Distributed Parameter Estimation Research Articles

Asymptotically Efficient Distributed Estimation With Exponential Family Statistics

This paper studies the problem of distributed parameter estimation in multiagent networks with exponential family observation statistics. A certainty-equivalence type distributed estimator of the consensus-plus-innovations form is proposed in which, at each observation sampling epoch, agents update their local parameter estimates by appropriately combining the data received from their neighbors and the locally sensed new information (innovation). Under global observability of the networked sensing model, i.e., the ability to distinguish between different instances of the parameter value based on the joint observation statistics, and mean connectivity of the inter-agent communication network, the proposed estimator is shown to yield consistent parameter estimates at each network agent. Further, it is shown that the distributed estimator is asymptotically efficient, in that, the asymptotic covariances of the agent estimates coincide with that of the optimal centralized estimator, i.e., the inverse of the centralized Fisher information rate. From a technical viewpoint, the proposed distributed estimator leads to non-Markovian mixed time-scale stochastic recursions and the analytical methods developed in this paper contribute to the general theory of distributed stochastic approximation.

Modeling of groundwater recharge using a multiple linear regression (MLR) recharge model developed from geophysical parameters: a case of groundwater resources management

In this paper we developed a simple multiple linear regression (MLR) recharge model that relates the recharge estimates obtained from rainfall to the geophysical parameters obtained from the interpretation of two-dimensional (2D) resistivity imaging data for the purpose of efficient groundwater resources management in the southern part of Perak, Malaysia through recharge rate estimation and prediction. Through application of linear regression model, the estimated recharge from rainfall and the corresponding estimated unsaturated layer resistivity and its thickness (Depth to aquifer top) parameters obtained from geophysical measurements were regressed in R software written code environment for generating a MLR recharge model. The sensitivity of analyzed results of the MLR recharge model based on the parameter estimation of the model predictors (resistivity and depth) evaluated at Pr ≤ 0.05 is 5.39 × 10−06 and 8.39 × 10−04, respectively. The accuracy and predictive power test conducted on the developed model using both t test and $$ \chi^{2} $$ distribution at α = 5 % significance level established the model estimation and prediction capability. The obtained results of $$ \chi^{2} $$ distribution test and parameters estimation test confirmed the reliability and accuracy of the proposed model in recharge rate estimation and prediction in the area. The application of the MLR recharge model gives estimate of 242.30 mm/year for regional groundwater recharge rate in the area. Through GIS tool, the MLR recharge model was used to produce groundwater recharge rate prediction map. A quick and independent estimate of recharge by simple geophysical measurement has been established based on these results. The information on the prediction map could serve as a scientific basis for groundwater resources management and exploration in the area. The approach suggests a new application of geoelectric parameters in determining recharge rate due to infiltration. The technique provides a good alternative to other methods used for this purpose.

E-Bayes Estimation of Burr Distribution Parameter under Square Loss Function

This paper provides the E-Bayes estimation and hierarchical Bayes estimation of Burr distribution parameter under square loss function when the prior distribution is Gamma distribution, and proves that the E-Bayes estimation and hierarchical Bayes estimation are progressively equal. Numerical simulation also shows that the results of these two types of estimation are close, and E-Bayes estimation is more convenient in terms of calculation complexity.

E-Bayes Estimation of Rayleigh Distribution Parameter

This paper provided the E-Bayes estimation and hierarchical Bayes estimation of Rayleigh distribution parameter under q-symmetric entropy loss function, when the prior distribution is Beta distribution, and the relation between E-Bayes estimation and hierarchical Bayes estimation was discussed. Numerical simulation shows that the results of these two types of estimation are close, and E-Bayes estimation is more convenient in terms of calculation complexity.

Using type IV Pearson distribution to calculate the probabilities of underrun and overrun of lists of multiple cases.

An efficient operating room needs both little underutilised and overutilised time to achieve optimal cost efficiency. The probabilities of underrun and overrun of lists of cases can be estimated by a well defined duration distribution of the lists. To propose a method of predicting the probabilities of underrun and overrun of lists of cases using Type IV Pearson distribution to support case scheduling. Six years of data were collected. The first 5 years of data were used to fit distributions and estimate parameters. The data from the last year were used as testing data to validate the proposed methods. The percentiles of the duration distribution of lists of cases were calculated by Type IV Pearson distribution and t-distribution. Monte Carlo simulation was conducted to verify the accuracy of percentiles defined by the proposed methods. Operating rooms in John D. Dingell VA Medical Center, United States, from January 2005 to December 2011. Differences between the proportion of lists of cases that were completed within the percentiles of the proposed duration distribution of the lists and the corresponding percentiles. Compared with the t-distribution, the proposed new distribution is 8.31% (0.38) more accurate on average and 14.16% (0.19) more accurate in calculating the probabilities at the 10th and 90th percentiles of the distribution, which is a major concern of operating room schedulers. The absolute deviations between the percentiles defined by Type IV Pearson distribution and those from Monte Carlo simulation varied from 0.20 min (0.01) to 0.43 min (0.03). Operating room schedulers can rely on the most recent 10 cases with the same combination of surgeon and procedure(s) for distribution parameter estimation to plan lists of cases. Values are mean (SEM). The proposed Type IV Pearson distribution is more accurate than t-distribution to estimate the probabilities of underrun and overrun of lists of cases. However, as not all the individual case durations followed log-normal distributions, there was some deviation from the true duration distribution of the lists.

Synthetic Aperture Radar Image Clustering with Curvelet Subband Gauss Distribution Parameters

Curvelet transform is a multidirectional multiscale transform that enables sparse representations for signals. Curvelet-based feature extraction for Synthetic Aperture Radar (SAR) naturally enables utilizing spatial locality; the use of curvelet-based feature extraction is a novel method for SAR clustering. The implemented method is based on curvelet subband Gaussian distribution parameter estimation and cascading these estimated values. The implemented method is compared against original data, polarimetric decomposition features and speckle noise reduced data with use of k-means, fuzzy c-means, spatial fuzzy c-means and self-organizing maps clustering methods. Experimental results show that the curvelet subband Gaussian distribution parameter estimation method with use of self-organizing maps has the best results among other feature extraction-clustering performances, with up to 94.94% overall clustering accuracies. The results also suggest that the implemented method is robust against speckle noise.

Curvelet-Based Synthetic Aperture Radar Image Classification

Curvelet transform (CT) is a multiscale directional transform that enables the use of texture and spatial locality information. In synthetic aperture radar (SAR) imaging, CT is mostly used in speckle noise reduction. This letter utilizes CT for feature extraction in land use classification. Two types of curvelet-based feature extraction methods are implemented for SAR. The first one is defined and used in content-based image retrieval and is based on generalized Gaussian distribution parameter estimation for each curvelet subband. The second implementation is a genuine method that utilizes the use of curvelet subband histograms, namely, histogram of curvelets (HoC). Using the proposed curvelet-based feature extraction method (HoC) on SAR data, better classification accuracies up to 99.56% are achieved compared to original data and H/A/α decomposition features. Compared to speckle-noise-reduced data classification results, it can be said that curvelet-based feature extraction is also robust against speckle noise.

On quantiles of the temporal aggregation of a stable moving average process and their applications

A stochastic volatility model is proposed for the daily log returns of a financial asset based on conditional log quantile differences, assuming the availability of high frequency intraday log returns. Calculation of the conditional log quantile differences is performed with the assumption that the intraday log returns follow a stable moving average process. The use of conditional log quantile difference in the proposed model, rather than conditional variance in standard models, offers an increase in flexibility, with the potential for a different dependency structure at different parts of the conditional distribution. The proposed model makes use of high frequency intraday log returns which are generally neglected in standard models. Formulae for the calculation of the conditional log quantile differences are provided and a method for their estimation is described The proposed model was applied to the ASX200 index from 2009 and 2010. References R. J. Adler, R. E. Feldman, and C. Gallagher. Analysing stable time series. In R. J. Adler, R. E. Feldman, and M. S. Taqqu, editors, A Practical Guide to Heavy Tails: Statistical Techniques and Applications . Birkhauser, 1998. A. W. Barker. Estimation of stable distribution parameters from a dependent sample. Technical report, 2014. http://arxiv.org/abs/1405.0374 A. W. Barker. On the log quantile difference of the temporal aggregation of a stable moving average process. Technical report, 2014. http://arxiv.org/abs/1404.6875 T. Bollerslev. Generalized autoregressive conditional heteroskedasticity. J. Econometrics , 31:307–327, 1986. doi:10.1016/0304-4076(86)90063-1 R. Cont. Empirical properties of asset returns: stylized facts and statistical issues. Quant. Financ. , 1:223–236, 2001. doi:10.1080/713665670 R. A. Davis. Gauss–Newton and M-estimation for ARMA processes with infinite variance. Stoch. Proc. Appl. , 63:75–95, 1996. doi:10.1016/0304-4149(96)00063-4 R. A. Davis and S. Resnick. Limit theory for the sample covariance and correlation functions of moving averages. Ann. Stat. , 14:533–558, 1986. http://www.jstor.org/stable/2241234 Y. Dominicy, S. Hormann, H. Ogata, and D. Veredas. On sample marginal quantiles for stationary processes. Stat. Prob. Lett. , 83:28–36, 2013. doi:10.1016/j.spl.2012.07.016 J. McCulloch. Simple consistent estimators of stable distribution parameters. Commun. Stat. Simulat. , 15:1109–1136, 1986. doi:10.1080/03610918608812563 J. P. Nolan. Parameterizations and modes of stable distributions. Stat. Prob. Lett. , 38:187–195, 1998. doi:10.1016/S0167-7152(98)00010-8 S. J. Taylor. Modelling stochastic volatility: A review and comparative study. Math. Financ. , 4:183–204, 1994. doi:10.1111/j.1467-9965.1994.tb00057.x R. S. Tsay. Analysis of Financial Time Series . Wiley, 3rd edition, 2010. K. Zhu and S. Ling. The global weighted LAD estimators for finite/infinite variance ARMA(p,q) models. Economet. Theor. , 28:1065–1086, 2012. doi:10.1017/S0266466612000059

Application of quantile methods to estimation of Cauchy distribution parameters

Quantile methods are used for estimation of population parameters when other methods such as the maximum likelihood method and the method of moments cannot be applied. In the paper the percentile method, the quantile least squares method and its two modifications are considered. The proposed methods allow estimators to be obtained with smaller bias and smaller mean squared error than estimators of the quantile least squares method. The considered methods can be applied to estimation of the Cauchy distribution parameters. The results of the simulation analysis of the estimator properties have allowed conclusions to be drawn as concerning the application of the considered methods.

Modern methods for optimal spatio-temporal signal processing in active, passive, and combined active-passive radio-engineering systems

Using the concept of the search for the optimal signal parameter estimates and related to them parameters of electromagnetic and regression models of scattering and radio-thermal radiation of electromagnetic waves by various objects and natural medias on the basis of modern theory of statistical decisions and estimates of probability distribution parameters, a number of fundamental results developing the theory and methods of optimal spatio-temporal signal processing are obtained for the first time. Corresponding directions of their practical application in active, passive, and combined (complex) active-passive radar and remote-sensing radio systems are considered. Special attention is given to application of Kravchenko weight functions (windows) in problems of radio engineering systems synthesis.

Sound Pressure Distribution and Acoustic Parameters Estimation by Simulation

A study on the sound pressure distribution and related acoustic parameters estimation bymeans of the acoustics simulation software EASE is presented in this paper. By defining the sound-absorbing material, the types of sound source, the location of sound source, and the related factors, a more accurate model for the specified acoustic field distribution is obtained. It provides certain theory reference for the design of indoor electroacoustics, which saves the cost and time for the development of construction engineering.

Modeling European hot spells using extreme value analysis

Atmospheric blocking in mainland Europe is often cited as the cause of extremely high temperatures lasting several days. By definition, extreme temperatures are rare, and yet the theory of extreme value statistics has seldom been applied to quantify the influence of atmospheric blocking on hot spells. Similarly, a comparison of the relative influence of other well-known atmospheric drivers, such as the North Atlantic Oscillation (NAO) and the El Nino-Southern Oscillation (ENSO), has seldom been explored. We applied a novel combination of extreme value and geometric distributions to observed daily temperature maxima from 74 stations across Europe, covering 1951−2010, to establish a stationary model of the expected magnitude, frequency and duration of hot spells that did not explicitly account for atmospheric drivers. Monthly time series of NAO, ENSO and 4 coherent atmospheric blocking regions were then incorporated as nonstationary covariates in the distribution parameter estimates to assess the dependence of hot spells on atmospheric covariates. We concluded that ENSO does not have a significant influence on hot spell magnitude or frequency; the NAO is a significant driver of hot spell magnitude (maximum attained temperature), frequency (annual event count) and duration (length of event) in northern Europe and Atlantic bordering stations; and atmospheric blocking is a significant driver of all aspects of hot spells in all parts of Europe. While NAO may increase peak temperatures by 2−4°C only in the north, relatively strong atmospheric blocking could result in increased temperatures of at least 4°C higher across Europe, with a commensurate increase in hot spell duration of 2−4 d.

Inference for a step-stress partially accelerated life test model with an adaptive Type-II progressively hybrid censored data from Weibull distribution

In this paper, the maximum likelihood estimators of Weibull distribution parameters and the acceleration factor are discussed based on two different types of progressively hybrid censoring schemes under step-stress partially accelerated life test model. The performances of the estimators of the model parameters using the two progressively hybrid censoring schemes are evaluated and compared in terms of biases and mean squared errors through a Monte Carlo simulation study.

Combining markers with and without the limit of detection.

In this paper, we consider the combination of markers with and without the limit of detection (LOD). LOD is often encountered when measuring proteomic markers. Because of the limited detecting ability of an equipment or instrument, it is difficult to measure markers at a relatively low level. Suppose that after some monotonic transformation, the marker values approximately follow multivariate normal distributions. We propose to estimate distribution parameters while taking the LOD into account, and then combine markers using the results from the linear discriminant analysis. Our simulation results show that the ROC curve parameter estimates generated from the proposed method are much closer to the truth than simply using the linear discriminant analysis to combine markers without considering the LOD. In addition, we propose a procedure to select and combine a subset of markers when many candidate markers are available. The procedure based on the correlation among markers is different from a common understanding that a subset of the most accurate markers should be selected for the combination. The simulation studies show that the accuracy of a combined marker can be largely impacted by the correlation of marker measurements. Our methods are applied to a protein pathway dataset to combine proteomic biomarkers to distinguish cancer patients from non-cancer patients.

Percentile Estimation in Inverse Gaussian Distributions

This paper presents procedures for percentile estimation in the three-parameter inverse Gaussian (IG3) and the two-parameter inverse Gaussian (IG2) distributions. All procedures require first the estimation of distribution parameters and second the computation of the desired quantile at the estimated parameters. Parameter estimation is accomplished by maximum likelihood (ML) or a mixed moments (MXM) method. A Newton-Rahpson (NR) procedure is used for inverting the CDF. Simulation and asymptotic results are given for the resulting estimators. Two sets of real data are used to illustrate the procedures.

Reply to the Discussion by Makkonen et al. of “Plotting positions for fitting distributions and extreme value analysis”

Fuglem et al. (2013) discuss the use of plotting positions in civil engineering for fitting distributions to data for the purposes of extreme value analysis. The authors support previous work by Cunnane (1978) and others who have shown that when fitting specific probability distributions to a set of data using linear regression and appropriate probability paper, plotting position methods appropriate to each of the specific distributions being considered should be used. This is shown theoretically (following Cunnane 1978) and by clear example, using Monte-Carlo simulation. The authors would like to thank Dr. Hong and Mr. Li (Hong and Li 2013) for providing further insight regarding selection of plotting position methods and regression methods for estimating distribution parameters. Hong and Li (2013) point out that the use of ordinary least squares regression methods does not account for the variance–covariance structure of order statistics, and reference a number of studies providing more appropriate methods (namely, generalized and weighted least squares). Useful comparisons are provided for the use of different regressionmethods and plotting positions for the Gumbel distribution in terms of both variance and bias for different samples sizes and coefficients of variance. Dr. Hong should be commended for the development of an improved plotting position for Gumbel distributions that takes the number of samples into account.

Estimation of Location and Scale Parameters in Two-Parameter Exponential Distribution Based on Ranked Set Sample

In this article, we are interested in simultaneous comparison of the location and scale estimators of a two-parameter exponential distribution based on simple random sample (SRS) and ranked set sample (RSS) by using generalized variance (GV). We suggest various RSS strategies to estimate the scale parameter. Their performances in terms of GV are compared with SRS strategy. Finally, we illustrate the minimum values of set size, n, based on RSS, which would result in smaller GV than that based on SRS.

Naive possibilistic classifiers for imprecise or uncertain numerical data

In real-world problems, input data may be pervaded with uncertainty. In this paper, we investigate the behavior of naive possibilistic classifiers, as a counterpart to naive Bayesian ones, for dealing with classification tasks in the presence of uncertainty. For this purpose, we extend possibilistic classifiers, which have been recently adapted to numerical data, in order to cope with uncertainty in data representation. Here the possibility distributions that are used are supposed to encode the family of Gaussian probabilistic distributions that are compatible with the considered dataset. We consider two types of uncertainty: (i) the uncertainty associated with the class in the training set, which is modeled by a possibility distribution over class labels, and (ii) the imprecision pervading attribute values in the testing set represented under the form of intervals for continuous data. Moreover, the approach takes into account the uncertainty about the estimation of the Gaussian distribution parameters due to the limited amount of data available. We first adapt the possibilistic classification model, previously proposed for the certain case, in order to accommodate the uncertainty about class labels. Then, we propose an algorithm based on the extension principle to deal with imprecise attribute values. The experiments reported show the interest of possibilistic classifiers for handling uncertainty in data. In particular, the probability-to-possibility transform-based classifier shows a robust behavior when dealing with imperfect data.

Comparison of different approaches to fit log-normal mixtures on radar-derived precipitation data

Mixture models of precipitation frequency distributions describe the precipitation spectrum more adequately than simple probability distributions. The estimation of mixture distribution parameters by the maximum likelihood approach is commonly known. The reliability of these models and their parameters derived by the maximum likelihood method and by temporal classifications over Saxony was investigated using a radar-based precipitation product on a daily basis. Therefore, two different ‘unsupervised’ classification approaches were applied, a cluster analysis and a neural network, to derive subpopulation estimates. The temporal classification summarized high-resolution spatial grids of daily precipitation fields into 10 precipitation classes. The mixture model evaluation consists of two parts. First, an information criterion was calculated to describe the model complexity and the significance of the number of parameters. Second, the qualities of the fitted models were compared with the database through ordinary Kolmogorov–Smirnov tests and Kolmogorov–Smirnov tests in the context of field significance. Under the assumption of log-normal distributed precipitation, the neural network delivered the best mixture models for a spatial resolution of 2 and 3 km while the cluster analysis delivered the better initial parameters for an expectation-maximization algorithm on mixture distributions over the considered domain.

비정상성 GEV 모형을 이용한 행정구역별 미래 확률강우량 산정

국내에서는 설계강우량을 산정하기 위해서 정상성 강우빈도해석법이 일반적으로 적용되고 있다. 그러나, 기후변화 또는 기후 변동으로 인한 극치사상의 증가 등으로 최근의 강우패턴은 과거와는 다른 양상을 보여주고 있으며, 이러한 경향은 수문학적 설계를 위한 확률강우량 산정에 고려될 필요가 있다. 본 연구에서는 행정구역별 비정상성 강우빈도해석을 수행하였다. 이를 위하여 1973년부터 2012년까지 관측된 지점강우량을 이용하여 행정구역별 연최대강우량 자료를 구축하였다. 25년 이동평균방법으로 관측자료의 통계량과 GEV 분포함수의 모수 사이의 상관성을 검토한 후, 미래 특정 시점에 대한 분포함수의 모수를 추정할 수 있는 비선형 회귀식을 유도하였다. 본 연구에서 제시한 방법은 관측된 연최대강우량에 대하여 검증을 하였으며, 강우패턴의 변화를 정상성 강우빈도해석법에 비해 보다 적절히 반영하는 것으로 나타났다. 따라서, 본 연구에서 제시하는 행정구역별 비정상성 강우빈도해석법은 가까운 미래의 확률강우량 산정과 최근에 도입된 행정구역별 방재성능 목표강우량 산정에 유용할 것으로 판단된다. In South Korea, stationary frequency analysis methods are generally used for estimating design rainfalls in practice. However, due to climate change and/or variability, recent rainfall observations have significantly different patterns from the past so that the recent trends need to be considered to estimate extreme rainfall quantiles for hydrologic design. This study focused on estimating extreme rainfall quantiles in administrative districts across South Korea, after building nonstationary GEV model using annual maximum rainfall (AMR) datasets for 228 administrative districts from point rainfall measures from 1973 to 2012. A moving average method with 25-year window was used for investigating time-dependent statistics of AMR, such as mean, variance and skewness, and parameters of GEV distribution. From the analyses of relationships between statistics and distribution parameters, this study derived nonlinear regression equations for distribution parameters, which provide the estimates of distribution parameters at any future time. The overall results achieved in this study illustrate that the nonlinear regression equations can be easily incorporated into the hydrologic frequency analysis and provide appropriate estimates of design rainfalls in the near future.