Estimation of reliability with cumulative stress and strength degradation

In many real-life scenarios, system reliability depends on dynamic stress–strength interference where strength degrades and stress accumulates concurrently over time. In this paper, we consider the problem of estimating reliability of a system under deterministic strength degradation and cumulative damage due to shocks arriving according to a point process. Maximum likelihood estimation under two different sampling plans has been considered. Large sample properties in general are discussed. The method is illustrated through simulation and real-life data analysis.     

On prediction of population and subpopulation characteristics for future periods

The estimation or prediction of population characteristics based on the sample information is the key issue in survey sampling. If the sample sizes in subpopulations (domains) are large enough, similar methods as used for the whole population can be used to estimate or to predict subpopulations characteristics as well. To estimate or to predict characteristics of domains with small or even zero sample sizes, small area estimation methods “borrowing strength” from other subpopulations or time periods are widely used. We extend this problem and study methods of prediction of future population and subpopulations’ characteristics based on the longitudinal data.     

Modelling conditional variance function in industrial data: A case study

We study the suitability of different modelling methods for joint prediction of mean and variance based on large data sets. We review the approaches to the modelling of conditional variance function that are capable of handling a problem where conditional variance depends on about 10 explanatory variables and training dataset consists of 100 000 observations. We present a promising approach for neural network modelling of mean and dispersion. We compare different approaches in predicting the mechanical properties of steel in two case data sets collected from the production line of a steel plate mill. As a conclusion we give some recommendations concerning the modelling of conditional variance in large datasets.     

Estimating the Prediction Mean Squared Error in Gaussian Stochastic Processes with Exponential Correlation Structure

Given one or more realizations from the finite dimensional marginal distribution of a stochastic process, we consider the problem of estimating the squared prediction error when predicting the process at unobserved locations. An approximation taking into account the additional variability due to estimating parameters involved in the correlation structure was developed by Kackar & Harville (1984) and was revisited by Harville & Jeske (1992) as well as Zimmerman & Cressie (1992). The present paper discusses an extension of these methods. The approaches will be compared via an extensive simulation study for models with and without random error term. Effects due to the designs used for prediction and for model fitting as well as due to the strength of the correlation between neighbouring observations of the stochastic process are investigated. The results show that considering the additional variability in the predictor due to estimating the covariance structure is of great importance and should not be neglected in practical applications.     

A non-homogeneous hidden Markov model for predicting the distribution of sea surface elevation

The prediction problem of sea state based on the field measurements of wave and meteorological factors is a topic of interest from the standpoints of navigation safety and fisheries. Various statistical methods have been considered for the prediction of the distribution of sea surface elevation. However, prediction of sea state in the transitional situation when waves are developing by blowing wind has been a difficult problem until now, because the statistical expression of the dynamic mechanism during this situation is very complicated. In this article, we consider this problem through the development of a statistical model. More precisely, we develop a model for the prediction of the time-varying distribution of sea surface elevation, taking into account a non-homogeneous hidden Markov model in which the time-varying structures are influenced by wind speed and wind direction. Our prediction experiments suggest the possibility that the proposed model contributes to an improvement of the prediction accuracy by using a homogenous hidden Markov model. Furthermore, we found that the prediction accuracy is influenced by the circular distribution of the circular hidden Markov model for the directional time series wind direction data.     

A series of two-urn biased sampling problems

Much of the literature on matching problems in statistics has focused on single items chosen from independent, but fully overlapping sets. This paper considers a more general problem of sampling without replacement from partially overlapping sets and presents new theory on probability problems involving two urns and the selection of balls from these urns according to a biased without-replacement sampling scheme. The strength of the sampling bias is first considered as known, and then as unknown, with a discussion of how that strength may be assessed using observed data. Each scenario is illustrated with a numerical example, and the theory is applied to a gender bias problem in committee selection, and to a problem where competing retailers select products to place on promotion.     

Empirical best linear unbiased and empirical Bayes prediction in multivariate small area estimation

Small area estimation plays a prominent role in survey sampling due to a growing demand for reliable small area estimates from both public and private sectors. Popularity of model-based inference is increasing in survey sampling, particularly, in small area estimation. The estimates of the small area parameters can profitably ‘borrow strength’ from data on related multiple characteristics and/or auxiliary variables from other neighboring areas through appropriate models. Fay (1987, Small Area Statistics, Wiley, New York, pp. 91–102) proposed multivariate regression for small area estimation of multiple characteristics. The success of this modeling rests essentially on the strength of correlation of these dependent variables. To estimate small area mean vectors of multiple characteristics, multivariate modeling has been proposed in the literature via a multivariate variance components model. We use this approach to empirical best linear unbiased and empirical Bayes prediction of small area mean vectors. We use data from Battese et al. (1988, J. Amer. Statist. Assoc. 83, 28 –36) to conduct a simulation which shows that the multivariate approach may achieve substantial improvement over the usual univariate approach.     

A novel auto-regressive fractionally integrated moving average–least-squares support vector machine model for electricity spot prices prediction

In the framework of competitive electricity market, prices forecasting has become a real challenge for all market participants. However, forecasting is a rather complex task since electricity prices involve many features comparably with those in financial markets. Electricity markets are more unpredictable than other commodities referred to as extreme volatile. Therefore, the choice of the forecasting model has become even more important. In this paper, a new hybrid model is proposed. This model exploits the feature and strength of the auto-regressive fractionally integrated moving average model as well as least-squares support vector machine model. The expected prediction combination takes advantage of each model's strength or unique capability. The proposed model is examined by using data from the Nordpool electricity market. Empirical results showed that the proposed method has the best prediction accuracy compared to other methods.     

Stress–strength reliability of a non-identical-component-strengths system based on upper record values from the family of Kumaraswamy generalized distributions

In an attempt to produce more realistic stress–strength models, this article considers the estimation of stress–strength reliability in a multi-component system with non-identical component strengths based on upper record values from the family of Kumaraswamy generalized distributions. The maximum likelihood estimator of the reliability, its asymptotic distribution and asymptotic confidence intervals are constructed. Bayes estimates under symmetric squared error loss function using conjugate prior distributions are computed and corresponding highest probability density credible intervals are also constructed. In Bayesian estimation, Lindley approximation and the Markov Chain Monte Carlo method are employed due to lack of explicit forms. For the first time using records, the uniformly minimum variance unbiased estimator and the closed form of Bayes estimator using conjugate and non-informative priors are derived for a common and known shape parameter of the stress and strength variates distributions. Comparisons of the performance of the estimators are carried out using Monte Carlo simulations, the mean squared error, bias and coverage probabilities. Finally, a demonstration is presented on how the proposed model may be utilized in materials science and engineering with the analysis of high-strength steel fatigue life data.     

Prediction bands for the EDF of a future sample

We develop both nonparametric and parametric methods for obtaining prediction bands for the empirical distribution function (EDF) of a future sample. These methods yield simultaneous prediction intervals for all order statistics of the future sample, and they also correspond to tests for the two-sample problem. The nonparametric prediction bands correspond to the two-sample Kolmogorov-Smirnov test and related nonparametric tests, but the parametric prediction bands correspond to entirely new parametric two-sample tests. The parametric prediction bands tend to outperform the nonparametric bands when the parametric assumptions hold, but they may have true coverage probabilities well below their nominal levels when the parametric assumptions fail. A new computational algorithm is used to obtain critical values in the nonparametric case.     

Asymptotically Optimal Nonparametric Empirical Bayes Via Predictive Recursion

An empirical Bayes problem has an unknown prior to be estimated from data. The predictive recursion (PR) algorithm provides fast nonparametric estimation of mixing distributions and is ideally suited for empirical Bayes applications. This article presents a general notion of empirical Bayes asymptotic optimality, and it is shown that PR-based procedures satisfy this property under certain conditions. As an application, the problem of in-season prediction of baseball batting averages is considered. There the PR-based empirical Bayes rule performs well in terms of prediction error and ability to capture the distribution of the latent features.     

Predicting Insurance Losses Under Cross-Classification: A Comparison of Alternative Approaches

Various mathematical and statistical models for estimation of automobile insurance pricing are reviewed. The methods are compared on their predictive ability based on two sets of automobile insurance data for two different states collected over two different periods. The issue of model complexity versus data availability is resolved through a comparison of the accuracy of prediction. The models reviewed range from the use of simple cell means to various multiplicative-additive schemes to the empirical-Bayes approach. The empirical-Bayes approach, with prediction based on both model-based and individual cell estimates, seems to yield the best forecast.     

Statistical Modelling and Deconvolution of Yield Meter Data

Abstract.  This paper considers the problem of mapping spatial variation of yield in a field using data from a yield monitoring system on a combine harvester. The unobserved yield is assumed to be a Gaussian random field and the yield monitoring system data is modelled as a convolution of the yield and an impulse response function. This results in an unusual spatial covariance structure (depending on the driving pattern of the combine harvester) for the yield monitoring system data. Parameters of the impulse response function and the spatial covariance function of the yield are estimated using maximum likelihood methods. The fitted model is assessed using certain empirical directional covariograms and the yield is finally predicted using the inferred statistical model.     

Automatic odor prediction for electronic nose

An electronic nose (e-nose), or artificial olfaction, is a device that analyzes the air to quantify odor concentration using an array of gas sensors. This equipment is a monitoring tool for industrial firms. There is a shortage of an algorithm to address odor prediction challenges in an automatic fashion. These challenges include unreliable data transfer due to sensor malfunction or missing data due to anomalies in mobile data connection. Providing such an algorithm avoids human intervention in data handling, and elevates electronic nose towards smart nose. We address these challenges by proposing a data validation and data imputation method combined with a robust odor prediction machinery. Our proposed algorithm is successfully implemented on the e-nose equipment and is serving the industry currently.     

Bayesian prediction based on type-I censored data from a mixture of Burr type XII distribution and its reciprocal

This paper is concerned with the problem of obtaining Bayesian prediction bounds of future observables from a finite mixture of Burr type XII distribution with its reciprocal based on type-I censored data. We consider the one-sample and two-sample prediction schemes using the Markov chain Monte Carlo algorithm. Numerical examples are given to illustrate the procedures and the accuracy of prediction intervals is investigated via extensive Monte Carlo simulation.     

Bayesian variable selection and estimation in maximum entropy quantile regression

Quantile regression has gained increasing popularity as it provides richer information than the regular mean regression, and variable selection plays an important role in the quantile regression model building process, as it improves the prediction accuracy by choosing an appropriate subset of regression predictors. Unlike the traditional quantile regression, we consider the quantile as an unknown parameter and estimate it jointly with other regression coefficients. In particular, we adopt the Bayesian adaptive Lasso for the maximum entropy quantile regression. A flat prior is chosen for the quantile parameter due to the lack of information on it. The proposed method not only addresses the problem about which quantile would be the most probable one among all the candidates, but also reflects the inner relationship of the data through the estimated quantile. We develop an efficient Gibbs sampler algorithm and show that the performance of our proposed method is superior than the Bayesian adaptive Lasso and Bayesian Lasso through simulation studies and a real data analysis.     

BUSDM – an algorithm for the bottom-up search of departures from a model

Searching for regions of the input space where a statistical model is inappropriate is useful in many applications. The study proposes an algorithm for finding local departures from a regression-type prediction model. The algorithm returns low-dimensional hypercubes where the average prediction error clearly departs from zero. The study describes the developed algorithm, and shows successful applications on the simulated and real data from the steel plate production. The algorithms that have been originally developed for searching regions of the high-response value from the input space are reviewed and considered as alternative methods for locating model departures. The proposed algorithm succeeds in locating the model departure regions better than the compared alternatives. The algorithm can be utilized in sequential follow-up of a model as time goes along and new data are observed.     

Bayesian inference and prediction of the Rayleigh distribution based on ordered ranked set sampling

Based on ordered ranked set sample, Bayesian estimation of the model parameter as well as prediction of the unobserved data from Rayleigh distribution are studied. The Bayes estimates of the parameter involved are obtained using both squared error and asymmetric loss functions. The Bayesian prediction approach is considered for predicting the unobserved lifetimes based on a two-sample prediction problem. A real life dataset and simulation study are used to illustrate our procedures.     

Improving prediction performance of stellar parameters using functional models

This paper investigates the problem of prediction of stellar parameters, based on the star's electromagnetic spectrum. The knowledge of these parameters permits to infer on the evolutionary state of the star. From a statistical point of view, the spectra of different stars can be represented as functional data. Therefore, a two-step procedure decomposing the spectra in a functional basis combined with a regression method of prediction is proposed. We also use a bootstrap methodology to build prediction intervals for the stellar parameters. A practical application is also provided to illustrate the numerical performance of our approach.     

Atypical observations in linear models

The problem of ‘atypical data point’ in the estimation of model parameters and its effect on prediction are discussed. A cross-validity procedure is then proposed to accommodate the unusual observations in the estimation and thereby to improve the prediction of future data points. Each atypical point, weighted according to cross-validitory procedure, is used in the estimation of model parameters.