Conventional Maximum Likelihood Method Research Articles

Reliability Estimation of Weibull Distribution with Zero-Failure Data

This paper focuses on the reliability estimation of Weibull distributions with zero-failure data. Since no product failure occurred in the tests, the conventional maximum likelihood method was not applicable. Recent methods ignore the estimation of location parameter and tend to be conservative. This study developed a new estimation technique to address these problems. A prior model between the life dispersion boundary and shape parameter is constructed by considering the historical failure data of similar high-reliability products. The failure probabilities for all samples were inferred using the E-Bayesian method, after which the reliability was estimated. Afterward, a confidence interval for reliability was obtained based on the bootstrap confidence interval and modified maximum likelihood method. A Monte Carlo simulation study demonstrated that the proposed method is satisfactory in terms of point estimates, confidence intervals, coverage probabilities, and computational efficiency. Finally, a real engineering example is introduced to illustrate the application of this method.

Fast parameter estimation of generalized extreme value distribution using neural networks

AbstractThe heavy‐tailed behavior of the generalized extreme‐value distribution makes it a popular choice for modeling extreme events such as floods, droughts, heatwaves, wildfires and so forth. However, estimating the distribution's parameters using conventional maximum likelihood methods can be computationally intensive, even for moderate‐sized datasets. To overcome this limitation, we propose a computationally efficient, likelihood‐free estimation method utilizing a neural network. Through an extensive simulation study, we demonstrate that the proposed neural network‐based method provides generalized extreme value distribution parameter estimates with comparable accuracy to the conventional maximum likelihood method but with a significant computational speedup. To account for estimation uncertainty, we utilize parametric bootstrapping, which is inherent in the trained network. Finally, we apply this method to 1000‐year annual maximum temperature data from the Community Climate System Model version 3 across North America for three atmospheric concentrations: 289 ppm (pre‐industrial), 700 ppm (future conditions), and 1400 ppm , and compare the results with those obtained using the maximum likelihood approach.

A novel point process model for neuronal spike trains

Point process provides a mathematical framework for characterizing neuronal spiking activities. Classical point process methods often focus on the conditional intensity function, which describes the likelihood at any time point given its spiking history. However, these models do not describe the central tendency or importance of the spike train observations. Based on the recent development on the notion of center-outward rank for point process, we propose a new modeling framework on spike train data. The new likelihood of a spike train is a product of the marginal probability on the number of spikes and the probability of spike timings conditioned on the same number. In particular, the conditioned distribution is calculated by adopting the well-known Isometric Log-Ratio transformation. We systematically compare the new likelihood with the state-of-the-art point process likelihoods in terms of ranking, outlier detection, and classification using simulations and real spike train data. This new framework can effectively identify templates as well as outliers in spike train data. It also provides a reasonable model, and the parameters can be efficiently estimated with conventional maximum likelihood methods. It is found that the proposed likelihood provides an appropriate ranking on the spike train observations, effectively detects outliers, and accurately conducts classification tasks in the given data.

VaR calculation by binary response models

<p>The original Risk-Metrics method is underpinned by the assumption that daily asset returns are conditional Gaussian independently identically distributed (iid) random variables with a mean of zero. In this paper, a new method to calculate Value at Risk (VaR) was suggested to overcome the shortcoming of Risk-Metrics by employing binary response models to compute probability forecasts of the portfolio return by exceeding a grid of candidate quantile values. From those values, the VaR quantile value was selected. The proposed model was called BRV (Binary Response VaR method). Consistent application of BRV to the Dow Jones Industrial Average (INDEXDJX: DJI) and Dow Jones U.S. Marine Transportation Index (DJUSMT) time series proved that it was more accurate than the Risk-Metric system. This method not only worked similar to quantile regression but had the advantage that conventional maximum likelihood methods could be used for parameter estimation and inference. The BRV method was the best performing method for computing the daily VaR at both the 95% and 99% confidence levels over the period 02/01/06–31/12/08. The BRV and the QR (quantile regression) methods performed similarly, but the BRV method had the practical advantage that conventional maximum likelihood (ML) technique could be used for parameter estimation and robust inference.</p>

The GMM estimation of semiparametric spatial stochastic frontier models

In this paper, we consider the estimation of semiparametric spatial stochastic frontier (SF) models, in which the spatial dependence is modeled by adding the spatially lagged dependent variable as an additional independent variable (following the convention of spatial autoregressive models) and specifying various spatial structures on the inefficiency and/or idiosyncratic error. Thus, the proposed models are inclusive compared with most previous studies. Efficiency modeling in the SF literature has not given enough attention to the spatial interaction of inefficiency, primarily because the estimation of inefficiency in spatial models is challenging using the conventional maximum likelihood method. Therefore, we propose a two-step estimation procedure for our spatial frontier models under the framework of the generalized method of moments (GMM). The proposed method is easy to implement. Further, Monte Carlo Simulations show that our GMM estimators have good finite-sample performance. We apply our GMM estimators to examine the technical efficiency of 41 European countries and the effects of spatial dependence on production (GDP).

Accuracy enhancement in indoor positioning system based on visible light communication

The travelled signals that used to estimate the distances between LEDs and the target undergo from non-line-of-sight (NLOS) link in indoor positioning system (IPS) utilizing visible light communication (VLC) technology. This could present a significant errors in identifying their positions. In this paper, we design an IPS based on a new hybrid technique using VLC technology for accuracy enhancing. To begin, the target's position is determined using a weighted least squares positioning method. Next, a maximum likelihood positioning approach is used to relocate the target's position, starting with the estimated position as an initial point. Simulations present that the created algorithm performs better than weight least squares and conventional maximum likelihood methods.

Analysis of Modified Kies Exponential Distribution with Constant Stress Partially Accelerated Life Tests under Type-II Censoring

This study investigates, for the first time, the product of spacing estimation of the modified Kies exponential distribution parameters as well as the acceleration factor using constant-stress partially accelerated life tests under the Type-II censoring scheme. Besides this approach, the conventional maximum likelihood method is also considered. The point estimates and the approximate confidence intervals of the unknown parameters are obtained using the two methods. In addition, two parametric bootstrap confidence intervals are discussed based on both estimation methods. Extensive simulation studies are conducted by considering different censoring schemes to examine the efficiency of each estimation method. Finally, two real data sets for oil breakdown times of insulating fluid and minority electron mobility are analyzed to show the applicability of the different methods. Moreover, the reliability function and the mean time-to-failure under the normal use condition are estimated using both methods. Based on Monte Carlo simulation outcomes and real data analysis, we recommend using the maximum product of spacing to evaluate both the point and interval estimates for the modified Kies exponential distribution parameters in the presence of constant-stress partially accelerated Type-II censored data.

A robust method for the assessment of average bioequivalence in the presence of outliers and skewness.

In this paper, we propose a robust Bayesian method for the assessment of average bioequivalence based on data from conventional crossover studies. We evaluate and motivate empirically the need for robust methods in bioequivalence studies by comparing the results of robust and conventional statistical methods in a large data pool of bioequivalence studies. Robustness of the statistical methodology is achieved by replacing the normal distributions for residuals in the linear mixed model with skew-t distributions. In this way, the statistical model can accommodate skew and heavy-tailed data, particularly outliers, yielding robust statistical inference without the need for excluding outliers from the analysis. We performed a simulation study to investigate and compare the performance of the robust and conventional models. Our study shows that in some trials, the distribution of residuals is skew and heavy-tailed. In the presence of outliers, the 90% confidence intervals for the ratio of geometric means tend to be narrower for the robust methods than for the conventional method. Our simulation study shows that the robust method has suitable frequentist properties and yields more precise confidence intervals and higher statistical power than the conventional maximum likelihood method when outliers are present in the data. As a sensitivity analysis, we recommend the fit of robust models for handling outliers that are occasionally encountered in crossover design bioequivalence data.

Enhanced RSS-Based UAV Localization Via Trajectory and Multi-Base Stations

To improve the localization precision of unmanned aerial vehicle (UAV), a novel framework is established by jointly utilizing multiple measurements of received signal strength (RSS) from multiple base stations (BSs) and multiple points on trajectory. First, a joint maximum likelihood (ML) of exploiting both trajectory information and multi-BSs is proposed. To reduce its high complexity, two low-complexity localization methods are designed. The first method is from BS to trajectory (BST), called LCSL-BST. First, fixing the nth BS, by exploiting multiple measurements along trajectory, the position of UAV is computed by ML rule. Finally, all computed positions of UAV for different BSs are combined to form the resulting position. The second method reverses the order, called LCSL-TBS. We also derive the Cramer-Rao lower boundary (CRLB) of the joint ML method. From simulation results, we can see that the proposed joint ML and separate LCSL-BST methods have made a significant improvement over conventional ML method without use of trajectory knowledge in terms of location performance. The former achieves the joint CRLB and the latter is of low-complexity.

Low-Complexity Deep-Learning-Based DOA Estimation for Hybrid Massive MIMO Systems With Uniform Circular Arrays

This letter proposes a low-complexity deep-learning-based direction-of-arrival (DOA) estimation method for a hybrid massive multiple-input multiple-output (MIMO) system with a uniform circular array at the base station. In the proposed method, we first input the received signal vector into some small deep feedforward networks that are trained offline. Based on the outputs of the networks, we then generate a set of candidate angles. By selecting the optimal one from all candidate angles, we finally obtain the DOA estimation. Simulation results demonstrate that, compared with the conventional maximum likelihood (ML) method, the proposed DOA estimation method can achieve similar or even better performance with much less complexity.

Mixed Hidden Markov Models for Clinical Research with Discrete Repeated Measurements

A hidden Markov model (HMM) is a method for analyzing a sequence of transitions for a set of data by considering the outcomes Y to be output from latent state X, which has the Markov property. The HMM has been widely applied, with applications that include speech recognition, genomic analysis, and finance forecasting. The HMM was originally a method for dealing with single-process data. Thus, it is a natural extension to apply it to data with a repeated measure structure by incorporating random effects in it. This is called the mixed hidden Markov model (MHMM). With this extension, the MHMM was recently applied to clinical research data with repeated measurements, e.g. multiple sclerosis, alcohol consumption, and primary biliary cirrhosis. In relation to parameter inference, because regular HMM methods can be used in an MHMM framework, some legacy knowledge is applicable. The likelihood can be obtained by simply adding a random effect parameter to a single process HMM, and the conventional maximum-likelihood method can be used for parameter estimation. On the other hand, much work must still be performed. For instance, the mathematical property of the maximum likelihood estimator has not yet been thoroughly examined. In this study, the asymptotic normality and consistency of the maximum likelihood estimator of the MHMM concerned with time points are examined via simulation, and found that these properties were almost fine. These methods are applied to actual study data, and future perspectives are provided in the conclusion.

Maximum Likelihood and Firth Logistic Regression of the Pedestrian Route Choice

To investigate how a pedestrian chooses a particular route in an urban center, this study analyzes the effects of individual and built environment characteristics on the route choice using binary logistic regression of 524 survey responses. Conducted in a strategic area, the survey, as often is the case, collects data that are skewed and face the separation issue—the same outcome always occurs for a particular value of a predictor—according to which estimates by the conventional maximum likelihood (ML) method are inflated. Thus, one mechanical and one statistical alternative are employed: (1) exclusion of a variable that causes separation and (2) estimation by Firth’s penalized method. The two alternatives produce comparable results of the significance testing, that is, p values, but their coefficient estimates considerably differ inasmuch as the mechanical approach used for the ML logistic regression forcefully omits the important variable and subsequently biases the estimates of other predictors. Compared to these ML estimates, empirical findings from the Firth logistic regression are presented in a way that corrects for the ML bias.

PET image reconstruction using kernel method.

Image reconstruction from low-count positron emission tomography (PET) projection data is challenging because the inverse problem is ill-posed. Prior information can be used to improve image quality. Inspired by the kernel methods in machine learning, this paper proposes a kernel based method that models PET image intensity in each pixel as a function of a set of features obtained from prior information. The kernel-based image model is incorporated into the forward model of PET projection data and the coefficients can be readily estimated by the maximum likelihood (ML) or penalized likelihood image reconstruction. A kernelized expectation-maximization algorithm is presented to obtain the ML estimate. Computer simulations show that the proposed approach can achieve better bias versus variance trade-off and higher contrast recovery for dynamic PET image reconstruction than the conventional maximum likelihood method with and without post-reconstruction denoising. Compared with other regularization-based methods, the kernel method is easier to implement and provides better image quality for low-count data. Application of the proposed kernel method to a 4-D dynamic PET patient dataset showed promising results.

A Low-Complexity ML Estimator for Carrier and Sampling Frequency Offsets in OFDM Systems

This letter considers the joint acquisition of the carrier frequency offset (CFO) and sampling frequency offset (SFO) in OFDM systems using two long training symbols in the preamble. Conventional maximum-likelihood (ML) methods require a two-dimensional exhaustive search. To overcome this problem, a low-complexity closed-form ML estimator is proposed. It is shown that the CFO can be solved in closed-form. Then we develop an approximate ML estimation algorithm for the SFO by taking the second-order Taylor series expansion. Simulation results show that the proposed algorithm achieves almost the same performance as existing ML methods, but no exhaustive search is needed.

Fast Maximum Likelihood Localization of Near-Field Sources

Conventional methods for locating near-field sources generally suffer performance degradation when the assumption of uniform spatial Gaussian noise does not hold. In this paper study the scenario of non-uniform spatial Gaussian noise. First we construct the near-field signal model based on planar sensor array and derive the maximum likelihood method for obtaining the azimuth and distance of sound sources, then we proposed two fast algorithms-stepwise-concentrated maximum likelihood method(SML) and approximate maximum likelihood method(AML) to reduce the high computational complexity of maximum likelihood localization method. Simulation results show that the two proposed methods outperform conventional maximum likelihood method, with lower computational complexity and less mean squared error of both azimuth estimation and distance estimation.

Application of Artificial Bee Colony Algorithm to Maximum Likelihood DOA Estimation

Maximum Likelihood (ML) method has an excellent performance for Direction-Of-Arrival (DOA) estimation, but a multidimensional nonlinear solution search is required which complicates the computation and prevents the method from practical use. To reduce the high computational burden of ML method and make it more suitable to engineering applications, we apply the Artificial Bee Colony (ABC) algorithm to maximize the likelihood function for DOA estimation. As a recently proposed bio-inspired computing algorithm, ABC algorithm is originally used to optimize multivariable functions by imitating the behavior of bee colony finding excellent nectar sources in the nature environment. It offers an excellent alternative to the conventional methods in ML-DOA estimation. The performance of ABC-based ML and other popular meta-heuristic-based ML methods for DOA estimation are compared for various scenarios of convergence, Signal-to-Noise Ratio (SNR), and number of iterations. The computation loads of ABC-based ML and the conventional ML methods for DOA estimation are also investigated. Simulation results demonstrate that the proposed ABC based method is more efficient in computation and statistical performance than other ML-based DOA estimation methods.

A Comparison of the Bayesian and Other Methods for Estimation of Reliability Function for Burr-XII Distribution

Problem statement: The Burr-XII distribution has been widely used especially in the modeling of life time event data. It provides a statistical model which has a wide variety of application in many areas and the main advantage is its ability in the context of life time event among other distributions. The conventional maximum likelihood method is the usual way to estimate the parameters of a distribution. Bayesian approach has received much attention in contention with other estimation methods. In this study we explore and compare the performance of the maximum likelihood and median estimates with the Bayesian estimate of Reliability function for the two parameter Burr-XII distribution. Approach: The maximum likelihood estimation, median estimation, Bayesian using Jeffrey prior, modified Jeffery prior and extension of Jeffery prior information for estimation the Reliability function of Burr-XII distribution of life time are presented. We explore the performance of these estimators numerically under varying conditions. Through the simulation study a comparison are made on the performance of these estimators with respect to the Integrated Mean Square Error (IMSE) and Integrated Mean Absolute Percentage Error (IMAPE). Results: For all the varying sample size, several values of the shifting parameter for the two parameter Burr-XII distribution and for the values for the extension of Jeffery prior, the estimator of Bayesian methods result in smaller IMSE compared to the classical methods in majority of the cases especially in small size of shape parameter. Also in all cases for both methods the IMSE and IMAPE decreases as sample size increases. Conclusion: Based on the results of this simulation study the Bayesian approach used in the estimating of reliability function for the two parameter Burr-XII distribution is found to be superior compared to the conventional methods with respect to IMSE values.

Regularization of voxelwise autoregressive model for analysis of functional magnetic resonance imaging data

AbstractThis study reports the construction of a simple and elegant method to improve the detection of brain regions with increased neuronal activity in functional magnetic resonance imaging (fMRI). The main advantages of the method are regularization of voxelwise autoregressive parameters and accurate estimation of parameters and statistical inferences as compared to the conventional restricted maximum likelihood (ReML) method, where each voxel uses the two voxel‐wide (global) hyperparameters. The model is tested for its accuracy and efficiency in analysis of fMRI data for stimulated and real brains of healthy individuals. Receiver operating characteristic curves are used to show that the proposed method is superior to the conventional ReML method. The proposed method will improve the diagnostic accuracy of fMRI studies in the human brain. © 2011 Wiley Periodicals, Inc. Concepts Magn Reson Part A 38: 187–196, 2011.

Comparison of the Bayesian and Maximum Likelihood Estimation for Weibull Distribution

Problem statement: The Weibull distribution has been widely used especially in the modeling of lifetime event data. It provides a statistical model which has a wide variety of applications in many areas, and the main advantage is its ability in the context of lifetime event, to provide reasonably accurate failure analysis and failure forecasts especially with extremely small samples. The conventional maximum likelihood method is the usual way to estimate the parameters of a distribution. Bayesian approach has received much attention and in contention with other estimation methods. In this study we explore and compare the performance of the maximum likelihood estimate with the Bayesian estimate for the Weibull distribution. Approach: The maximum likelihood estimation, Bayesian using Jeffrey prior and the extension of Jeffrey prior information for estimating the parameters of Weibull distribution of life time are presented. We explore the performance of these estimators numerically under varying conditions. Through the simulation study comparison are made on the performance of these estimators with respect to the Mean Square Error (MSE) and Mean Percentage Error (MPE). Results: For all the varying sample size, several specific values of the scale parameter of the Weibull distribution and for the values specify for the extension of Jeffrey prior, the estimators of the maximum likelihood method result in smaller MSE and MPE compared to Bayesian in majority of the cases. Nevertheless in all cases for both methods the MSE and MPE decrease as sample size increases. Conclusion: Based on the results of this simulation study the Bayesian approach used in the estimating of Weibull parameters is found to be not superior compared to the conventional maximum likelihood method with respect to MSE and MPE values.

Maximum a posteriori blind image deconvolution with Huber–Markov random-field regularization

We propose a maximum a posteriori blind deconvolution approach using a Huber-Markov random-field model. Compared with the conventional maximum-likelihood method, our algorithm not only suppresses noise effectively but also significantly alleviates the artifacts produced by the deconvolution process. The performance of this method is demonstrated by computer simulations.