ML Estimation Research Articles

Generalized Lindley and Power Lindley distributions for modeling the wind speed data

In this study, we propose to use Generalized Lindley (GL) and Power Lindley (PL) distributions as an alternative to the Weibull distribution for modeling the wind speed data. In the application part of the study, we consider the actual wind speed data collected in hourly basis from the Bilecik, Bursa, Eskisehir and Sakarya sites, Turkey in 2009. These data sets are modeled by using GL and PL distributions. To compare their modeling performance with well known and widely used Weibull distribution, Weibull distribution is also included into the study. The results show that GL distribution provides the best fitting according to root mean square error (RMSE), coefficient of determination (R2), maximum value of the likelihood function corresponding to the ML estimates of the parameters (lnL) and Akaike information criterion (AIC). It is also seen that PL distribution is preferable in terms of power density error (PDE) criterion.

Stress Affection of Two Scale Truncated Generalized Logistic Parameters with Progressive Censoring

This paper deals with non-Bayesian estimation problem of constant-stress Accelerated Life Tests (ALTs) when the lifetime of the items follow truncated Generalized Logistic Distribution (GLD). Some considerations on inference based on the use of asymptotically normality of the ML estimators are presented considering the stress effects on the two scale parameters of the truncated GLD with a k-level constant-stress ALT under progressive type-I censored grouped data. The EM algorithm method is used to obtain the estimators of the unknown parameters. In addition, estimator of the two scale parameters, reliability function under usual conditions and Fisher information matrix of the estimators are given. Finally, we present a Simulation Study to illustrate the proposed procedure.

Bayesian Hypothesis Testing for One Bit Compressed Sensing with Sensing Matrix Perturbation

This letter proposes a low-computational Bayesian algorithm for noisy sparse recovery in the context of one bit compressed sensing with sensing matrix perturbation. The proposed algorithm which is called BHT-MLE comprises a sparse support detector and an amplitude estimator. The support detector utilizes Bayesian hypothesis test, while the amplitude estimator uses an ML estimator which is obtained by solving a convex optimization problem. Simulation results show that BHT-MLE algorithm offers more reconstruction accuracy than that of an ML estimator (MLE) at a low computational cost.

Automated learning oftfactor analysis models with complete and incomplete data

The t factor analysis (tFA) model is a promising tool for robust reduction of high-dimensional data in the presence of heavy-tailed noises. When determining the number of factors of the tFA model, a two-stage procedure is commonly performed in which parameter estimation is carried out for a number of candidate models, and then the best model is chosen according to certain penalized likelihood indices such as the Bayesian information criterion. However, the computational burden of such a procedure could be extremely high to achieve the optimal performance, particularly for extensively large data sets. In this paper, we develop a novel automated learning method in which parameter estimation and model selection are seamlessly integrated into a one-stage algorithm. This new scheme is called the automated tFA (AtFA) algorithm, and it is also workable when values are missing. In addition, we derive the Fisher information matrix to approximate the asymptotic covariance matrix associated with the ML estimators of tFA models. Experiments on real and simulated data sets reveal that the AtFA algorithm not only provides identical fitting results, as compared to traditional two-stage procedures, but also runs much faster, especially when values are missing.

Interpretation of mixed models and marginal models with cohort attrition due to death and drop-out.

Mixed models estimated by maximum likelihood and marginal models estimated by generalized estimating equations are the standard methods for the analysis of longitudinal data. However, their use is highly debated when attrition may be due to death. While some authors consider that mixed model estimates are interpretable only in an immortal cohort, we show that their subject-specific interpretation still holds in the population currently alive, but their population-averaged interpretation is valid only in the immortal cohort. We propose an approximation of the population-averaged mean among the population alive that highlights the difference with the population-averaged mean in the immortal cohort. The interpretation of ML estimates of mixed models and joint models for the marker and the time-to-death as well as unweighted and weighted GEE of marginal models is then illustrated in a simulation study and in an application regarding cognitive decline in the elderly.

English

When some sample values at either or both the extremes might have been assorted, a censoring scheme is much useful. Nevertheless, in some reliability experiments, the number of items fell out the experiment cannot be prexed random in some situations. For such situations, a random removal scheme with censoring scheme may oer a good result. Here, a random removal scheme with the Progressive censoring plan is assumed for statis- tical inference, when ll out items of the experiments cannot be prexed. The analysis of the present discussion has carried out with the help of a real data set for the Burr Type-XII distribution. Key words: Random Removal Scheme, Progressive Type-II Censoring Plan, ML Estimation, Bayes Estimation, and Bayes Prediction Bound Length.

Nested algorithms for joint DOD and DOA estimation in bistatic MIMO radar

This paper presents two nested algorithms—one based on the Estimation of Signal Parameters via Rotational Invariance Technique (ESPRIT) algorithm and the other one on the maximum likelihood estimation—for joint direction of departure (DOD) and direction of arrival (DOA) estimation in bistatic multiple-input multiple-output radar. Both of the proposed nested algorithms interweaves signal grouping schemes and DOD/DOA estimation. Thereby, in each stage only DODs or DOAs, but not both, need to be estimated, and thus the complexity called for can be reduced. Also, the signals in each group have close DOAs, yet diverse DODs, and vice versa, so both DODs and DOAs can be precisely estimated even some of them are very close. Additionally, the estimated DODs and DOAs are automatically paired together without extra computations. Also, for the proposed nested-ML, a non-iterative importance sampling-based ML estimator is developed which is ensured to attain global optimum. Simulation results show that the proposed nested-ESPRIT can provide competing performance, yet with much lower complexity compared with the main state-of-the-art works; whereas, nested-ML can reach the Cramer–Rao lower bound with slightly higher complexity.

GMM and ML Estimation of Dynamic Panel Data Models with Heterogeneous Time Trends

In this paper, we consider dynamic panel data models with heterogeneous time trends. We propose the GMM and ML estimators for this model. We conduct Monte Carlo simulation to compare the performance of these two estimators. The simulation results show that the GMM estimator performs very poorly whereas the ML estimator performs well.

Estimation of Time-Varying Coefficient Dynamic Panel Data Models

In this paper, we consider dynamic panel data models where the autoregressive parameter changes over time. We propose the GMM and ML estimators for this model. We conduct Monte Carlo simulation to compare the performance of these two estimators. The simulation results show that the ML estimator outperforms the GMM estimator.

Parameter estimation for compound‐Gaussian clutter with inverse‐Gaussian texture

This study deals with the estimation problem of the inverse-Gaussian (IG)–compound-Gaussian (CG) distributed clutter parameters. Under the assumption of the absence of thermal noise, non-integer moments, log-moments and maximum-likelihood-based approaches are employed for model parameter estimation in the cases of single pulse and non-coherent integration of N pulses. The forms of the non-integer-order moments estimator and the [z log(z)] estimator are derived in terms of the Bessel and the exponential–integral functions, respectively. These formulas maintain monotonic nature over all values of the ratio between the shape parameter and the mean clutter power. For a single look data, the ML estimate combined with the mean clutter power is constructed in one dimension search for the shape parameter. By accommodating the mean square error metric, the estimation assessments are investigated via simulated and real data. Authors’ results illustrate that the derived non-integer-order moments estimator is asymptotically efficient for the IG–CG distributed clutter parameters particularly in heavy tailed clutter situations.

Estimation of the PDF and the CDF of exponentiated moment exponential distribution

This article addresses the different methods of estimation of the probability density function and the cumulative distribution function for the exponentiated moment exponential distribution. Following estimation methods are considered: uniformly minimum variance unbiased estimators, maximum likelihood estimators, percentile estimators, least squares estimators, weighted least square estimators, maximum product of spacings estimators, Cramer–von-Mises estimators and Anderson–Darling estimators. Analytical expressions are derived for the bias and the mean squared error. Monte Carlo simulations are performed to compare the performances of the proposed methods of estimation for both small and large samples. Simulation studies and real data applications show that the ML estimator performs better than others. Finally, one real data set has been analyzed for illustrative purposes.

Efficient Estimation of the PDF and the CDF of the Frechet Distribution

In this paper, we consider the estimation of the PDF and the CDF of the Frechet distribution. In this regard, following estimators are considered: uniformly minimum variance unbiased estimator, maximum likelihood estimator, percentile estimator, least squares estimator and weighted least squares estimator. To do so, analytical expressions are derived for the bias and the mean squared error. As the result of simulation studies and real data applications indicate, the ML estimator performs better than the others.

A computationally efficient non-local maximum likelihood estimation approach for Rician noise reduction in MRI

Magnetic resonance images are subjected to degradation due to the presence of noise from various sources. For further processing of the MR images and for effective visual analysis, the noise should be removed. Many denoising algorithms have been proposed for enhancing MR images. Preserving the structural details has its own importance in image denoising, and especially for medical images it should not be compromised. For effective image denoising, the data distribution in the images should be known in advance. Data in the magnitude MR images are Rician distributed (if acquired with single coil). Among the recently proposed denoising methods for reducing Rician noise, non-local maximum likelihood estimation method (NLML) proved to be an efficient one. But the superior performance of the NLML is restricted by its high computational complexity and non optimal way of selecting the samples for ML estimation. In this paper we address the above problems to some extend by introducing rotation invariant similarity measures. The proposed method aims to reduce the computational complexity and preserves the edges by discarding the dissimilar pixels by using a two-level refining approach. Comparative analysis of the proposed method with conventional NLML method based on the execution time and quantitative analysis in terms of PSNR, SSIM, FSIM and UIQI shows that the proposed method has an edge over the conventional method.

Computational aspects of the EM algorithm for spatial econometric models with missing data

ABSTRACTMaximum likelihood (ML) estimation with spatial econometric models is a long-standing problem that finds application in several areas of economic importance. The problem is particularly challenging in the presence of missing data, since there is an implied dependence between all units, irrespective of whether they are observed or not. Out of the several approaches adopted for ML estimation in this context, that of LeSage and Pace [Models for spatially dependent missing data. J Real Estate Financ Econ. 2004;29(2):233–254] stands out as one of the most commonly used with spatial econometric models due to its ability to scale with the number of units. Here, we review their algorithm, and consider several similar alternatives that are also suitable for large datasets. We compare the methods through an extensive empirical study and conclude that, while the approximate approaches are suitable for large sampling ratios, for small sampling ratios the only reliable algorithms are those that yield exact ML or restricted ML estimates.

Estimation of the relatedness coefficients from biallelic markers, application in plant mating designs.

The problem of inferring the relatedness distribution between two individuals from biallelic marker data is considered. This problem can be cast as an estimation task in a mixture model: at each marker the latent variable is the relatedness state, and the observed variable is the genotype of the two individuals. In this model, only the prior proportions are unknown, and can be obtained via ML estimation using the EM algorithm. When the markers are biallelic and the data unphased, the identifiability of the model is known not to be guaranteed. In this article, model identifiability is investigated in the case of phased data generated from a crossing design, a classical situation in plant genetics. It is shown that identifiability can be guaranteed under some conditions on the crossing design. The adapted ML estimator is implemented in an R package called Relatedness. The performance of the ML estimator is evaluated and compared to that of the benchmark moment estimator, both on simulated and real data. Compared to its competitor, the ML estimator is shown to be more robust and to provide more realistic estimates.

The Impact of Model Parameterization and Estimation Methods on Tests of Measurement Invariance With Ordered Polytomous Data.

Evaluations of measurement invariance provide essential construct validity evidence-a prerequisite for seeking meaning in psychological and educational research and ensuring fair testing procedures in high-stakes settings. However, the quality of such evidence is partly dependent on the validity of the resulting statistical conclusions. Type I or Type II errors can render measurement invariance conclusions meaningless. The present study used Monte Carlo simulation methods to compare the effects of multiple model parameterizations (linear factor model, Tobit factor model, and categorical factor model) and estimators (maximum likelihood [ML], robust maximum likelihood [MLR], and weighted least squares mean and variance-adjusted [WLSMV]) on the performance of the chi-square test for the exact-fit hypothesis and chi-square and likelihood ratio difference tests for the equal-fit hypothesis for evaluating measurement invariance with ordered polytomous data. The test statistics were examined under multiple generation conditions that varied according to the degree of metric noninvariance, the size of the sample, the magnitude of the factor loadings, and the distribution of the observed item responses. The categorical factor model with WLSMV estimation performed best for evaluating overall model fit, and the categorical factor model with ML and MLR estimation performed best for evaluating change in fit. Results from this study should be used to inform the modeling decisions of applied researchers. However, no single analysis combination can be recommended for all situations. Therefore, it is essential that researchers consider the context and purpose of their study.

Quantile regression in linear mixed models: a stochastic approximation EM approach.

This paper develops a likelihood-based approach to analyze quantile regression (QR) models for continuous longitudinal data via the asymmetric Laplace distribution (ALD). Compared to the conventional mean regression approach, QR can characterize the entire conditional distribution of the outcome variable and is more robust to the presence of outliers and misspecification of the error distribution. Exploiting the nice hierarchical representation of the ALD, our classical approach follows a Stochastic Approximation of the EM (SAEM) algorithm in deriving exact maximum likelihood estimates of the fixed-effects and variance components. We evaluate the finite sample performance of the algorithm and the asymptotic properties of the ML estimates through empirical experiments and applications to two real life datasets. Our empirical results clearly indicate that the SAEM estimates outperforms the estimates obtained via the combination of Gaussian quadrature and non-smooth optimization routines of the Geraci and Bottai (2014) approach in terms of standard errors and mean square error. The proposed SAEM algorithm is implemented in the R package qrLMM().

Fixed Effects versus Random Effects Estimation of Dynamic Panel Data Models

This paper proposes new GMM estimators for the panel AR(1) model when the ratio of the variance of the individual effects to the variance of the idiosyncratic errors is large. First, we present a necessary condition for large N, fixed T consistency of any Fixed Effects or Random Effects estimator for this model. This condition is also sufficient for consistency of the FE estimators, which only depend on differences of the data. Next we show that RE estimators can still be consistent when the data is mean-stationary and the ratio of the variances is infinite. For instance, when T>3, the 2-step optimal System estimator is consistent provided that the elements of the weight matrix are consistently estimated. We argue that the RE Quasi ML estimator can be used for this purpose. The commonly used 1-step and 2-step System estimators are inconsistent in this case. We also propose local asymptotic approximations to the distributions of RE GMM estimators that are more accurate than conventional approximations when the data are mean-stationary and the ratio of the variances is large and we discuss conditions for redundancy of the moment conditions that include levels of the data. Finally, we conduct a Monte Carlo study into the finite sample properties of various estimators and related confidence intervals, and to illustrate the usefulness of our new System estimator we revisit the growth study of Levine et al. (2000).

Novel Method for 5G Systems NLOS Channels Parameter Estimation

For the development of new 5G systems to operate in mm bands, there is a need for accurate radio propagation modelling at these bands. In this paper novel approach for NLOS channels parameter estimation will be presented. Estimation will be performed based on LCR performance measure, which will enable us to estimate propagation parameters in real time and to avoid weaknesses of ML and moment method estimation approaches.

Pilot-based joint ML estimation of timing offset, CFO and channel for OFDMA uplink using minimum residue decomposition technique

This paper addresses the challenging issue of joint maximum-likelihood estimation of carrier frequency offset, timing offset and channel response for orthogonal frequency division multiple access (OFDMA) uplink transmissions. A pilot preamble based approach is proposed that makes use of the concept of signal decomposition. Earlier works have demonstrated that it is possible to decompose the multidimensional optimization involved in this joint estimation problem into a series of one-dimensional searches. However, the computational complexity involved with such methods is also very high. In this work, we propose a new signal decomposition method based on a minimum residue criterion. The method with appropriate signal structures provides a computationally-efficient solution for the joint estimation of all required parameters of all users at the base station in an OFDMA link, leading to energy-efficient system design. Another advantage of the proposed technique is that it offers the flexibility of application to OFDMA systems with any subcarrier assignment scheme. Performance advantages of the proposed estimation method are substantiated through extensive computer simulation studies and are compared with that of some important recently-developed algorithms for the problem. Proof of convergence of the new estimation algorithm is also illustrated.