A comparative study for the location and scale parameters of the Weibull distribution with given shape parameter

Nine parametric estimators of the location and scale parameters of a two-parameter Weibull distribution are compared in terms of their bias and efficiency in a simulation study. The estimators considered are the maximum likelihood estimators (MLE), moment estimators (ME), generalized spacing estimators (GSE), modified maximum likelihood estimators I (MMLE-I), modified maximum likelihood estimators II (MMLE-II), Tiku's modified maximum likelihood estimators (TMMLE), least-squares estimators (LSE), weighted least-squares estimators (WLSE) and percentile estimators (PCE). The aim of the comparisons is to identify the most efficient estimators among these nine estimators for different shape parameters and sample sizes.     

Adaptive detection of distributed targets in compound-Gaussian clutter with inverse gamma texture

The problem of coherent detection for distributed target in compound-Gaussian clutter with inverse gamma texture is studied and three detectors. One-step generalized likelihood ratio test (GLRT), maximum a-posteriori GLRT and two-step GLRT, are proposed respectively in a Bayesian architecture. Resultantly, these detectors have similar detection structures with their test statistics modulated by the shape and scale parameters of the texture. Alternatively, they can be reformulated into another form with their test statistics associated with the scale parameter and detection thresholds related with the shape parameter. And this detection structure can be seen as a matched filter form with a shape-parameter-dependent threshold like the detectors for point target. Subsequently, the proposed detectors are compared with two-step GLRT based on compound-Gaussian clutter without considering texture model, their detection performances are evaluated, and their robustness are analyzed via Monte Carlo simulations. Results enlighten us that: (1) the three Bayesian detectors bear pretty much the same detection performances; (2) the detection performances fluctuate more intensely when the shape parameter or the scale parameter is smaller; (3) the shape parameter has more influences on the detection performances than the scale parameter, as it is an indication of the clutter impulsiveness.     

Estimation of the female labor supply models by Heckman’s two-step estimator and the maximum likelihood estimator

The female labor supply models have been widely used in labor economics. The models are usually estimated by Heckman’s two-step estimator. However, Heckman’s two-step estimator often performs poorly. This paper considers an estimation of the models by the maximum likelihood method. An algorithm which makes calculation of the maximum likelihood estimator (MLE) possible is proposed. The finite sample properties are compared using Monte Carlo experiments.     

A simulation-based hyperparameter selection for quantile estimation of the generalized extreme value distribution

A systematic way of selecting hyperparameters of the prior on the shape parameter of the generalized extreme value distribution (GEVD) is presented. The optimal selection is based on a Monte Carlo simulation in the generalized maximum likelihood estimation (GMLE) framework. A scaled total misfit measure for the accurate estimation of upper quantiles is used for the selection criterion. The performance evaluations for GEVD and non-GEVD show that the GMLE with selected hyperparameters produces more accurate quantile estimates than the MLE, the L-moments estimator, and Martins–Stedinger’s GMLE.     

Maximum likelihood parameter estimation algorithm for controlled autoregressive autoregressive models

A maximum likelihood parameter estimation algorithm is derived for controlled autoregressive autoregressive (CARAR) models based on the maximum likelihood principle. In this derivation, we use an estimated noise transfer function to filter the input–output data. The simulation results show that the proposed estimation algorithm can effectively estimate the parameters of such class of CARAR systems and give more accurate parameter estimates than the recursive generalized least-squares algorithm.     

Estimation of body and tail distribution under extreme events for reliability analysis

In the past decades, many reliability analyses have been developed and applied to engineering fields considering uncertainties of input and output random variables as normal distributions. However, when input uncertainty is taken into the system as extreme events such as weather, temperature, environmental conditions etc., output distribution cannot be described by normal distribution. On the other hand, one of distributions to analyze reliability of a system under extreme events is generalized Pareto distribution. Generalized Pareto distribution has been developed and applied for modelling extreme events. However, conventional methods estimate only the shape and scale parameters by assuming that the location parameter is chosen by experiences focused only on the tail distribution. However, since the tail distribution affected by the body distribution and vice versa, both the body and tail distributions should be considered when the parameters of distribution are estimated. In this study, therefore, a new parameter estimation method is proposed to determine shape, scale and location parameters simultaneously by combining likelihood functions of body and tail distributions using Akaike information criterion and generalized Pareto distribution, respectively. Finally, the parameters of body and tail distributions are estimated by maximum likelihood estimation. The proposed method is verified by using mathematical examples with and without inclusion of extreme events. Results show that the proposed method can estimate parameters and distributions for body and tail distributions as well as the more accurate reliability of system under extreme events.     

Adaptive non-local level-set model for despeckling and deblurring of synthetic aperture radar imagery

ABSTRACT

In this article, we modify Mumford–Shah level-set model to handle speckles and blur in synthetic aperture radar (SAR) imagery. The proposed model is formulated using a non-local regularization framework. Hence, the model duly cares about local gradient oscillations (corresponding to the fine details/textures) during the evolution process. It is assumed that the speckle intensity is gamma distributed, while designing a maximum a posteriori estimator of the functional. The parameters of the gamma distribution (i.e. scale and shape) are estimated using a maximum likelihood estimator. The regularization parameter of the model is evaluated adaptively using these (estimated) parameters at each iteration. The split-Bregman iterative scheme is employed to improve the convergence rate of the model. The proposed and the state-of-the-art despeckling models are experimentally verified and compared using a large number of speckled and blurred SAR images. Statistical quantifiers are used to numerically evaluate the performance of various models under consideration.     

Geometrical Parameter Estimation for Industrial Manipulators Using Two-step Estimation Schemes

This paper proposes a new solution for estimating the kinematic parameters of a manipulator, using a two-step linear estimator. The estimator is based on the recursive least-squares (RLS) method. The main characteristics of the method are that one singularity in estimation is overcome and parameters estimates approach the true values more quickly and smoothly than for algorithms using a one-step estimator. The algorithm can be applied for the estimation of parameters of both serial-link robots and robots having a kinematic closed-loop. Simulation results are given, comparing the proposed method with conventional approaches.     

On Birnbaum–Saunders inference

The Birnbaum–Saunders distribution, also known as the fatigue-life distribution, is frequently used in reliability studies. We obtain adjustments to the Birnbaum–Saunders profile likelihood function. The modified versions of the likelihood function were obtained for both the shape and scale parameters, i.e., we take the shape parameter to be of interest and the scale parameter to be of nuisance, and then consider the situation in which the interest lies in performing inference on the scale parameter with the shape parameter entering the modeling in nuisance fashion. Modified profile maximum likelihood estimators are obtained by maximizing the corresponding adjusted likelihood functions. We present numerical evidence on the finite sample behavior of the different estimators and associated likelihood ratio tests. The results favor the adjusted estimators and tests we propose. A novel aspect of the profile likelihood adjustments obtained in this paper is that they yield improved point estimators and tests. The two profile likelihood adjustments work well when inference is made on the shape parameter, and one of them displays superior behavior when it comes to performing hypothesis testing inference on the scale parameter. Two empirical applications are briefly presented.     

Toward a model-based Bayesian theory for estimating and recognizingparameterized 3-D objects using two or more images taken from differentpositions

A parametric modeling and statistical estimation approach is proposed and simulation data are shown for estimating 3-D object surfaces from images taken by calibrated cameras in two positions. The parameter estimation suggested is gradient descent, though other search strategies are also possible. Processing image data in blocks (windows) is central to the approach. After objects are modeled as patches of spheres, cylinders, planes and general quadrics-primitive objects, the estimation proceeds by searching in parameter space to simultaneously determine and use the appropriate pair of image regions, one from each image, and to use these for estimating a 3-D surface patch. The expression for the joint likelihood of the two images is derived and it is shown that the algorithm is a maximum-likelihood parameter estimator. A concept arising in the maximum likelihood estimation of 3-D surfaces is modeled and estimated. Cramer-Rao lower bounds are derived for the covariance matrices for the errors in estimating the a priori unknown object surface shape parameters     

Estimation of interclass correlation via a Kotz-type distribution

We estimate interclass (mom-sib) correlation by maximizing the log-likelihood function of a Kotz-type distribution. The results are illustrated on a real life data set due to Galton. Using extensive simulations and the three criteria, namely, bias, MSE and Pitman nearness probability, we compare the proposed estimator with the maximum likelihood estimator based on normal distribution and with a non-iterative estimator due to Srivastava. We conclude that the proposed estimator performs well when the data are not from multivariate normal distribution. However, if the data are from multivariate normal distribution then Srivastava's estimator and normal based maximum likelihood estimator perform well as expected. Testing of hypothesis about this correlation is also discussed using likelihood based tests. It is concluded that score test derived using Kotz-type density performs the best.     

Maximum likelihood estimation of vessel parameters from scale space analysis

We describe a method of detecting features in retinal images using a model-based approach. The image is processed using a bank of filters in a scale space. A parametric model of the target feature is then proposed and the filter responses to the model calculated. A noise model is proposed, and incorporated into a maximum likelihood estimator to estimate model parameters. The estimator uses the generative parametric model to explore smoothly the scale space. This method is applied to the detection of retinal blood vessels, using a Gaussian-profiled valley as a model. A simple thresholding method is proposed as an example of using the rich estimated parameter maps to detect vessels and the results are compared against two existing vessel detectors. Our system is compared against ground truth and the output of existing systems. It is found to be comparable and, in addition, produces direct estimates of vessel calibres and contrasts. It does not use any form of region growing or vessel tracking, but thresholds a function of the estimated vessel parameters to determine vessel regions.     

Multi-objective parameter estimation via minimal correlation criterion

The paper deals with the problem of parameter estimation using two different sources of information, namely a time series with dynamic data and steady-state data. The new estimator is based on a two-step procedure: first a multi-objective optimization is performed, leading to a set of Pareto-optimal vectors of parameter estimates and, second, a single model is chosen based on the free-run simulation error which is required to be minimally correlated with the model output. The procedure is general in nature and can be applied to any model representation, but for the sake of simplicity, the new procedure is illustrated using NARX polynomial models for which closed formulae for generating the Pareto-set are readily available. Monte Carlo simulation studies suggest that the new estimator, which does not assume any particular noise model, is fairly unbiased even when the conventional least-squares estimator is biased.     

Numerical maximum log likelihood estimation for generalized lambda distributions

This paper presents a two-step procedure using the method of moment or percentile to find initial values and then maximize the numerical log likelihood to fit the appropriate generalized lambda distribution to data. This paper demonstrates the use of this procedure to fit well-known statistical distributions as well as some empirical data. Overall, the use of numerical maximum log likelihood estimation is a valuable alternative among existing methods of fitting. It provides not only convincing results in terms of quantile plots and goodness of fit tests but also has the advantage of a lower variability in its parameter estimation compared to the existing starship (King and MacGillivray, 1999) and method of moment (Karian and Dudewicz, 2000) fitting schemes.     

An adjustment for edge effects using an augmented neighborhood model in the spatial auto-logistic model

Parameter estimation in the spatial auto-regressive models has difficulty due to the edge sites which have unobserved neighborhood sites. Some ad hoc remedies suggested in the literature are the free boundary condition, the toroidal boundary condition or estimation using only internal data sites. However, parameter estimates are often sensitive to assumptions on the unobserved neighborhood sites and all the above assumptions have some apparent shortcomings such as systematic bias or inflated variance. In this paper, we propose a new way to incorporate the edge sites by introducing an augmented random neighborhood, denoted by the augmented neighborhood model, which represents the entire external field. To estimate the model, we derive the EM procedures for the maximum pseudo-likelihood estimator and the maximum likelihood estimator. Several simulation studies show that the random external field provides better performance of the maximum pseudo-likelihood estimator and the maximum likelihood estimator than other assumptions on the edge sites. As an example, we apply the random external field to modeling the distribution of Plantago lanceolata in Kansas.     

基于似然方程校正的时差定位算法

针对传统时差定位闭式解法在量测噪声较大情况下定位性能不佳的缺点,提出了一种新的时差定位算法。该算法首先在无约束条件下利用加权最小二乘得到目标的初始位置估计值,然后利用最大似然方程对初始位置估计值进行校正,校正后的位置估计值将更加接近最大似然估计。通过对算法的仿真分析,结果表明在量测噪声较大的情况下,算法的定位均方误差要小于经典的Chan算法。     

Maximum Likelihood Estimation of the Cox–Ingersoll–Ross Model Using Particle Filters

This paper shows how to build in a computationally efficient way a maximum simulated likelihood procedure to estimate the Cox–Ingersoll–Ross model from multivariate time series. The advantage of this estimator is that it takes into account the exact likelihood function while avoiding the huge computational burden associated with MCMC methods and without the ad hoc assumption that certain bond yields are measured without error. The proposed methodology is implemented and tested on simulated data. For realistic parameter values the estimator seems to have good small sample properties, compared to the popular quasi maximum likelihood approach, even using moderate simulation sizes. The effect of simulation errors does not seem to undermine the estimation procedure.     

Generalized method of moments estimation for cointegrated vector autoregressive models

In this study, a generalized method of moments (GMM) for the estimation of nonstationary vector autoregressive models with cointegration is considered. Two iterative methods are considered: a simultaneous estimation method and a switching estimation method. The asymptotic properties of the GMM estimators of these methods are found to be the same as those of the Gaussian reduced-rank estimator. Through Monte Carlo simulation, the small-sample properties of the GMM estimators are studied and compared with those of the Gaussian reduced-rank estimator and the maximum likelihood estimator considered by other researchers. In the case of small samples, the GMM estimators are more robust to deviations from normality assumptions, particularly to outliers.     

A Long Memory Model with Normal Mixture GARCH

We present an exploratory analysis of a class of long memory models with a normal mixture generalized autoregressive conditional heteroskedasticity innovation process. Monte Carlo results are used to infer the performance of the maximum likelihood estimator. The estimation biases are associated with, amongst others, the mixing parameter, and these biases are usually insignificant. As an illustration, we fit the proposed model to four countries inflation data. It is found that the performance of the long memory model with normal mixture generalized autoregressive conditional heteroskedasticity is better than, say, both autoregressive moving average and long memory models with a standard generalized autoregressive conditional heteroskedasticity specification in terms of the flexibility to describe both the time-varying conditional skewness and kurtosis.     

Performance of speaker localization using microphone array

Speaker localization is a technique to locate and track an active speaker from multiple acoustic sources using microphone array. Microphone array is used to improve the speech quality of recorded speech signal in meeting room and other places. In this work, the time delay estimation between source and each microphone is calculated using a localization method called time differences of arrival (TDOA). TDOA localization consists of two steps namely (a) a time delay estimator and (b) a localization estimator. For time delay estimation, the generalized cross-correlation using phase transform, the generalized cross correlation using maximum likelihood, linear prediction (LP) residual and the Hilbert envelope of the LP residual are chosen for estimating the location of a person. A new speaker localization algorithm known as group search optimization (GSO) algorithm is proposed. The performance of this algorithm is analyzed and compared with Gauss–Newton nonlinear least square method and genetic algorithm. Experimental results show that the proposed GSO method outperforms the other methods in terms of mean square error, root mean square error, mean absolute error, mean absolute percentage error, euclidean distance and mean absolute relative error.