Classical Estimation Methods Research Articles

Paule-Mandel estimators for network meta-analysis with random inconsistency effects.

Network meta‐analysis is used to simultaneously compare multiple treatments in a single analysis. However, network meta‐analyses may exhibit inconsistency, where direct and different forms of indirect evidence are not in agreement with each other, even after allowing for between‐study heterogeneity. Models for network meta‐analysis with random inconsistency effects have the dual aim of allowing for inconsistencies and estimating average treatment effects across the whole network. To date, two classical estimation methods for fitting this type of model have been developed: a method of moments that extends DerSimonian and Laird's univariate method and maximum likelihood estimation. However, the Paule and Mandel estimator is another recommended classical estimation method for univariate meta‐analysis. In this paper, we extend the Paule and Mandel method so that it can be used to fit models for network meta‐analysis with random inconsistency effects. We apply all three estimation methods to a variety of examples that have been used previously and we also examine a challenging new dataset that is highly heterogenous. We perform a simulation study based on this new example. We find that the proposed Paule and Mandel method performs satisfactorily and generally better than the previously proposed method of moments because it provides more accurate inferences. Furthermore, the Paule and Mandel method possesses some advantages over likelihood‐based methods because it is both semiparametric and requires no convergence diagnostics. Although restricted maximum likelihood estimation remains the gold standard, the proposed methodology is a fully viable alternative to this and other estimation methods.

Classical and Bayesian methods of estimation for power Lindley distribution with application to waiting time data

The power Lindley distribution with some of its properties is considered in this article. Maximum likelihood, least squares, maximum product spacings, and Bayes estimators are proposed to estimate all the unknown parameters of the power Lindley distribution. Lindley`s approximation and Markov chain Monte Carlo techniques are utilized for Bayesian calculations since posterior distribution cannot be reduced to standard distribution. The performances of the proposed estimators are compared based on simulated samples. The waiting times of research articles to be accepted in statistical journals are fitted to the power Lindley distribution with other competing distributions. Chi-square statistic, Kolmogorov-Smirnov statistic, Akaike information criterion and Bayesian information criterion are used to access goodness-of-fit. It was found that the power Lindley distribution gives a better fit for the data than other distributions.

SOME CHARACTERISTICS OF DIMENSIONAL AND QUALITATIVE STRUCTURE OF AESCULUS HIPPOCASTANIUM TREES IN URBAN FOREST IN THE CITY OF KYIV

Existing scientifically based regulatory framework for the assessment of the volume and quality of its size-structure is a prerequisite for efficient registration and use of wood, which is harvested during reconstructive cuttings in urban plantings. Therefore, the research aims at developing standards of volume and size-structure of high-quality trees Aesculus hippocastanum greenery in Kyiv. To study the features of size-quality structure of Aesculus hippocastanum trees we used materials collected during the reconstruction of urban forest. Collection of the research information was carried according to the classical forest estimation method taking into account the features of forest estimation object. Product specification of tree trunks was carried out according to GOST 9462-88. Due to biological features of Aesculus hippocastanum trees, lack of central axis of a tree trunk around tree height total volume was divided into volume of the tree trunk (Vст) and crown (Vкр). In further studies given volumes in relative terms (Рст, Ркр) were adjusted with the help of regression analysis and analyzed using correlation analysis. The regularity of distribution of the total trunk volume on industrial wood, waste, wood from the total trunk volume and rough, medium and small wood from the volume of industrial wood were studied (Pділ, Рдров, Рвідх, Ргрб, Рсрд, Рдрб) and the correlations between the given indexes and diameter and height of the tree, and height of the tree to the branching were analyzed. Data given in the correlation matrix show that indexes of size-quality wood structure closely correlate with a tree diameter. This fact, as well as the analysis of the literature gave us the reason to use only the tree diameter as an argument in regression equations. In a conducted study the system of regulatory reference data was made for preliminary estimate of volume and size-quality tree structure that is harvested during reconstructive cuttings in urban forest of Kyiv. Standards developed for material estimates of wood material, including stacked-volume ratio and other features of trees that have grown in the conditions of urban environment. Thus, these standards according to the form relate to no category and they are determined by the diameter, tree height and tree height to the branching.

Particle Swarm Optimization Applied to Parameter Estimation of the Four-Parameter Burr III Distribution

The Burr III distribution is a very popular distribution for modeling real data in terms of risk, reliability, and process capability, and thus the estimation of its parameters is essential in most real applications. The classical estimation methods, such as maximum likelihood and least squares, are often used to estimate the parameters of the Burr III distribution. However, maximizing the likelihood function developed for the parameter estimation of the four-parameter Burr type III distribution is a quite difficult problem. Hence, the heuristic approaches must be used to discover good solutions. Particle swarm optimization (PSO) is one of the heuristic approaches, which is a population-based technique developed from swarm intelligence. This paper proposes an alternative parameter estimation method for Burr III distribution using the PSO heuristic approach. Simulation results show that the PSO approach provides accurate estimates and the PSO method is satisfactory for the parameter estimation of Burr III distribution.

Exploiting joint sparsity for underwater acoustic MIMO communications

MIMO communication has been recognized as a potential solution for high speed underwater acoustic communication, which unfortunately encounters significant difficulties posed by simultaneous presence of multipath and Co-channel interference (CoI). Sparsity contained in the multipath structure of underwater acoustic channels offers an effective way for improving channel estimation quality and thus enhancing the communication performance in the form of time reversal or channel estimation based equalization. However, for MIMO channels with extensive multipath and CoI, the performance gain achieved by classic sparsity exploitation channel estimation methods such as orthogonal matching pursuit (OMP) is still not enough to yield satisfactory performance. Under quasi-stationary assumption, underwater acoustic channels of adjacent data blocks exhibit correlated multipath structure, namely, multipath arrivals with similar time delay but different magnitude, which has not been exploited. In this paper, a joint sparse recovery approach is proposed to exploit the sparse correlation among adjacent data blocks to improve the performance of channel estimation. Under the framework of distributed compressed sensing (DCS), a joint sparse model which treats the multipath arrivals as sparse solutions with common time support is adopted to derive a joint sparse recovery algorithm for efficient channel estimation, the results of which are used to initialize and periodly update a channel estimation based time reversal receiver. Finally, underwater MIMO communication experimental results obtained in a shallow water channel are provided to demonstrate the effectiveness of the proposed method, compared to the same type of receiver that do not exploit the joint sparse.

Reliability Estimation of Modified Weibull Distribution with Type-II Hybrid Censored Data

The study deals with the analysis of Type-II hybrid censored data from the modified Weibull distribution. We provide maximum-likelihood estimates of the parameters, reliability, and hazard rate functions along with their standard errors. The confidence intervals along with their widths have also been obtained. Assuming gamma and Jeffrey’s invariant priors for the unknown parameters, Bayes estimates along with its posterior errors and highest posterior density credible intervals are obtained. The Markov Chain Monte Carlo technique has been used to simulate draws from the complicated posterior densities of the parameters. A simulation study is conducted to compare the performances of classical and Bayesian methods of estimation. Finally, a real data analysis is performed for illustrative purpose.

A new phasor estimation method for digital protective relays

Faults and maneuvers in the system may trigger undesirable voltage and current waveforms of non-fundamental frequency that may affect the performance of protection and control systems. In this context, the proposed method aims to improve the characteristic of filtering out undesirable frequency components of signals. Comparisons are made in relation to time response and frequency response for the proposed method and four classical phasor estimation methods. A distance relay was implemented by using the MODELS language of the ATP (Alternative Transients Program) in order to evaluate the relay performance. As expected, for the proposed method, the relay exhibited good performance in terms of accuracy. In terms of relay speed, the method showed a performance comparable to that of the other methods. Theoretically, the phasor estimation proposed method here has a better frequency response than those of the four used methods. Besides, it has a response time fully compatible with these methods. Another advantage of the proposed method is that it can be easily programmed, allowing users to change design parameters according to their needs.

Underdetermined DOA Estimation Using MVDR-Weighted LASSO.

The direction of arrival (DOA) estimation problem is formulated in a compressive sensing (CS) framework, and an extended array aperture is presented to increase the number of degrees of freedom of the array. The ordinary least square adaptable least absolute shrinkage and selection operator (OLS A-LASSO) is applied for the first time for DOA estimation. Furthermore, a new LASSO algorithm, the minimum variance distortionless response (MVDR) A-LASSO, which solves the DOA problem in the CS framework, is presented. The proposed algorithm does not depend on the singular value decomposition nor on the orthogonality of the signal and the noise subspaces. Hence, the DOA estimation can be done without a priori knowledge of the number of sources. The proposed algorithm can estimate up to sources using M sensors without any constraints or assumptions about the nature of the signal sources. Furthermore, the proposed algorithm exhibits performance that is superior compared to that of the classical DOA estimation methods, especially for low signal to noise ratios (SNR), spatially-closed sources and coherent scenarios.

Estimation of the energy spectrums of reflections in pulse Doppler weather radars. Part 2. Extreme performance

This is the second paper in a series of papers dedicated to the peculiarities of estimation of the continuous energy spectra of random processes of different nature, which are determined by their samples at discrete moments of time. In this paper we analyze extreme performance of the reconstruction of continuous energy spectra, in particular, the ones of interperiod fluctuations of reflections from meteorological objects in pulse Doppler weather radars under the hypothetical conditions of a priori known covariance matrix of the analyzed processes. The reasons, which cause known disadvantages of classical (nonparametric) spectral estimation (SE) methods for energy spectrums shape reconstruction, are discussed. We have considered known and suggested criteria, using which the extreme performance of classical SE methods and parametric superresolution ones has been quantitatively compared. It has been demonstrated that the extreme performance of SE methods contains important but not comprehensive information. In order to choose a SE method appropriate for operation under real-world conditions, this information should be used together with information on a corresponding method’s adaptive performance under a priori unknown statistical characteristics of input effects.

The reliability assessment of the electromagnetic valve of high-speed electric multiple units braking system based on two-parameter exponential distribution

In order to solve the reliability assessment of braking system component of high-speed electric multiple units, this article, based on two-parameter exponential distribution, provides the maximum likelihood estimation and Bayes estimation under a type-I life test. First of all, we evaluate the failure probability value according to the classical estimation method and then obtain the maximum likelihood estimation of parameters of two-parameter exponential distribution by performing and using the modified likelihood function. On the other hand, based on Bayesian theory, this article also selects the beta and gamma distributions as the prior distribution, combines with the modified maximum likelihood function, and innovatively applies a Markov chain Monte Carlo algorithm to parameters assessment based on Bayes estimation method for two-parameter exponential distribution, so that two reliability mathematical models of the electromagnetic valve are obtained. Finally, through type-I life test, the failure rates according to maximum likelihood estimation and Bayes estimation method based on Markov chain Monte Carlo algorithm are, respectively, 2.650 × 10−5 and 3.037 × 10−5. Compared with the failure rate of a electromagnetic valve 3.005 × 10−5, it proves that the Bayes method can use a Markov chain Monte Carlo algorithm to estimate reliability for two-parameter exponential distribution and Bayes estimation is more closer to the value of electromagnetic valve. So, by fully integrating multi-source, Bayes estimation method can preferably modify and precisely estimate the parameters, which can provide a certain theoretical basis for the safety operation of high-speed electric multiple units.

Parameter estimation of complex mixed models based on meta-model approach

Complex biological processes are usually experimented along time among a collection of individuals, longitudinal data are then available. The statistical challenge is to better understand the underlying biological mechanisms. A standard statistical approach is mixed-effects model where the regression function is highly-developed to describe precisely the biological processes (solutions of multi-dimensional ordinary differential equations or of partial differential equation). A classical estimation method relies on coupling a stochastic version of the EM algorithm with a Monte Carlo Markov Chain algorithm. This algorithm requires many evaluations of the regression function. This is clearly prohibitive when the solution is numerically approximated with a time-consuming solver. In this paper a meta-model relying on a Gaussian process emulator is proposed to approximate the regression function, that leads to what is called a mixed meta-model. The uncertainty of the meta-model approximation can be incorporated in the model. A control on the distance between the maximum likelihood estimates of the mixed meta-model and the maximum likelihood estimates of the exact mixed model is guaranteed. Eventually, numerical simulations are performed to illustrate the efficiency of this approach.

A Geostatistical Framework for Estimating Compositional Data Avoiding Bias in Back-transformation

Estimation of some mineral deposits involves chemical species or a granulometric mass balance that constitute a closed constant sum (e.g., 100%). Data that add up to a constant are known as compositional data (CODA). Classical geostatistical estimation methods (e.g., kriging) are not satisfactory when CODA are used, since bias is expected when estimated mean block values are back-transformed to the original space. CODA methods use nonlinear transformations, and when the transformed data are interpolated, they cannot be returned directly to the space of the original data. If these averages are back-transformed using the inverse function, bias is generated. To avoid this bias, this article proposes geostatistical simulation of the isometric logratio ratio (ilr) transformations back-transforming point simulated values (instead of block estimations), with the averaging being postponed to the end of the process. The results show that, in addition to maintaining the mass balance and the correlations among the variables, the means (E-types) of the simulations satisfactorily reproduce the statistical characteristics of the grades without any sort of bias. A complete case study of a major bauxite deposit illustrates the methodology.

Estimation and prediction for Type-I hybrid censored data from generalized Lindley distribution

This paper consider the problems of estimation and prediction using Type-I hybrid censored lifetime data that follow generalized Lindley distribution. Maximum likelihood estimators as well as Bayes estimators have been proposed for estimating the parameters and reliability characteristics from the generalized Lindley distribution. Since posteriors are not in closed forms, Markov Chain Monte Carlo techniques such as Gibbs sampler and Metropolis-Hastings algorithm have been utilized to explore the properties of the posteriors. Monte Carlo simulation study has been carried out to compare the classical and Bayesian estimation methods. One and two sample predictive posteriors of future order statistics are also derived on the basis of Type-I hybrid censored data. Finally, a set of real data is analysed for illustration.

Estimating the parameters of lifetime distributions under progressively Type-II censoring from fuzzy data

Abstract The problem of estimating lifetime distribution parameters under progressively Type-II censoring originated in the context of reliability. But traditionally it is assumed that the available data from this censoring scheme are performed in exact numbers. However, some collected lifetime data might be imprecise and are represented in the form of fuzzy numbers. Thus, it is necessary to generalize classical statistical estimation methods for real numbers to fuzzy numbers. This paper deals with the estimation of lifetime distribution parameters under progressively Type-II censoring scheme when the lifetime observations are reported by means of fuzzy numbers. A new method is proposed to determine the maximum likelihood estimates of the parameters of interest. The methodology is illustrated with two popular models in lifetime analysis, the Rayleigh and Lognormal lifetime distributions.

Modeling jointly low, moderate, and heavy rainfall intensities without a threshold selection

AbstractIn statistics, extreme events are often defined as excesses above a given large threshold. This definition allows hydrologists and flood planners to apply Extreme‐Value Theory (EVT) to their time series of interest. Even in the stationary univariate context, this approach has at least two main drawbacks. First, working with excesses implies that a lot of observations (those below the chosen threshold) are completely disregarded. The range of precipitation is artificially shopped down into two pieces, namely large intensities and the rest, which necessarily imposes different statistical models for each piece. Second, this strategy raises a nontrivial and very practical difficultly: how to choose the optimal threshold which correctly discriminates between low and heavy rainfall intensities. To address these issues, we propose a statistical model in which EVT results apply not only to heavy, but also to low precipitation amounts (zeros excluded). Our model is in compliance with EVT on both ends of the spectrum and allows a smooth transition between the two tails, while keeping a low number of parameters. In terms of inference, we have implemented and tested two classical methods of estimation: likelihood maximization and probability weighed moments. Last but not least, there is no need to choose a threshold to define low and high excesses. The performance and flexibility of this approach are illustrated on simulated and hourly precipitation recorded in Lyon, France.

Optimal input experiment design and parameter estimation in core-scale pressure oscillation experiments

Summary This paper considers Pressure Oscillation (PO) experiments for which we find the minimum experiment time that guarantees user-imposed parameter variance upper bounds and honours actuator limits. The parameters permeability and porosity are estimated with a classical least-squares estimation method for which an expression of the covariance matrix of the estimates is calculated. This expression is used to tackle the optimization problem. We study the Dynamic Darcy Cell experiment set-up (Heller et al., 2002) and focus on data generation using square wave actuator signals, which, as we shall prove, deliver shorter experiment times than sinusoidal ones. Parameter identification is achieved using either inlet pressure/outlet pressure measurements (Heller et al., 2002) or actuator position/outlet pressure measurements, where the latter is a novel approach. The solution to the optimization problem reveals that for both measurement methods an optimal excitation frequency, an optimal inlet volume, and an optimal outlet volume exist. We find that under the same parameter variance bounds and actuator constraints, actuator position/outlet pressure measurements result in required experiment times that are a factor fourteen smaller compared to inlet pressure/outlet pressure measurements. This result is analysed in detail and we find that the dominant effect driving this difference originates from an identifiability problem when using inlet–outlet pressure measurements for joint estimation of permeability and porosity. We illustrate our results with numerical simulations, and show excellent agreement with theoretical expectations.

Time delay estimation method of X-ray pulsar observed profile based on the optimal frequency band

In order to improve the time delay estimation accuracy of the observed profile in the X-ray pulsar based navigation, the spectral characteristics of the observed profile of X-ray pulsar and the drawback of the classical Taylor fast Fourier transform (FFT) time delay estimation method are analyzed. It is found that when estimating the time delay, we can abandon the higher frequency components that are always affected by noise seriously, but only utilize the information about the low frequency part. Based on this idea, by modifying the weigh function of the classical Taylor FFT time delay estimation method, a new time delay estimation algorithm based on the optimal frequency band is proposed, in which the optimal frequency band is determined by establishing the relationship between the selected frequency band and the time delay estimation accuracy under different signal-to-noise ratios (SNRs). Then by using the real data obtained with the proportional counter array, the low-energy (2-60 keV) detection instrument boarded on the Rossi X-ray Timing Explorer satellite, the optimal frequency as a function the SNR of observed profile is given for the PSR B0531+21 (namely the Crab pulsar) through the Monte-Carlo technique. Since the parameters of different pulsars are known, in practical navigation, the optimal frequency in an observation time for a certain pulsar can be estimated in advance by using the simulation data or the obtained real data of the pulsar, which can remarkably alleviate the onboard computational burden. Finally, a series of numerical simulations and experiments using real data of Crab pulsar are designed to evaluate the performance of the proposed time delay estimation algorithm. The main results can be summarized as follows: the proposed estimator outperforms the normally used fast approximate maximum-likelihood (FAML), cross correlation (CC), nonlinear least square (NLS) and weighted nonlinear least-square (WNLS) estimators when the observation time is short or the source flux is small; when the observation time is long or the source flux is large, its estimation accuracy is almost the same as those of CC and NLS estimators and lower than those of the FAML and WNLS estimators, but its computational complexity is smaller than those of NLS, FAML and WNLS estimators. The above results indicate the high estimation accuracy and high computational efficiency of the proposed time delay estimation method, which can be used in the case that the observation time is restricted to be short or the source flux of the usable pulsar is small in X-ray pulsar based navigation.

Estimation of the energy spectrums of reflections in pulse doppler weather radars. Part 1. Modifications of the spectral estimation algorithms

This is the first paper in a series of papers devoted to the peculiarities of estimation of the continuous energy spectra of random processes of different nature, which are defined by their samples at discrete moments of time. In the paper we consider two kinds of the generalized spectrum analyzers (GSA), whose structure fits the majority of classical (nonparametric) and modern noneigenstructured spectral estimation (SE) methods. It has been demonstrated that a number of known superresolution SE methods may be considered as particular cases of parametric GSA based on whitening or inversing filters of the input process. We focus on the autoregressive models of analyzed processes with continuous energy spectrums, for which the whitening or inversing filters are the transversal filters of various structures with proper parameters. The utilized interpretation allows one to modify the well-known superresolution SE methods for the problem of continuous spectrums reconstruction and, what is more important, to establish their new varieties with practically useful properties, that are going to be explored in the following two papers.

Damage tolerance and classic fatigue life prediction of a helicopter main rotor blade

Fatigue life of the main rotor blade of a helicopter is investigated from two different approaches. The blade is comprised of many different parts such as spar, skin, abrasive strip, doublers, box beam doublers, etc. and it undergoes complex random load spectra. A finite element analysis is carried out to assess the stress distribution in the blade parts. Then, using the Miner’s rule the fatigue life of the blade is calculated following a classic life estimation method under random loading. At the next step, damage tolerance approach is used for life estimation of the blade. Fatigue crack growth properties and threshold stress intensity range of the spar is obtained based on ASTM E647 test method. Then, crack growth analysis is done using Zencrack software. In order to calculate the length of the smallest growing cracks and their fatigue crack growth life, no crack growth and slow crack growth approaches are used. A comprehensive investigation is carried out on the effect of initial crack length and aspect ratio on growth or no growth of cracks. Comparing the obtained fatigue life from two different approaches, some conclusive results are drawn.

Robust Moderation Analysis Using a Two-Level Regression Model

Moderation analysis has many applications in social and behavioral sciences. Classical estimation methods typically assume that errors are normally distributed and homoscedastic. When these assumpt...