Spatial–temporal interpolation of non methane hydrocarbon levels in Kuwait

This article handles the prediction of hourly concentrations ofnon methane hydrocarbon (NMHC) pollutants at 15 unmonitored sites in Kuwait using the data recorded from 6 monitored stations at successive time points. The trend model depends on hourly meteorological variables and seasonal effects. The stochasticcomponent of the trend model which has spatiotemporal features is modeled as autoregressive temporal process. A spatial predictive distribution for residuals of the AR model is developed for the unmonitored sites. By transforming the predicted residuals back to the original data scales, we impute Kuwait’s hourly NMHC field.     

Hidden Markov model for discrete circular–linear wind data time series

ABSTRACT

In this work, we deal with a bivariate time series of wind speed and direction. Our observed data have peculiar features, such as informative missing values, non-reliable measures under a specific condition and interval-censored data, that we take into account in the model specification. We analyse the time series with a non-parametric Bayesian hidden Markov model, introducing a new emission distribution, suitable to model our data, based on the invariant wrapped Poisson, the Poisson and the hurdle density. The model is estimated on simulated datasets and on the real data example that motivated this work.     

Spatial–temporal variation of casuarina spread in Cauvery delta and north eastern zone of Tamil Nadu,India: a spatial autoregressive model

The low forest cover and productivity are the major obstacles for mitigating the demand supply gap of raw material for forest-based industries, which could be fulfilled from a tree outside forest area. Casuarina is a multi-utile, short rotation tree which adapts to all ecosystems. The casuarina wood is predominantly demanded for fuel, construction and paper industries which is mostly preferred by farmers, traders and industries. This study explores the spatial and temporal variability of casuarina spread in mitigating the gap of demand and supply in Tamil Nadu using a spatial autoregressive model. The spread of casuarina was spatially and temporally significant, which was negatively influenced by the gross area irrigated as main and direct effects and positively in an indirect effect. An assured irrigation forces the farmers to choose traditional agricultural crops for their livelihood in their own district. The increase in the price of casuarina would increase the spread of casuarina in both own district and neighbouring districts. The spread of casuarina would augment the supply of raw material for forest-based industries.     

Testing for random effect in the Fuller–Battese model

We consider the Fuller–Battese model where random effects are allowed to be from non-normal universes. The asymptotic distribution of the F-statistic in this model is derived as the number of groups tends to infinity (is large) and sample size from any group is either fixed or large. The result is used to establish an approximate test for the significance of the random effect variance component. Robustness of the established approximate test is given.     

Test for homogeneity in Hardy–Weinberg normal mixture model

The phenotype of a quantitative trait locus (QTL) is often modeled by a finite mixture of normal distributions. If the QTL effect depends on the number of copies of a specific allele one carries, then the mixture model has three components. In this case, the mixing proportions have a binomial structure according to the Hardy–Weinberg equilibrium. In the search for QTL, a significance test of homogeneity against the Hardy–Weinberg normal mixture model alternative is an important first step. The LOD score method, a likelihood ratio test used in genetics, is a favored choice. However, there is not yet a general theory for the limiting distribution of the likelihood ratio statistic in the presence of unknown variance. This paper derives the limiting distribution of the likelihood ratio statistic, which can be described by the supremum of a quadratic form of a Gaussian process. Further, the result implies that the distribution of the modified likelihood ratio statistic is well approximated by a chi-squared distribution. Simulation results show that the approximation has satisfactory precision for the cases considered. We also give a real-data example.     

Reliability estimation in multicomponent stress–strength model for Topp-Leone distribution

In this paper, we consider the estimation reliability in multicomponent stress-strength (MSS) model when both the stress and strengths are drawn from Topp-Leone (TL) distribution. The maximum likelihood (ML) and Bayesian methods are used in the estimation procedure. Bayesian estimates are obtained by using Lindley’s approximation and Gibbs sampling methods, since they cannot be obtained in explicit form in the context of TL. The asymptotic confidence intervals are constructed based on the ML estimators. The Bayesian credible intervals are also constructed using Gibbs sampling. The reliability estimates are compared via an extensive Monte-Carlo simulation study. Finally, a real data set is analysed for illustrative purposes.     

Tests for the variance parameter in the Fay–Herriot model

The Fay–Herriot model is a linear mixed model that plays a relevant role in small area estimation (SAE). Under the SAE set-up, tools for selecting an adequate model are required. Applied statisticians are often interested on deciding if it is worthwhile to use a mixed effect model instead of a simpler fixed-effect model. This problem is not standard because under the null hypothesis the random effect variance is on the boundary of the parameter space. The likelihood ratio test and the residual likelihood ratio test are proposed and their finite sample distributions are derived. Finally, we analyse their behaviour under simulated scenarios and we also apply them to real data.     

Testing lack of symmetry in spatial–temporal processes

Symmetry and separability of a covariance function are common assumptions to simplify the modeling effort of spatial–temporal processes. However, many studies in environmental sciences show that real data have complex spatial–temporal dependency structures resulting from lack of symmetry or violation of other standard assumptions of the covariance function. In this study, we propose new formal tests for lack of symmetry by using spectral representations of the spatial–temporal covariance functions of regularly spaced spatial–temporal data. The advantage of the proposed tests is that classical analysis of variance (ANOVA) models can be used for detecting lack of symmetry inherent in spatial–temporal processes. We evaluate the performance of the tests with simulation studies and we apply them to air pollution data.     

Additive–multiplicative rates model for recurrent events

Recurrent events are frequently encountered in biomedical studies. Evaluating the covariates effects on the marginal recurrent event rate is of practical interest. There are mainly two types of rate models for the recurrent event data: the multiplicative rates model and the additive rates model. We consider a more flexible additive–multiplicative rates model for analysis of recurrent event data, wherein some covariate effects are additive while others are multiplicative. We formulate estimating equations for estimating the regression parameters. The estimators for these regression parameters are shown to be consistent and asymptotically normally distributed under appropriate regularity conditions. Moreover, the estimator of the baseline mean function is proposed and its large sample properties are investigated. We also conduct simulation studies to evaluate the finite sample behavior of the proposed estimators. A medical study of patients with cystic fibrosis suffered from recurrent pulmonary exacerbations is provided for illustration of the proposed method.     

Adaptive robust estimation in joint mean–covariance regression model for bivariate longitudinal data

The estimation of the covariance matrix is important in the analysis of bivariate longitudinal data. A good estimator for the covariance matrix can improve the efficiency of the estimators of the mean regression coefficients. Furthermore, the covariance estimation itself is also of interest, but it is a challenging job to model the covariance matrix of bivariate longitudinal data due to the complex structure and positive definite constraint. In addition, most of existing approaches are based on the maximum likelihood, which is very sensitive to outliers or heavy-tail error distributions. In this article, an adaptive robust estimation method is proposed for bivariate longitudinal data. Unlike the existing likelihood-based methods, the proposed method can adapt to different error distributions. Specifically, at first, we utilize the modified Cholesky block decomposition to parameterize the covariance matrices. Secondly, we apply the bounded Huber's score function to develop a set of robust generalized estimating equations to estimate the parameters both in the mean and the covariance models simultaneously. A data-driven approach is presented to select the parameter c in the Huber's score function, which can ensure that the proposed method is robust and efficient. A simulation study and a real data analysis are conducted to illustrate the robustness and efficiency of the proposed approach.     

Group heterogeneity in the Jolly–Seber-Tag-Loss model

Mark–recapture experiments involve capturing individuals from populations of interest, marking and releasing them at an initial sample time, and recapturing individuals from the same populations on subsequent occasions. The Jolly–Seber model is widely used in open-population models since it can estimate important parameters such as population size, recruitment, and survival. However, one of the Jolly–Seber model assumptions that can be easily violated is that of no tag loss. Cowen and Schwarz [L. Cowen, C.J. Schwarz, The Jolly–Seber model with tag loss, Biometrics 62 (2006) 677–705] developed the Jolly–Seber-Tag-Loss (JSTL) model to avoid this violation; this model was extended to deal with group heterogeneity by Gonzalez and Cowen [S. Gonzalez, L. Cowen, The Jolly–Seber-tag-loss model with group heterogeneity, The Arbutus Review 1 (2010) 30–42]. In this paper, we studied the group heterogeneous JSTL (GJSTL) model through simulations and found that as sample size and fraction of double tagged individuals increased, bias of parameter estimates is reduced and precision increased. We applied this model to a study of rock lobsters Jasus edwardsii in Tasmania, Australia.     

Generalized Poisson–Lindley linear model for count data

The purpose of this paper is to develop a new linear regression model for count data, namely generalized-Poisson Lindley (GPL) linear model. The GPL linear model is performed by applying generalized linear model to GPL distribution. The model parameters are estimated by the maximum likelihood estimation. We utilize the GPL linear model to fit two real data sets and compare it with the Poisson, negative binomial (NB) and Poisson-weighted exponential (P-WE) models for count data. It is found that the GPL linear model can fit over-dispersed count data, and it shows the highest log-likelihood, the smallest AIC and BIC values. As a consequence, the linear regression model from the GPL distribution is a valuable alternative model to the Poisson, NB, and P-WE models.     

Joint mean–covariance model in generalized partially linear varying coefficient models for longitudinal data

In longitudinal data analysis, efficient estimation of regression coefficients requires a correct specification of certain covariance structure, and efficient estimation of covariance matrix requires a correct specification of mean regression model. In this article, we propose a general semiparametric model for the mean and the covariance simultaneously using the modified Cholesky decomposition. A regression spline-based approach within the framework of generalized estimating equations is proposed to estimate the parameters in the mean and the covariance. Under regularity conditions, asymptotic properties of the resulting estimators are established. Extensive simulation is conducted to investigate the performance of the proposed estimator and in the end a real data set is analysed using the proposed approach.     

Remedying the Neyman–Scott phenomenon in model discrimination

The objective of this paper is to investigate through simulation the possible presence of the incidental parameters problem when performing frequentist model discrimination with stratified data. In this context, model discrimination amounts to considering a structural parameter taking values in a finite space, with k points, k≥2. This setting seems to have not yet been considered in the literature about the Neyman–Scott phenomenon. Here we provide Monte Carlo evidence of the severity of the incidental parameters problem also in the model discrimination setting and propose a remedy for a special class of models. In particular, we focus on models that are scale families in each stratum. We consider traditional model selection procedures, such as the Akaike and Takeuchi information criteria, together with the best frequentist selection procedure based on maximization of the marginal likelihood induced by the maximal invariant, or of its Laplace approximation. Results of two Monte Carlo experiments indicate that when the sample size in each stratum is fixed and the number of strata increases, correct selection probabilities for traditional model selection criteria may approach zero, unlike what happens for model discrimination based on exact or approximate marginal likelihoods. Finally, two examples with real data sets are given.     

Bayesian inference for the Birnbaum–Saunders nonlinear regression model

We develop a Bayesian analysis for the class of Birnbaum–Saunders nonlinear regression models introduced by Lemonte and Cordeiro (Comput Stat Data Anal 53:4441–4452, 2009). This regression model, which is based on the Birnbaum–Saunders distribution (Birnbaum and Saunders in J Appl Probab 6:319–327, 1969a), has been used successfully to model fatigue failure times. We have considered a Bayesian analysis under a normal-gamma prior. Due to the complexity of the model, Markov chain Monte Carlo methods are used to develop a Bayesian procedure for the considered model. We describe tools for model determination, which include the conditional predictive ordinate, the logarithm of the pseudo-marginal likelihood and the pseudo-Bayes factor. Additionally, case deletion influence diagnostics is developed for the joint posterior distribution based on the Kullback–Leibler divergence. Two empirical applications are considered in order to illustrate the developed procedures.     

The Cox–Aalen model for left-truncated and right-censored data

We analyze left-truncated and right-censored (LTRC) data using an additive-multiplicative Cox–Aalen model proposed by Scheike and Zhang (2002), which extends the Cox regression model as well as the additive Aalen model. Based on the conditional likelihood function, we derive the weighted least-squared (WLS) estimators for the regression parameters and cumulative intensity functions of the model. The estimators are shown to be consistent and asymptotically normal. A simulation study is conducted to investigate the performance of the proposed estimators.     

Testing for the partial Koziol–Green model with covariates

In this paper we consider some non-parametric goodness-of-fit statistics for testing the partial Koziol–Green regression model. In this model, the response at a given covariate value is subject to random right censoring by two independent censoring times. One of these censoring times is informative in the sense that its survival function is some power of the survival function of the response. The goodness-of-fit statistics are based on an underlying empirical process for which large sample theory is obtained.     

Optimal design for the Bradley–Terry paired comparison model

Paired comparisons are a popular tool for questionnaires in psychological marketing research. The quality of the statistical analysis of the responses heavily depends on the design, i.e. the choice of the alternatives in the comparisons. In this paper we show that the structure of locally optimal designs changes substantially with the parameters in the underlying utility. This fact is illustrated by elementary examples, where the optimal designs can be completely characterized. As an alternative maximin efficient designs are proposed which perform well for all parameter settings. Research supported by grant Ho 1286 of the German Research Council (Deutsche Forschungsgemeinschaft).