x(ni) is an element of [0, 1], is an element of(ni)'s are independent identically distributed random variables with median zero, g(x) is the smooth function of interest, Suppose the local median estimate (g) over tilde(n, h)(x) of g(x) admits the Bahadur's representation. Under some regular conditions, the relative stability of the local median estimate is established in the L-2 sense.

An Efficient Topography Adaptive Filter for Insar Processing

An efficient implementation of the topography adaptive filter based on local frequency estimation is proposed, where chirp z transform is applied to enhance the accuracy of the frequency estimation. As a by product of this adaptive filter, the linear approximated phase model of the interferogram is employed to improve the coherence estimation. The impacts of the adaptive filter on global and local phase unwrapping algorithms are discussed. Finally, aiming at the negative effect that the adaptive filter can bring to local phase unwrapping algorithms, a fusion scheme that takes advantage of least square and several local phase unwrapping algorithms is presented.

Testing Equality of Nonparametric Functions in Two Partially Linear Models

We propose the test statistic to check whether the nonpararnetric functions in two partially linear models are equality or not in this paper. We estimate the nonparametric function both in null hypothesis and the alternative by the local linear method, where we ignore the parametric components, and then estimate the parameters by the two stage method. The test statistic is derived, and it is shown to be asymptotically normal under the null hypothesis.

Asymptotic Confidence Bands for Copulas Based on the Local Linear Kernel Estimator

In this paper, we establish asymptotically optimal simultaneous confidence bands for the copula function based on the local linear kernel estimator proposed by Chen and Huang [1]. For this, we prove under smoothness conditions on the derivatives of the copula a uniform in bandwidth law of the iterated logarithm for the maximal deviation of this estimator from its expectation. We also show that the bias term converges uniformly to zero with a precise rate. The performance of these bands is illustrated by a simulation study. An application based on pseudo-panel data is also provided for modeling the dependence structure of Senegalese households’ expense data in 2001 and 2006.

Source localization using a non-cocentered orthogonal loop and dipole (NCOLD) array

A uniform array of scalar-sensors with intersensor spacings over a large aperture size generally offers enhanced resolution and source localization accuracy,but it may also lead to cyclic ambiguity.By exploiting the polarization information of impinging waves,an electromagnetic vector-sensor array outperforms the unpolarized scalar-sensor array in resolving this cyclic ambiguity.However,the electromagnetic vector-sensor array usually consists of cocentered orthogonal loops and dipoles（COLD）,which is easily subjected to mutual coupling across these cocentered dipoles/loops.As a result,the source localization performance of the COLD array may substantially degrade rather than being improved.This paper proposes a new source localization method with a non-cocentered orthogonal loop and dipole（NCOLD）array.The NCOLD array contains only one dipole or loop on each array grid,and the intersensor spacings are larger than a half-wavelength.Therefore,unlike the COLD array,these well separated dipoles/loops minimize the mutual coupling effects and extend the spatial aperture as well.With the NCOLD array,the proposed method can effciently exploit the polarization information to offer high localization precision.

Weighted local polynomial estimations of a non-parametric function with censoring indicators missing at random and their applications

In this paper,we consider the weighted local polynomial calibration estimation and imputation estimation of a non-parametric function when the data are right censored and the censoring indicators are missing at random,and establish the asymptotic normality of these estimators.As their applications,we derive the weighted local linear calibration estimators and imputation estimations of the conditional distribution function,the conditional density function and the conditional quantile function,and investigate the asymptotic normality of these estimators.Finally,the simulation studies are conducted to illustrate the finite sample performance of the estimators.

M-Cross-Validation in Local Median Estimation

M-cross-validation criterion is proposed for selecting a smoothing parameter in a nonparametric median regression model in which a uniform weak convergency rate for the M-cross-validated local median estimate, and the upper and lower bounds of the smoothing parameter selected by the proposed criterion are established. The main contribution of this study shows a drastic difference from those encountered in the classical L2-, L1- cross-validation technique, which leads only to the consistency in the sense of the average. Obviously, our results are novel and nontrivial from the point of view of mathematics and statistics, which provides insight and possibility for practitioners substituting maximum deviation for average deviation to evaluate the performance of the data-driven technique.

Asymptotic properties of a nonparametric conditional density estimator in the local linear estimation for functional data via a functional single-index model

This paper deals with the conditional density estimator of a real response variable given a functional random variable(i.e.,takes values in an infinite-dimensional space).Specifically,we focus on the functional index model,and this approach represents a good compromise between nonparametric and parametric models.Then we give under general conditions and when the variables are independent,the quadratic error and asymptotic normality of estimator by local linear method,based on the single-index structure.Finally,wecomplete these theoretical advances by some simulation studies showing both the practical result of the local linear method and the good behaviour for finite sample sizes of the estimator and of the Monte Carlo methods to create functional pseudo-confidence area.

ASYMPTOTIC NORMALITY OF THE NONPARAMETRIC KERNEL ESTIMATION OF THE CONDITIONAL HAZARD FUNCTION FOR LEFT-TRUNCATED AND DEPENDENT DATA

Under some mild conditions, we derive the asymptotic normality of the Nadaraya-Watson and local linear estimators of the conditional hazard function for left-truncated and dependent data. The estimators were proposed by Liang and Ould-Sa?d [1]. The results confirm the guess in Liang and Ould-Sa?d [1].

A priori estimates versus arbitrarily large solutions for fractional semi-linear elliptic equations with critical Sobolev exponent

We study positive solutions to the fractional semi-linear elliptic equation(−∆)σu=K(x)u n+2σn−2σin B2\{0}with an isolated singularity at the origin,where K is a positive function on B2,the punctured ball B2\{0}⊂Rn with n>2,σ∈(0,1),and(−∆)σis the fractional Laplacian.In lower dimensions,we show that for any K∈C1(B2),a positive solution u always satisfies that u(x)6 C|x|−(n−2σ)/2 near the origin.In contrast,we construct positive functions K∈C1(B2)in higher dimensions such that a positive solution u could be arbitrarily large near the origin.In particular,these results also apply to the prescribed boundary mean curvature equations on B n+1.

Explicit Representations for Local Lagrangian Numerical Differentiation

It is shown that in Lagrangian numerical differentiation formulas, the coefficients are explicitly expressed by means of cycle indicator polynomials of symmetric group. Moreover, asymptotic expansions of the remainders are also explicitly represented as a fixed number of interpolation nodes approaching infinitely to the point at which the derivative is evaluated. This implies that complete explicit formulas for local Lagrangian numerical differentiation can be obtained.

Maximal estimate for solutions to a class of dispersive equation with radial initial value

Consider the general dispersive equation defined bywhere φ（√-△） is a pseudo-differential operator with symbol φ（｜ξ｜）. In this paper, for φ satisfying suitable growth conditions and the radial initial data f in Sobolev space, we give the local and global Lq estimate for the maximal operator S; defined by Sφf（x） = sup0〈t〈1｜St,φf（x）｜, where St,φ f is the solution of equation （＊）. These estimates imply the a.e. convergence of the solution of equation （＊）.

Harmonic moments and large deviations for a critical Galton-Watson process with immigration

In this paper,a critical Galton-Watson branching process with immigration Z_(n)is studied.We first obtain the convergence rate of the harmonic moment of Z_(n).Then the large deviation of S_(Z_(n)):∑_(i=1)^(Z_(n))X_(i)is obtained,where{X_(i)}is a sequence of independent and identically distributed zero-mean random variables with the tail indexα>2.We shall see that the converging rate is determined by the immigration mean,the variance of reproducing and the tail index of X_(1)^(+),compared with the previous result for the supercritical case,where the rate depends on the Schroder constant and the tail index.