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In this paper, we approached the concept of real estate bubble, analyzing the risk its bursting could generate for the Chilean financial market. Specifically, we analyzed the relationship between real housing prices, the economic activity index, and mortgage interest rates denominated in inflation-linked units from 1994 to 2020. The analysis was based on a second order Markov switching model with the predetermined variables mentioned later, whose parameters were obtained through the expectation-maximization algorithm. Then, we built a probability index as early warning indicator for potential imbalances in the real estate price that could put financial market stability at risk. The indicator is important to evaluate economic policy calibrations in time. A main finding was that the real housing price had a non-linear relationship with economic activity and the mortgage interest rate. Therefore, the evolution of the real estate price has been consistent with fundamental macroeconomic variables, even under a high growth regime, with increases above 12% per year. About 92% of housing price variability derived from changing macrofinancial conditions, suggesting a low margin of speculative behavior.

The 'expectation—conditional maximization either' (ECME) algorithm has proven to be an effective way of accelerating the expectation—maximization algorithm for many problems. Recognizing the limitation of using prefixed acceleration subspaces in the ECME algorithm, we propose a dynamic ECME (DECME) algorithm which allows the acceleration subspaces to be chosen dynamically. The simplest DECME implementation is what we call DECME-1, which uses the line that is determined by the two most recent estimates as the acceleration subspace. The investigation of DECME-1 leads to an efficient, simple, stable and widely applicable DECME implementation, which uses two-dimensional acceleration subspaces and is referred to as DECME-2. The fast convergence of DECME-2 is established by the theoretical result that, in a small neighbourhood of the maximum likelihood estimate, it is equivalent to a conjugate direction method. The remarkable accelerating effect of DECME-2 and its variant is also demonstrated with several numerical examples.

Summary During the service life of bridges, the bridge management systems (BMSs) seek to handle all performed assessment activities by controlling regular inspections, evaluations, and maintenance of these structures. However, the BMSs still rely heavily on qualitative and visual bridge inspections, which compromise the structural evaluation and, consequently, the maintenance decisions as well as the avoidance of bridge collapses. The structural health monitoring appears as a natural field to aid the bridge management, providing more reliable and quantitative information. Herein, the machine learning algorithms have been used to unveil structural anomalies from monitoring data. In particular, the Gaussian mixture models (GMMs), supported by the expectation‐maximization (EM) on the parameter estimation, have been proposed to model the main clusters that correspond to the normal and stable state conditions of a bridge, even when it is affected by unknown sources of operational and environmental variations. Unfortunately, the performance of the EM algorithm is strongly dependent on the choice of the initial parameters. This paper proposes a hybrid approach based on a standard genetic algorithm (GA) to improve the stability of the EM algorithm on the searching of the optimal number of clusters and their parameters, strengthening the damage classification performance. The superiority of the GA‐EM‐GMM approach, over the classic EM‐GMM one, is tested on a damage detection strategy implemented through the Mahalanobis‐squared distance, which permits one to track the outlier formation in relation to the chosen main group of states, using real‐world data sets from the Z‐24 Bridge, in Switzerland. Copyright © 2016 John Wiley & Sons, Ltd.

Mixed latent Markov (MLM) models represent an important tool of analysis of longitudinal data when response variables are affected by time‐fixed and time‐varying unobserved heterogeneity, in which the latter is accounted for by a hidden Markov chain. In order to avoid bias when using a model of this type in the presence of informative drop‐out, we propose an event‐history (EH) extension of the latent Markov approach that may be used with multivariate longitudinal data, in which one or more outcomes of a different nature are observed at each time occasion. The EH component of the resulting model is referred to the interval‐censored drop‐out, and bias in MLM modeling is avoided by correlated random effects, included in the different model components, which follow common latent distributions. In order to perform maximum likelihood estimation of the proposed model by the expectation–maximization algorithm, we extend the usual forward‐backward recursions of Baum and Welch. The algorithm has the same complexity as the one adopted in cases of non‐informative drop‐out. We illustrate the proposed approach through simulations and an application based on data coming from a medical study about primary biliary cirrhosis in which there are two outcomes of interest, one continuous and the other binary.

We discuss how to fit mixtures of Erlangs to censored and truncated data by iteratively using the EM algorithm. Mixtures of Erlangs form a very versatile, yet analytically tractable, class of distributions making them suitable for loss modeling purposes. The effectiveness of the proposed algorithm is demonstrated on simulated data as well as real data sets.

The article studies non-Gaussian extensions of a recently discovered link between certain Gaussian random fields, expressed as solutions to stochastic partial differential equations (SPDEs), and Gaussian Markov random fields. The focus is on non-Gaussian random fields with Matérn covariance functions, and in particular, we show how the SPDE formulation of a Laplace moving-average model can be used to obtain an efficient simulation method as well as an accurate parameter estimation technique for the model. This should be seen as a demonstration of how these techniques can be used, and generalizations to more general SPDEs are readily available.

One goal of human microbiome studies is to relate host traits with human microbiome compositions. The analysis of microbial community sequencing data presents great statistical challenges, especially when the samples have different library sizes and the data are overdispersed with many zeros. To address these challenges, we introduce a new statistical framework, called predictive analysis in metagenomics via inverse regression (PAMIR), to analyze microbiome sequencing data. Within this framework, an inverse regression model is developed for overdispersed microbiota counts given the trait, and then a prediction rule is constructed by taking advantage of the dimension-reduction structure in the model. An efficient Monte Carlo expectation-maximization algorithm is proposed for maximum likelihood estimation. The method is further generalized to accommodate other types of covariates. We demonstrate the advantages of PAMIR through simulations and two real data examples.

Traditional voxel-level multiple testing procedures in neuroimaging, mostly p-value based, often ignore the spatial correlations among neighboring voxels and thus suffer from substantial loss of power. We extend the local-significance-index based procedure originally developed for the hidden Markov chain models, which aims to minimize the false nondiscovery rate subject to a constraint on the false discovery rate, to three-dimensional neuroimaging data using a hidden Markov random field model. A generalized expectation–maximization algorithm for maximizing the penalized likelihood is proposed for estimating the model parameters. Extensive simulations show that the proposed approach is more powerful than conventional false discovery rate procedures. We apply the method to the comparison between mild cognitive impairment, a disease status with increased risk of developing Alzheimer's or another dementia, and normal controls in the FDG-PET imaging study of the Alzheimer's Disease Neuroimaging Initiative.

Varying-coefficient models have become a common tool to determine whether and how the association between an exposure and an outcome changes over a continuous measure. These models are complicated when the exposure itself is time-varying and subjected to measurement error. For example, it is well known that longitudinal physical fitness has an impact on cardiovascular disease (CVD) mortality. It is not known, however, how the effect of longitudinal physical fitness on CVD mortality varies with age. In this paper, we propose a varying-coefficient generalized odds rate model that allows flexible estimation of age-modified effects of longitudinal physical fitness on CVD mortality. In our model, the longitudinal physical fitness is measured with error and modeled using a mixed-effects model, and its associated age-varying coefficient function is represented by cubic B-splines. An expectation-maximization algorithm is developed to estimate the parameters in the joint models of longitudinal physical fitness and CVD mortality. A modified pseudoadaptive Gaussian-Hermite quadrature method is adopted to compute the integrals with respect to random effects involved in the E-step. The performance of the proposed method is evaluated through extensive simulation studies and is further illustrated with an application to cohort data from the Aerobic Center Longitudinal Study.

In this research, the statistical inference of unknown lifetime parameters is proposed in the presence of independent competing risks using a progressive Type-II censored dataset. The lifetime distribution associated with a failure mode is assumed to follow the new Pareto distribution, with consideration given to two distinct competing failure reasons. Maximum likelihood estimators (MLEs) for the unknown model parameters, as well as reliability and hazard functions, are derived, noting that they are not expressible in closed form. The Newton–Raphson, expectation maximization (EM), and stochastic expectation maximization (SEM) methods are employed to generate maximum likelihood (ML) estimations. Approximate confidence intervals for the unknown parameters, reliability, and hazard rate functions are constructed using the normal approximation of the MLEs and the normal approximation of the log-transformed MLEs. Additionally, the missing information principle is utilized to derive the closed form of the Fisher information matrix, which, in turn, is used with the delta approach to calculate confidence intervals for reliability and hazards. Bayes estimators are derived under both symmetric and asymmetric loss functions, with informative and non-informative priors considered, including independent gamma distributions for informative priors. The Monte Carlo Markov Chain sampling approach is employed to obtain the highest posterior density credible intervals and Bayesian point estimates for unknown parameters and reliability characteristics. A Monte Carlo simulation is conducted to assess the effectiveness of the proposed techniques, with the performances of the Bayes and maximum likelihood estimations examined using average values and mean squared errors as benchmarks. Interval estimations are compared in terms of average lengths and coverage probabilities. Real datasets are considered and examined for each topic to provide illustrative examples.