Asymptotic Comparison of Method of Moments Estimators and Maximum Likelihood Estimators of Parameters in Zero-Inflated Poisson Model

This paper discusses the estimation of parameters in the zero-inflated Poisson (ZIP) model by the method of moments. The method of moments estimators (MMEs) are analytically compared with the maximum likelihood estimators (MLEs). The results of a modest simulation study are presented.

Estimation of Poisson-Generalized Pareto Compound Extreme Value Distribution by Probability-Weighted Moments and Empirical Analysis

This paper puts forward a Poisson-generalized Pareto (Poisson-GP) distribution. This new form of compound extreme value distribution expands the existing application of compound extreme value distribution, and can be applied to predicting financial risk, large insurance settlement and high-grade earthquake, etc. Compared with the maximum likelihood estimation (MLE) and compound moment estimation (CME), probability-weighted moment estimation (PWME) is used to estimate the parameters of the distribution function. The specific formulas are presented. Through Monte Carlo simulation with sample sizes 10, 20, 50, 100, 1 000, it is concluded that PWME is an efficient method and it behaves steadily. The mean square errors (MSE) of estimators by PWME are much smaller than those of estimators by CME, and there is no significant difference between PWME and MLE. Finally, an example of foreign exchange rate is given. For Dollar/Pound exchange rates from 1990-01-02 to 2006-12-29, this paper formulates the distribution function of the largest loss among the investment losses exceeding a certain threshold by Poisson-GP compound extreme value distribution, and obtains predictive values at different confidence levels.

NONLINEAR STOCHASTIC HEAT EQUATION DRIVEN BY SPATIALLY COLORED NOISE:MOMENTS AND INTERMITTENCY

In this article, we study the nonlinear stochastic heat equation in the spatial domain R^d subject to a Gaussian noise which is white in time and colored in space. The spatial correlation can be any symmetric, nonnegative and nonnegative-definite function that satisfies Dalang's condition. We establish the existence and uniqueness of a random field solution starting from measure-valued initial data. We find the upper and lower bounds for the second moment. With these moment bounds, we first establish some necessary and sufficient conditions for the phase transition of the moment Lyapunov exponents, which extends the classical results from the stochastic heat equation on Z^d to that on R^d.Then, we prove a localization result for the intermittency fronts, which extends results by Conus and Khoshnevisan [9] from one space dimension to higher space dimension. The linear case has been recently proved by Huang et al [17] using different techniques.

AN EFFECTIVE IMAGE RETRIEVAL METHOD BASED ON KERNEL DENSITY ESTIMATION OF COLLAGE ERROR AND MOMENT INVARIANTS

In this paper, we propose a new method that combines collage error in fractal domain and Hu moment invariants for image retrieval with a statistical method - variable bandwidth Kernel Density Estimation (KDE). The proposed method is called CHK (KDE of Collage error and Hu moment) and it is tested on the Vistex texture database with 640 natural images. Experimental results show that the Average Retrieval Rate (ARR) can reach into 78.18%, which demonstrates that the proposed method performs better than the one with parameters respectively as well as the commonly used histogram method both on retrieval rate and retrieval time.

Some New Estimators of Integrated Volatility

We develop higher order accurate estimators of integrated volatility in a stochastic volatility models by using kernel smoothing method and using different weights to kernels. The weights have some relationship to moment problem. As the bandwidth of the kernel vanishes, an estimator of the instantaneous stochastic volatility is obtained. We also develop some new estimators based on smoothing splines.

Efficiency of Some Estimators for a Generalized Poisson Autoregressive Process of Order 1

Various models have been proposed in the literature to study non-negative integer-valued time series. In this paper, we study estimators for the generalized Poisson autoregressive process of order 1, a model developed by Alzaid and Al-Osh [1]. We compare three estimation methods, the methods of moments, quasi-likelihood and conditional maximum likelihood and study their asymptotic properties. To compare the bias of the estimators in small samples, we perform a simulation study for various parameter values. Using the theory of estimating equations, we obtain expressions for the variance-covariance matrices of those three estimators, and we compare their asymptotic efficiency. Finally, we apply the methods derived in the paper to a real time series.

基于LQ-moments的洪水频率分布参数计算方法研究

为改善频率曲线高尾部对实测洪水大值段的拟合效果,提高大重现期洪水设计值精度,研究LQmoments(LQM)法在洪水频率分布参数估计中的应用。LQM法是L-moments(LM)法的扩展方法,具有较好的不偏性和稳健性。以6个年最大洪峰流量系列为例,进行P-Ⅲ分布和GEV分布LQM法的参数估计,以累积相对偏差平方和(δ)、RMSE和平均绝对误差(MAE)为标准,评价和比较LQM法和LM法对P-Ⅲ和GEV分布参数的估计精度和拟合效果。结果表明,P-Ⅲ分布LQM法取得了很好的拟合效果,6个洪峰流量系列中,5个系列的最优参数估计方法为LQM法,其中3个系列的最优分布为P-Ⅲ分布;与LM法相比,LQM法能更好地拟合洪水序列大值部分,提高大重现期设计值估计精度,是洪水频率分布参数估计的有效方法。

A Low Sample Size Estimator for K Distributed Noise

In this paper, we derive a new method for estimating the parameters of the K-distribution when a limited number of samples are available. The method is based on an approximation of the Bessel function of the second kind that reduces the complexity of the estimation formulas in comparison to those used by the maximum likelihood algorithm. The proposed method has better performance in comparison with existing methods of the same complexity giving a lower mean squared error when the number of samples used for the estimation is relatively low.

Parameters Estimation of a Bivariate Generalized Poisson Distribution with Applications to Metabolic Syndrome Data

Background: Bivariate count data are commonly encountered in medicine, biology, engineering, epidemiology and many other applications. The Poisson distribution has been the model of choice to analyze such data. In most cases mutual independence among the variables is assumed, however this fails to take into accounts the correlation between the outcomes of interests. A special bivariate form of the multivariate Lagrange family of distribution, names Generalized Bivariate Poisson Distribution, is considered in this paper. Objectives: We estimate the model parameters using the method of maximum likelihood and show that the model fits the count variables representing components of metabolic syndrome in spousal pairs. We use the likelihood local score to test the significance of the correlation between the counts. We also construct confidence interval on the ratio of the two correlated Poisson means. Methods: Based on a random sample of pairs of count data, we show that the score test of independence is locally most powerful. We also provide a formula for sample size estimation for given level of significance and given power. The confidence intervals on the ratio of correlated Poisson means are constructed using the delta method, the Fieller’s theorem, and the nonparametric bootstrap. We illustrate the methodologies on metabolic syndrome data collected from 4000 spousal pairs. Results: The bivariate Poisson model fitted the metabolic syndrome data quite satisfactorily. Moreover, the three methods of confidence interval estimation were almost identical, meaning that they have the same interval width.

Small Sample Estimation in Dynamic Panel Data Models: A Simulation Study

We used simulated data to investigate both the small and large sample properties of the within-groups (WG) estimator and the first difference generalized method of moments (FD-GMM) estimator of a dynamic panel data (DPD) model. The magnitude of WG and FD-GMM estimates are almost the same for square panels. WG estimator performs best for long panels such as those with time dimension as large as 50. The advantage of FD-GMM estimator however, is observed on panels that are long and wide, say with time dimension at least 25 and cross-section dimension size of at least 30. For small-sized panels, the two methods failed since their optimality was established in the context of asymptotic theory. We developed parametric bootstrap versions of WG and FD-GMM estimators. Simulation study indicates the advantages of the bootstrap methods under small sample cases on the assumption that variances of the individual effects and the disturbances are of similar magnitude. The boostrapped WG and FD-GMM estimators are optimal for small samples.

On the Estimation of a Univariate Gaussian Distribution: A Comparative Approach

Estimation of the unknown mean, μ and variance, σ2 of a univariate Gaussian distribution given a single study variable x is considered. We propose an approach that does not require initialization of the sufficient unknown distribution parameters. The approach is motivated by linearizing the Gaussian distribution through differential techniques, and estimating, μ and σ2 as regression coefficients using the ordinary least squares method. Two simulated datasets on hereditary traits and morphometric analysis of housefly strains are used to evaluate the proposed method (PM), the maximum likelihood estimation (MLE), and the method of moments (MM). The methods are evaluated by re-estimating the required Gaussian parameters on both large and small samples. The root mean squared error (RMSE), mean error (ME), and the standard deviation (SD) are used to assess the accuracy of the PM and MLE;confidence intervals (CIs) are also constructed for the ME estimate. The PM compares well with both the MLE and MM approaches as they all produce estimates whose errors have good asymptotic properties, also small CIs are observed for the ME using the PM and MLE. The PM can be used symbiotically with the MLE to provide initial approximations at the expectation maximization step.

Texture invariant estimation of equivalent number of looks based on log-cumulants in polarimetric radar imagery

A novel estimation of the equivalent number of looks (ENL) is proposed in statistical modeling of multilook polarimetric synthetic aperture radar (PolSAR) images for the product model, which is based on the log-determinant moments (LDM). The LDM estimators discovered by looking at certain log-cumulants of the intensities of different polarization channels and the multilook polarimetric covariance matrix, which can be used for both the Gaussian model and all product models. This estimator has analytic expressions, and uses the full covariance matrix and intensities as input, which makes more statistical information available. Experiments based on simulated data and real data are performed. The comparisons among the widely used methods of equivalent number of looks (ENL) estimation for the product model such as K and G0 distributions show that the performance of the LDM estimator is outstanding. The performance of estimators for the real data of San Francisco and Flevoland is analyzed and the results are according to those of simulated data. Finally, it can be concluded that the LDM estimator is well robust to each product model with low computational complexity and high accuracy. © 1990-2011 Beijing Institute of Aerospace Information.

A Search for Solar Axions and Anomalous Neutrino Magnetic Moment with the Complete Panda X-Ⅱ Data

We report a search for new physics signals using the low energy electron recoil events in the complete data set from PandaX-Ⅱ,in light of the recent event excess reported by XENON1 T.The data correspond to a total exposure of 100.7 ton·day with liquid xenon.With robust estimates of the dominant background spectra,we perform sensitive searches on solar axions and neutrinos with enhanced magnetic moment.It is found that the axionelectron coupling gAe<4.6×10^(-12) for an axion mass less than 0.1 keV/c^(2) and the neutrino magnetic moment μv<4.9×10^(-11)μB at 90%confidence level.The observed excess from XENON1 T is within our experimental constraints.

Estimation of Parameter in a New Truncated Distribution

This paper discusses the estimation of the parameter in a truncated form of a discrete distribution which is analogous to Burr distribution. The maximum likelihood and the moment estimators of the parameter are obtained. Their asymptotic properties are also established.

Parameter Estimations for Generalized RayleighDistribution under Progressively Type-I IntervalCensored Data

In this paper, inference on parameter estimation of the generalized Rayleigh distribution are investigated for progressively type-I interval censored samples. The estimators of distribution parameters via maximum likelihood, moment method and probability plot are derived, and their performance are compared based on simulation results in terms of the mean squared error and bias. A case application of plasma cell myeloma data is used for illustrating the proposed estimation methods.

Zubair Lomax Distribution:Properties and Estimation Based on Ranked Set Sampling

In this article,we offer a new adapted model with three parameters,called Zubair Lomax distribution.The new model can be very useful in analyzing and modeling real data and provides better fits than some others new models.Primary properties of the Zubair Lomax model are determined by moments,probability weighted moments,Renyi entropy,quantile function and stochastic ordering,among others.Maximum likelihood method is used to estimate the population parameters,owing to simple random sample and ranked set sampling schemes.The behavior of the maximum likelihood estimates for the model parameters is studied using Monte Carlo simulation.Criteria measures including biases,mean square errors and relative efficiencies are used to compare estimates.Regarding the simulation study,we observe that the estimates based on ranked set sampling are more efficient compared to the estimates based on simple random sample.The importance and flexibility of Zubair Lomax are validated empirically in modeling two types of lifetime data.

Analysis of the Precision of Bispectral Estimation Methods

In order to evaluate the accuracy of bispectral estimation method, signals of cosine function were adopted. Because the cosine signals’ three order moment spectrum and three order cumulant spectrum are zero, Non zero part of the bispectrum estimated by no matter which method is the estimation error. Through the comparison of three kinds of estimation methods: the direct method, indirect method and AR parameter method, errors of various estimation methods were obtained, then changing the values of different parameters in all methods, and observing the bispectral error values changes with the parameters, so as to provide a basis for the various bispectrum estimation method and the selection.

Quasi-Negative Binomial: Properties, Parametric Estimation, Regression Model and Application to RNA-SEQ Data

Background: The Poisson and the Negative Binomial distributions are commonly used to model count data. The Poisson is characterized by the equality of mean and variance whereas the Negative Binomial has a variance larger than the mean and therefore both models are appropriate to model over-dispersed count data. Objectives: A new two-parameter probability distribution called the Quasi-Negative Binomial Distribution (QNBD) is being studied in this paper, generalizing the well-known negative binomial distribution. This model turns out to be quite flexible for analyzing count data. Our main objectives are to estimate the parameters of the proposed distribution and to discuss its applicability to genetics data. As an application, we demonstrate that the QNBD regression representation is utilized to model genomics data sets. Results: The new distribution is shown to provide a good fit with respect to the “Akaike Information Criterion”, AIC, considered a measure of model goodness of fit. The proposed distribution may serve as a viable alternative to other distributions available in the literature for modeling count data exhibiting overdispersion, arising in various fields of scientific investigation such as genomics and biomedicine.

Piecewise Filter of Infrared Image Based on Moment Theory

The disadvantages of IR images mostly include high noise, blurry edge and so on. The characteristics make the existent smoothing methods ineffective in preserving edge. To solve this problem, a piecewise moment filter (PMF) is put forward. By using moment and piecewise linear theory, the filter can preserve edge. Based on the statistical model of random noise, a related-coefficient method is presented to estimate the variance of noise. The edge region and model are then detected by the estimated variance. The expectation of first-order derivatives is used in getting the reliable offset of edge. At last, a fast moment filter of double-stair edge model is used to gain the piecewise smoothing results and reduce the calculation. The experimental result shows that the new method has a better capability than other methods in suppressing noise and preserving edge.

基于优化组合赋权的可拓学磷矿山岩体质量评价

为解决岩体质量评价相邻等级之间指标参数模糊不确定性问题,引入可拓学理论,提出基于优化组合赋权的可拓学岩体质量分级模型,对昆阳二矿磷矿山地下开采的岩石进行质量评价。首先,根据矿山地质特征选取岩石单轴饱和抗压强度(Rc)、岩石质量指标(RQD)、节理间距(Jd)、结构面条件(Jf)、地下水状态(W)和地应力影响系数(Z)6个影响指标,将每个指标划分为5个等级;然后通过改进的层次分析法和熵权法分别确定指标的主观和客观权重,引入矩估计法对主客观权重进行优化组合;最后应用修正的RMR法和Q系统法对岩体质量进行评价,将分级结果与基于优化组合赋权的可拓学岩体质量分级结果进行比较。研究表明:5个待评价岩体中,除上矿体N3的模型分级结果与修正RMR法存在差异之外,其余岩体的分级结果与修正RMR法相同,使用Q系统法的评价结果整体偏低。此外,该模型可得出岩体质量等级偏向于相邻等级的程度,分级结果符合昆阳二矿磷矿山生产勘探地质报告岩体质量范围,比修正RMR法和Q系统法更加准确,验证了本文方法的可靠性,为地下矿山开采提供了技术支撑。