Maximum Likelihood Estimation Technique Research Articles

High-order approximation algorithm using Gram-Schmidt QR transformations coupled with an iterative correction process for tracking frequency drift in OFDM systems

Abstract To jointly track frequency drift (or fine frequency offset) and channel state variation for orthogonal frequency division multiplexing (OFDM) communications over mobile wireless channels, the maximum-likelihood (ML) estimation techniques are commonly adopted. A major difficulty arises from the highly nonlinear nature of the log-likelihood function which renders local extrema or multiple solutions. The use of mathematical approximation coupled with an adaptive iteration algorithm is a viable approach to ease problem solving. The approximation methods used in existing works are usually of the first-order level. In this work, we devise a high-order approximation algorithm to improve the tracking performance. As shall be seen, the problem amounts to finding the roots of an approximate high-degree polynomial equation derived from the log-likelihood function. To this end, we triangularize the companion matrix constructed from the high-degree polynomial using iterative Gram-Schmidt QR transformations, an eigenvalue problem in matrix computation, coupled with another iterative correction process to produce a frequency offset estimate to good accuracy. It is found that a high-order approximation algorithm formulated can achieve much better tracking performance in terms of estimation accuracy, tracking range, and error rate results than various other tracking algorithms appearing in the literature.

Probability Model of Forward Birth Interval and Its Application

In renewal theory approach, it is well known that the limiting forms of the probability density function of backward recurrence time and forward recurrence time which are similar to open birth interval and forward birth interval are identical on the assumption that the renewal densities do not change over time. The forward birth interval defined as the time between the survey date and the date of next birth posterior to the survey date. Forward birth interval is a good index for current change in fertility behavior. The present model has been derived on the assumption that females are not exposed to the risk of conception immediately after the termination of Post-Partum Amenorrhea (PPA). However they may be exposed to the risk of conception at different point of time after the termination of PPA because of some socio-cultural factors or contraceptive practices. In this probability model for forward birth interval regardless of parity assuming that renewal density does not change over time and females are exposed to the risk of conception at different point of time. In this model, fecundability (λ) and the duration of time from the point of termination of PPA to the state of exposure as random variable (µ) which follows exponential distribution. The maximum likelihood estimation technique has been used for the estimation of parameters λ and µ through derived model. The estimated values of λ and µ are 1.1051 and 2.841 respectively. The variance of estimated λ and µ are 0.067 and 0.79 respectively. The co-variance in between estimated λ and µ is -0.026.With these estimates the expected frequencies for the distribution and χ2 = 0.6057 is highly significant. Thus, the derived probability model explains the fertility behavior of observed data satisfactorily well.

Imperfect debugging study of SRGM with fault reduction factor and multiple change point

The present investigation deals with the software reliability growth models (SRGMs) with imperfect debugging, testing effort function (TEF) and fault reduction factor (FRF). FRF is basically defined as the net number of faults removed in proportion to the failures experienced. We propose a new scheme for constructing SRGM based on non-homogeneous Poisson process (NHPP). The concept of Weibull type testing-effort function with multiple change point has been incorporated. The main focus in the present investigation is to obtain mean value function which is further employed to explore the software reliability indices. The model parameters are estimated by least square and maximum likelihood estimation techniques. The optimal release policy based on cost, reliability and testing efforts is also suggested. Numerical results are given to illustrate the validity of analytical results.

The Model of Severity Prediction of Traffic Crash on the Curve

With the study of traffic crashes on curved road segments as the focus of research, a logistic regression based curve road crash severity prediction model was established based on a sample crash database of 20000 entries collected from 4 regions of China and 15 evaluation indicators involving driver, driving environment, and traffic environment factors. Maximum Likelihood Estimation and step-back technique were deployed for data analysis, the conclusion of which is that the three main contributory factors on curve road crash severity are weather, roadside protection facility, and pavement structure. Hosmer and Lemeshow tests were used to verify the reliability of the model, and the model variables were discussed to a certain degree as well.

English

A study was carried out to investigate into factors responsible for technical inefficiency of food crop farmers in the oil polluted and non-polluted areas of Niger Delta. Data were collected from 270 (140 for oil polluted and 130 in unpolluted area) farmers selected through a multistage random sampling technique. A stochastic frontier function that incorporated inefficiency effect was estimated using the Maximum Likelihood Estimation (MLE) technique. The MLE of the stochastic production function revealed mean technical, efficiency of 78% in polluted area while the corresponding values in unpolluted area were 88%. The most efficient farmer had the technical efficiency (TE) of 0.93 and least efficient farmer of 4.48. Farmers with efficiency index between 4.48 and 0.65 constituted 31% while 68.2% of the farmers had efficiency index between 0.70 and 0.95. The predicted technical efficiency varied widely across farms between 28 and 86% for farmers in polluted area while between 38 and 96% for the farmers in unpolluted area. The results show that farmers generally in the study area are not technically efficient, although the farmers in the unpolluted area are relatively more efficient than farmers in the polluted area. The implications are that the policies that would reduce oil pollution and encourage farmers to utilize their resources optimally should be put in place. Hence, in order to halt the continual degradation of the Niger Delta environment there is need for the enactment and enforcement of stringent environmental laws to protect the area. Key words: Nigeria, Niger Delta, stochastic function, oil pollution, technical efficiency, food crops farmers.

Accounting for short samples and heterogeneous experience in rating crop insurance

Purpose – The purpose of this paper is to be an academic inquiry into rating issues confronted by the US Federal Crop Insurance program stemming from changes in participation rates as well as the weighting of data to reflect longer‐run weather patterns.Design/methodology/approach – The authors investigate two specific approaches that differ from those adopted by the Risk Management Agency, building upon standard maximum likelihood and Bayesian estimation techniques that consider parametric densities for the loss‐cost ratio.Findings – Both approaches indicate that incorporating weights into the priors for Bayesian estimation can inform the distribution.Originality/value – In most cases, the authors' results indicate that including weighting into priors for Bayesian estimation implied lower premium rates than found using standard methods.

Environmental resource collection: implications for children's schooling in Tigray, northern Ethiopia

AbstractThis paper examines the adverse effect of natural resources scarcity on children's schooling and the possible gender bias of resource collection work against girls' schooling. It uses cross-sectional data on 316 children aged 7–18 years collected from 120 rural households in Tigray, northern Ethiopia. The two-stage conditional maximum likelihood estimation technique is employed to take care of endogeneity between schooling and collection intensity decisions. The results revealed that a 50 per cent increase in collection intensity reduces the likelihood of child schooling by approximately 11 per cent. However, we find no evidence of gender bias against girls' schooling.

Learning to Obtain Reward, but Not Avoid Punishment, Is Affected by Presence of PTSD Symptoms in Male Veterans: Empirical Data and Computational Model

Post-traumatic stress disorder (PTSD) symptoms include behavioral avoidance which is acquired and tends to increase with time. This avoidance may represent a general learning bias; indeed, individuals with PTSD are often faster than controls on acquiring conditioned responses based on physiologically-aversive feedback. However, it is not clear whether this learning bias extends to cognitive feedback, or to learning from both reward and punishment. Here, male veterans with self-reported current, severe PTSD symptoms (PTSS group) or with few or no PTSD symptoms (control group) completed a probabilistic classification task that included both reward-based and punishment-based trials, where feedback could take the form of reward, punishment, or an ambiguous “no-feedback” outcome that could signal either successful avoidance of punishment or failure to obtain reward. The PTSS group outperformed the control group in total points obtained; the PTSS group specifically performed better than the control group on reward-based trials, with no difference on punishment-based trials. To better understand possible mechanisms underlying observed performance, we used a reinforcement learning model of the task, and applied maximum likelihood estimation techniques to derive estimated parameters describing individual participants’ behavior. Estimations of the reinforcement value of the no-feedback outcome were significantly greater in the control group than the PTSS group, suggesting that the control group was more likely to value this outcome as positively reinforcing (i.e., signaling successful avoidance of punishment). This is consistent with the control group’s generally poorer performance on reward trials, where reward feedback was to be obtained in preference to the no-feedback outcome. Differences in the interpretation of ambiguous feedback may contribute to the facilitated reinforcement learning often observed in PTSD patients, and may in turn provide new insight into how pathological behaviors are acquired and maintained in PTSD.

Pairing effect on spectral statistics of even and odd mass nuclei

The interplay of pairing is explored for the spectral statistics of nuclear systems with emphasis on the nearest neighbor spacing distributions by employing the kernel density and maximum-likelihood estimation techniques. Different sequences prepared by all the available empirical data for low-lying energy levels of even- and odd-mass nuclei in the \(34 \le A < 206\) mass region. A deviation to more regular dynamics is apparent for even-mass nuclei in comparison to the odd-mass ones, and there are suggestions of the effects due to unclosed proton shells on more chaotic dynamics.

Accounting for short samples and heterogeneous experience in rating crop insurance

PurposeThe purpose of this paper is to be an academic inquiry into rating issues confronted by the US Federal Crop Insurance program stemming from changes in participation rates as well as the weighting of data to reflect longer‐run weather patterns.Design/methodology/approachThe authors investigate two specific approaches that differ from those adopted by the Risk Management Agency, building upon standard maximum likelihood and Bayesian estimation techniques that consider parametric densities for the loss‐cost ratio.FindingsBoth approaches indicate that incorporating weights into the priors for Bayesian estimation can inform the distribution.Originality/valueIn most cases, the authors' results indicate that including weighting into priors for Bayesian estimation implied lower premium rates than found using standard methods.

Assessing market uncertainty by means of a time-varying intermittency parameter for asset price fluctuations

Maximum likelihood estimation techniques for multifractal processes are applied to high-frequency data in order to quantify intermittency in the fluctuations of asset prices. From time records as short as one month these methods permit extraction of a meaningful intermittency parameter λ characterising the degree of volatility clustering. We can therefore study the time evolution of volatility clustering and test the statistical significance of this variability. By analysing data from the Oslo Stock Exchange, and comparing the results with the investment grade spread, we find that the estimates of λ are lower at times of high market uncertainty.

The McDonald Generalized Beta-Binomial Distribution: A New Binomial Mixture Distribution and Simulation Based Comparison with Its Nested Distributions in Handling Overdispersion

The binomial outcome data are widely encountered in many real world applications. The Binomial distribution often fails to model the binomial outcomes since the variance of the observed binomial outcome data exceeds the nominal Binomial distribution variance, a phenomenon known as overdispersion. One way of handling overdispersion is modeling the success probability of the Binomial distribution using a continuous distribution defined on the standard unit interval. The resultant general class of univariate discrete distributions is known as the class of Binomial mixture distributions. The Beta-Binomial (BB) distribution is a prominent member of this class of distributions. The Kumaraswamy-Binomial (KB) distribution is another recent member of this class. In this paper we focus the emphasis on the McDonald's Generalized Beta distribution of the first kind as the mixing distribution and introduce a new Binomial mixture distribution called the McDonald Generalized Beta-Binomial distribution(McGBB). Some theoretical properties of McGBB are discussed. The parameters of the McGBB distribution are estimated via maximum likelihood estimation technique. A real world dataset is modeled by using the new McGBB mixture distribution, and it is shown that this model gives better fit than its nested models. Finally, an extended simulation study is presented to compare the McGBB distribution with its nested distributions in handling overdispersed binomial outcome data.

Technical and Economic Efficiencies in Poultry Production in Imo State, Nigeria

This study was carried out to estimate the technical and economic efficiencies of poultry farmers in Imo State, Nigeria. The data was collected with semi-structured questionnaire from 140 randomly selected poultry farmers. A stochastic frontier production function was estimated by using the maximum likelihood estimation technique to obtain the technical and economic efficiencies of poultry farmers. The mean technical efficiency of poultry farmers was 75 percent, while their mean economic efficiency was 21 percent. The generalized likelihood test indicated that, the poultry farmers are not fully technically and economically efficient in resource use. There is 79% allowance to increase economic efficiency of poultry farmers by improvement in technical efficiency.

Hybrid Scheme for CFO Cancellation in OFDM Systems

In this paper, we combine maximum likelihood estimation (MLE) technique with improved sinc power (ISP) pulse shaping to cancel inter-carrier interference caused by carrier frequency offset in coded orthogonal frequency division multiplexing (OFDM) systems, thereby achieving an improved bit error rate (BER) performance as compared to the above two schemes. The BER performance of the OFDM system was checked for ISP pulse shaping alone, MLE technique with low pass filtering, and a hybrid scheme of MLE technique with ISP pulse shaping. It has been shown that, at normalized carrier frequency offset of 0.2 and BER of 10−5, the hybrid scheme with convolutional coding could achieve a BER performance improvement of around 1.78 and 4.83 dB, respectively, as compared to MLE technique with low pass filtering and ISP pulse shaping alone.

A Logical Dynamical Systems Approach to Modeling and Control of Residual Gas Fraction in IC Engines

The stochastic logical dynamical system is described in a new framework by proposing a finite set of special functions. The optimization problem of the residual gas friction (RGF) is modeled as a stochastic logical dynamical system, applying maximum likelihood estimation (MLE) and quantification technique. The optimal controller is designed with receding horizon control (RHC) approach. Finally, to demonstrate the performances of the proposed control scheme, numerical simulation and experiment are expressed.

A Zeroinflated ARI(1,1)-IGARCH(1,1) Mixture Model to Forecast Milk-Based Commodity Prices

The weekly change of several German milkbased commodity prices do not only exhibit traditional patterns like mean dependence and volatility clustering, but also a high frequency of zero changes which can not be explained by well known ARIMA-GARCH models. Therefore, we develop a new mixture model which combines the elements of zero-infl ated models common in micro-econometrics and intermittent demand forecasting with a traditional ARIMA(1,1,0)-GARCH(1,1) model. We describe the model components, data generation processes, maximum likelihood estimation techniques and the generation of forecasting distributions and point forecasts by resampling techniques. The model is applied to a low frequency weekly time series of skimmed whey powder (SWP). Competing submodels are selected by likelihood ratio tests and the AIC information criteria. Furthermore, beyond the evaluation of the out-of-sample forecasting performance, several coverage and independence tests are computed.

Iterative Maximum Likelihood Estimators for High-Dynamic GNSS Signal Tracking

This paper presents novel signal-tracking algorithms for global navigation satellite system (GNSS) receivers using a maximum likelihood estimation (MLE) technique to carry out robust signal tracking under severe signal environments, such as high dynamics for maneuvering users. The cost function of the MLE of signal parameters such as code delay, carrier phase, and Doppler frequency is used to derive a discriminator function and thus generate error signals based on incoming and reference signals. Two distinct forms of algorithms are derived by means of mathematical programming using an iterative approach, which is based on the log-likelihood MLE cost function that assumes various signal parameters as unknown constants over an observation interval. First, the Levenberg-Marquardt method is employed using gradient and Hessian matrices. Second, a conventional nonlinear least-square estimation method is applied to determine the MLE cost function, assuming additive white Gaussian noise. An efficient and practical approach to Doppler frequency tracking is also derived based on the assumption of a code-free signal (i.e., a signal from which the code has been wipe off). The use of MLE for carrier tracking makes it possible to generalize the MLE equation for arbitrary codes and modulation schemes. This is ideally suited to various GNSS signals that have the same tracking module structure. Finally, performance of the receivers, in terms of robustness under dynamic stress, computational efficiency, accuracy, computational burden, and response speed, is assessed using analytical and/or numerical techniques.

Use of vector divisions in solving quasi-likelihood equations for a Poisson model

Maximum-likelihood estimation technique is known to provide consistent and most efficient regression estimates but often this technique is tedious to implement, particularly in the modelling of correlated count responses. To overcome this limitation, researchers have developed semi- or quasi-likelihood functions that depend only on the correct specification of the mean and variance of the responses rather than on the distribution function. Moreover, quasi-likelihood estimation provides consistent and equally efficient estimates as the maximum-likelihood approach. Basically, the quasi-likelihood estimating function is a non-linear equation constituting of the gradient, Hessian and basic score matrices. Henceforth, to obtain estimates of the regression parameters, the quasi-likelihood equation is solved iteratively using the Newton–Raphson technique. However, the inverse of the Jacobian matrix involved in the Newton–Raphson method may not be easy to compute since the matrix is very close to singularity. In this paper, we consider the use of vector divisions in solving quasi-likelihood equations. The vector divisions are implemented to form secant method formulas. To assess the performance of the use of vector divisions with the secant method, we generate cross-sectional Poisson counts using different sets of mean parameters. We compute the estimates of the regression parameters using the Newton–Raphson technique and vector divisions and compare the number of non-convergent simulations under both algorithms.

Seismic waves estimation and wavefield decomposition: application to ambient vibrations

SUMMARY Passive seismic surveying methods represent a valuable tool in local seismic hazard assessment, oil and gas prospection, and in geotechnical investigations. Array processing techniques are used in order to estimate wavefield properties such as dispersion curves of surface waves and ellipticity of Rayleigh waves. However, techniques presently in use often fail to properly merge information from three-components sensors and do not account for the presence of multiple waves. In this paper, a technique for maximum likelihood estimation of wavefield parameters including direction of propagation, velocity of Love waves and Rayleigh waves, and ellipticity of Rayleigh waves is described. This technique models jointly all the measurements and all the wavefield parameters. Furthermore it is possible to model the simultaneous presence of multiple waves. The performance of this technique is evaluated on a high-fidelity synthetic data set and on real data. It is shown that the joint modelling of all the sensor components, decreases the variance of wavenumber estimates and allows the retrieval of the ellipticity value together with an estimate of the prograde/retrograde motion.

Novel Methods and the Maximum Likelihood Estimation Technique for Estimating Traffic Critical Gap

SUMMARYMost unsignalised intersection capacity calculation procedures are based on gap acceptance models. Accuracy of critical gap estimation affects accuracy of capacity and delay estimation. Several methods have been published to estimate drivers' sample mean critical gap, the Maximum Likelihood Estimation (MLE) technique regarded as the most accurate. This study assesses three novel methods; Average Central Gap (ACG) method, Strength Weighted Central Gap method (SWCG), and Mode Central Gap method (MCG), against MLE for their fidelity in rendering true sample mean critical gaps. A Monte Carlo event based simulation model was used to draw the maximum rejected gap and accepted gap for each of a sample of 300 drivers across 32 simulation runs. Simulation mean critical gap is varied between 3s and 8s, while offered gap rate is varied between 0.05veh/s and 0.55veh/s. This study affirms that MLE provides a close to perfect fit to simulation mean critical gaps across a broad range of conditions. The MCG method also provides an almost perfect fit and has superior computational simplicity and efficiency to the MLE. The SWCG method performs robustly under high flows; however, poorly under low to moderate flows. Further research is recommended using field traffic data, under a variety of minor stream and major stream flow conditions for a variety of minor stream movement types, to compare critical gap estimates using MLE against MCG. Should the MCG method prove as robust as MLE, serious consideration should be given to its adoption to estimate critical gap parameters in guidelines. Copyright © 2012 John Wiley &amp; Sons, Ltd.