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Recent advancements in modeling suggest that microbial inactivation in leafy greens follows a nonlinear pattern, rather than the simple first‐order kinetics. In this study, we evaluated 17 inactivation models commonly used to describe microbial decline and established the conditions that govern microbial survival on leafy greens. Through a systematic review of 65 articles, we extracted 530 datasets to model the fate of Shiga toxin‐producing Escherichia coli O157:H7 on leafy greens. Various factor analysis methods were employed to evaluate the impact of identified conditions on survival metrics. A two‐parameter model (jm2) provided the best fit to most of both natural and antimicrobial‐induced persistence datasets, whereas the one‐parameter exponential model provided the best fit to less than 20% of the datasets. The jm2 model (adjusted R2 =.89) also outperformed the exponential model (adjusted R2 =.58) in fitting the pooled microbial survival data. In the context of survival metrics, the model averaging approach generated higher values than the exponential model for >4 log reduction times (LRTs), suggesting that the exponential model may be overpredicting inactivation at later time points. The random forest technique revealed that temperature and inoculum size were common factors determining inactivation in both natural and antimicrobial‐induced die‐offs.. The findings show the limitations of relying on the first‐order survival metric of 1 LRT and considering nonlinear inactivation in produce safety decision‐making. [ABSTRACT FROM AUTHOR]

The setting of priors is an important issue in Bayesian analysis. In particular, when external information is applied, a prior with too much information can dominate the posterior inferences. To prevent this effect, the effective sample size (ESS) can be used. Various ESSs have been proposed recently; however, all have the problem of limiting the applicable prior distributions. For example, one ESS can only be used with a prior that can be approximated by a normal distribution, and another ESS cannot be applied when the parameters are multidimensional. We propose an ESS to be applied to more prior distributions when the sampling model belongs to an exponential family (including the normal model and logistic regression models). This ESS has the predictive consistency and can be used with multidimensional parameters. It is confirmed from normally distributed data with the Student's‐t priors that this ESS behaves as well as an existing predictively consistent ESS for one‐parameter exponential families. As examples of multivariate parameters, ESSs for linear and logistic regression models are also discussed. [ABSTRACT FROM AUTHOR]

Identifiability constraints are necessary for parameter estimation when fitting models with nonlinear covariate associations. The choice of constraint affects standard errors of the estimated curve. Centring constraints are often applied by default because they are thought to yield lowest standard errors out of any constraint, but this claim has not been investigated. We show that whether centring constraints are optimal depends on the response distribution and parameterization, and that for natural exponential family responses under the canonical parametrization, centring constraints are optimal only for Gaussian response. [ABSTRACT FROM AUTHOR]

Robust principal component analysis (RPCA) is a widely used method for recovering low‐rank structure from data matrices corrupted by significant and sparse outliers. These corruptions may arise from occlusions, malicious tampering, or other causes for anomalies, and the joint identification of such corruptions with low‐rank background is critical for process monitoring and diagnosis. However, existing RPCA methods and their extensions largely do not account for the underlying probabilistic distribution for the data matrices, which in many applications are known and can be highly non‐Gaussian. We thus propose a new method called RPCA for exponential family distributions (eRPCA$$ {e}^{\mathrm{RPCA}} $$), which can perform the desired decomposition into low‐rank and sparse matrices when such a distribution falls within the exponential family. We present a novel alternating direction method of multiplier optimization algorithm for efficient eRPCA$$ {e}^{\mathrm{RPCA}} $$ decomposition, under either its natural or canonical parametrization. The effectiveness of eRPCA$$ {e}^{\mathrm{RPCA}} $$ is then demonstrated in two applications: the first for steel sheet defect detection and the second for crime activity monitoring in the Atlanta metropolitan area. [ABSTRACT FROM AUTHOR]

The semi‐parametric generalized linear model (SPGLM) proposed by Rathouz and Gao assumes that the response is from a general exponential family with unspecified reference distribution and can be applied to model the distribution of binomial event‐count data with a constant cluster size. We extend SPGLM to model response distributions of binomial data with varying cluster sizes by assuming marginal compatibility. The proposed model combines a non‐parametric reference describing the within‐cluster dependence structure with a parametric density ratio characterizing the between‐group effect. It avoids making parametric assumptions about higher order dependence and is more parsimonious than non‐parametric models. We fit the SPGLM with an expectation–maximization Newton–Raphson algorithm to the boron acid mouse data set and compare estimates with existing methods. [ABSTRACT FROM AUTHOR]

Generalized linear models, introduced by Nelder and Wedderburn, allowed to model the regression of normal and nonnormal data. While doing so, the analysis of these models could not be obtained without the explicit form of the variance function. In this paper, we determine the link and variance functions of the natural exponential family generated by the class of subordinated Lévy processes. In this framework, we introduce a class of variance functions that depends on the Lambert function. In this regard, we call it the Lambert class, which covers the variance functions of the natural exponential families generated by the subordinated gamma processes and the subordinated Lévy processes by the Poisson subordinator. Notice that the gamma process subordinated by the Poisson one is excluded from this class. The concept of reciprocity in natural exponential families was given in order to obtain an exponential family from another one. In this context, we get the reciprocal class of the natural exponential family generated by the class of subordinated Lévy processes. It is well known that the variance function represents an essential element for the determination of the quasi‐likelihood and deviance functions. Then, we use the expression of our variance function in order to maintain them. This leads us to analyze the proposed generalized linear model. We illustrate some of our models with applications to the daily exchange rate returns of the Tunisian Dinar against the U.S. Dollar and the damage incidents of ships. [ABSTRACT FROM AUTHOR]

Every random variable (rv) X (or random vector) with finite moments generates a set of orthogonal polynomials, which can be used to obtain properties related to the distribution of X. This technique has been used in statistical inference, mainly connected to the exponential family of distributions. In this paper a review of some of its more relevant uses is provided. The first one deals with properties of expansions in terms of orthogonal polynomials for the Uniformly Minimum Variance Unbiased Estimator of a given parametric function, when sampling from a distribution in the Natural Exponential Family of distributions with Quadratic Variance Function. The second one compares two relevant methods, based on expansions in Laguerre polynomials, existing in the literature to approximate the distribution of linear combinations of independent chi‐square variables. [ABSTRACT FROM AUTHOR]

We propose tractable symmetric exponential families of distributions for multivariate vectors of 0's and 1's in p dimensions, or what are referred to in this paper as binary vectors, that allow for nontrivial amounts of variation around some central value μ∈{0,1}p. We note that more or less standard asymptotics provides likelihood‐based inference in the one‐sample problem. We then consider mixture models where component distributions are of this form. Bayes analysis based on Dirichlet processes and Jeffreys priors for the exponential family parameters prove tractable and informative in problems where relevant distributions for a vector of binary variables are clearly not symmetric. We also extend our proposed Bayesian mixture model analysis to datasets with missing entries. Performance is illustrated through simulation studies and application to real datasets. [ABSTRACT FROM AUTHOR]

Modelling data in applied areas particularly in reliability engineering is a prominent research topic. Statistical models play a vital role in modelling reliability data and are useful for further decision-making policies. In this paper, we study a new class of distributions with one additional shape parameter, called a new generalized exponential-X family. Some of its properties are taken into account. The maximum likelihood approach is adopted to obtain the estimates of the model parameters. For assessing the performance of these estimators, a comprehensive Monte Carlo simulation study is carried out. The usefulness of the proposed family is demonstrated by means of a real-life application representing the failure times of electronic components. The fitted results show that the new generalized exponential-X family provides a close fit to data. Finally, considering the failure times data, the Bayesian analysis and performance of Gibbs sampling are discussed. The diagnostics measures such as the Raftery–Lewis, Geweke, and Gelman–Rubin are applied to check the convergence of the algorithm. [ABSTRACT FROM AUTHOR]

We investigate a generalized semiparametric regression. Such a model can avoid the risk of wrongly choosing the base measure function. We propose a profile likelihood to efficiently estimate both parameter and nonparametric function. The main difference from the classical profile likelihood is that the profile likelihood proposed is a functional of the base measure function, instead of a function of a real variable. By making the most of the structure information of the semiparametric exponential family, we get an explicit expression of the estimator of the least favorable curve. It ensures that the new profile likelihood is computationally simple. Due to the use of the least favorable curve, the semiparametric efficiency is achieved successfully and the estimation bias is reduced significantly. Simulation studies can illustrate that our proposal is much better than the existing methodologies for most cases under study, and is robust to the different model conditions. [ABSTRACT FROM AUTHOR]

Summary: This paper studies the data filtering‐based identification algorithms for an exponential autoregressive time‐series model with moving average noise. By means of the data filtering technique and the hierarchical identification principle, the identification model is transformed into three sub‐identification (Sub‐ID) models, and a filtering‐based three‐stage extended stochastic gradient algorithm is derived for identifying these Sub‐ID models. In order to improve the parameter estimation accuracy, a filtering‐based three‐stage multi‐innovation extended stochastic gradient (F‐3S‐MIESG) algorithm is developed by using the multi‐innovation identification theory. The simulation results indicate that the proposed F‐3S‐MIESG algorithm can work well. [ABSTRACT FROM AUTHOR]

In nonignorable missing response problems, we study a semiparametric model with unspecified missingness mechanism model and a exponential family model for response conditional density. Even though existing methods are available to estimate the parameters in exponential family, estimation or testing of the missingness mechanism model nonparametrically remains to be an open problem. By defining a "synthesis" density involving the unknown missingness mechanism model and the known baseline "carrier" density in the exponential family model, we treat this "synthesis" density as a legitimate one with biased sampling version. We develop maximum pseudo likelihood estimation procedures and the resultant estimators are consistent and asymptotically normal. Since the "synthesis" cumulative distribution is a functional of the missingness mechanism model and the known carrier density, proposed method can be used to test the correctness of the missingness mechanism model nonparametrically andindirectly. Simulation studies and real example demonstrate the proposed methods perform very well. [ABSTRACT FROM AUTHOR]

In this article, we propose a mean linear regression model where the response variable is inverse gamma distributed using a new parameterization of this distribution that is indexed by mean and precision parameters. The main advantage of our new parametrization is the straightforward interpretation of the regression coefficients in terms of the expectation of the positive response variable, as usual in the context of generalized linear models. The variance function of the proposed model has a quadratic form. The inverse gamma distribution is a member of the exponential family of distributions and has some distributions commonly used for parametric models in survival analysis as special cases. We compare the proposed model to several alternatives and illustrate its advantages and usefulness. With a generalized linear model approach that takes advantage of exponential family properties, we discuss model estimation (by maximum likelihood), black further inferential quantities and diagnostic tools. A Monte Carlo experiment is conducted to evaluate the performances of these estimators in finite samples with a discussion of the obtained results. A real application using minerals data set collected by Department of Mines of the University of Atacama, Chile, is considered to demonstrate the practical potential of the proposed model. [ABSTRACT FROM AUTHOR]

We consider a quaternionic analogue of the univariate complex Hermite polynomials and study some of their analytic properties in some detail. We obtain their integral representation as well as the operational formulas of exponential and Burchnall types they obey. We show that they form an orthogonal basis of the slice Hilbert space L2(LI;e−|q|2dλI) of all quaternionic‐valued functions defined the whole quaternions space and subject to norm boundedness with respect to the Gaussian measure on a given slice as well as of the full left quaternionic Hilbert space L2(H;e−|q|2dλ) of square integrable functions on quaternions with respect to the Gaussian measure on the whole H≡R4. We also provide different types of generating functions. Remarkable identities, including quadratic recurrence formulas of Nielsen type, are also derived. [ABSTRACT FROM AUTHOR]

The horizontal distribution of the vertical gradient of atmospheric refractivity is important for the assessment of the propagation of electromagnetic waves on nearly horizontal paths. A 5-year set of meteorological data, obtained from the ERA-Interim numerical weather product, has been used to analyze this distribution statistically. Vertical gradient maps of the Central European region have been processed to derive empirical probability distributions of the difference between local point gradient values at two locations. The difference of the effective (path-averaged) gradient along the path and the local gradient is shown to be statistically distributed so that the quantiles increase linearly with distance in the interval from 100 to 1000 km. Finally, a spatial correlation function is obtained and described by an exponential model with correlation distances determined in the range of 400-700 km. [ABSTRACT FROM AUTHOR]

In the context of heteroscedastic time-varying autoregressive (AR)-process we study the estimation of the error/innovation distributions. Our study reveals that the non-parametric estimation of the AR parameter functions has a negligible asymptotic effect on the estimation of the empirical distribution of the residuals even though the AR parameter functions are estimated non-parametrically. The derivation of these results involves the study of both function-indexed sequential residual empirical processes and weighted sum processes. Exponential inequalities and weak convergence results are derived. As an application of our results we discuss testing for the constancy of the variance function, which in special cases corresponds to testing for stationarity. [ABSTRACT FROM AUTHOR]

For two-arm randomized phase II clinical trials, previous literature proposed an optimal design that minimizes the total sample sizes subject to multiple constraints on the standard errors of the estimated event rates and their difference. The original design is limited to trials with dichotomous endpoints. This paper extends the original approach to be applicable to phase II clinical trials with endpoints from the exponential dispersion family distributions. The proposed optimal design minimizes the total sample sizes needed to provide estimates of population means of both arms and their difference with pre-specified precision. Its applications on data from specific distribution families are discussed under multiple design considerations. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Let X be lognormal( μ, σ2) with density f( x); let θ > 0 and define [ABSTRACT FROM AUTHOR]

Exponential varieties arise from exponential families in statistics. These real algebraic varieties have strong positivity and convexity properties, familiar from toric varieties and their moment maps. Among them are varieties of inverses of symmetric matrices satisfying linear constraints. This class includes Gaussian graphical models. We develop a general theory of exponential varieties. These are derived from hyperbolic polynomials and their integral representations. We compare the multidegrees and ML degrees of the gradient map for hyperbolic polynomials. [ABSTRACT FROM AUTHOR]

The paper describes a generalized iterative proportional fitting procedure that can be used for maximum likelihood estimation in a special class of the general log-linear model. The models in this class, called relational, apply to multivariate discrete sample spaces that do not necessarily have a Cartesian product structure and may not contain an overall effect. When applied to the cell probabilities, the models without the overall effect are curved exponential families and the values of the sufficient statistics are reproduced by the MLE only up to a constant of proportionality. The paper shows that Iterative Proportional Fitting, Generalized Iterative Scaling, and Improved Iterative Scaling fail to work for such models. The algorithm proposed here is based on iterated Bregman projections. As a by-product, estimates of the multiplicative parameters are also obtained. An implementation of the algorithm is available as an R-package. [ABSTRACT FROM AUTHOR]

Two methods to distinguish between polynomial and exponential tails are introduced. The methods are based on the properties of the residual coefficient of variation for the exponential and non-exponential distributions. A graphical method, called a CV-plot, shows departures from exponentiality in the tails. The plot is applied to the daily log-returns of exchange rates of US dollar and Japanese yen. New statistics are introduced for testing the exponentiality of tails using multiple thresholds. They give better control of the significance level than previous tests. The powers of the new tests are compared with those of some others for various sample sizes. [ABSTRACT FROM AUTHOR]

Exponential CUSUM charts are used in monitoring the occurrence rate of rare events because the interarrival times of events for homogeneous Poisson processes are independent and identically distributed exponential random variables. In these applications, it is assumed that the exponential parameter, i.e. the mean, is known or has been accurately estimated. However, in practice, the in-control mean is typically unknown and must be estimated to construct the limits for the exponential CUSUM chart. In this article, we investigate the effect of parameter estimation on the run length properties of one-sided lower exponential CUSUM charts. In addition, analyzing conditional performance measures shows that the effect of estimation error can be significant, affecting both the in-control average run length and the quick detection of process deterioration. We also provide recommendations regarding phase I sample sizes. This sample size must be quite large for the in-control chart performance to be close to that for the known parameter case. Finally, we provide an industrial example to highlight the practical implications of estimation error, and to offer advice to practitioners when constructing/analyzing a phase I sample. Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Adaptive natural gradient learning avoids singularities in the parameter space of multilayer perceptrons. However, it requires a larger number of additional parameters than ordinary backpropagation in the form of the Fisher information matrix. This article describes a new approach to natural gradient learning that uses a smaller Fisher information matrix. It also uses a prior distribution on the neural network parameters and an annealed learning rate. While this new approach is computationally simpler, its performance is comparable to that of Adaptive natural gradient learning. [ABSTRACT FROM AUTHOR]

Residual fluctuations produced in typical experimental methodologies are examined as correlated noises. The effective range of the correlations was assessed by determining whether the decay over look-back time is better described as a power law or exponential. Both of these decay laws contain free parameters and it is argued that it is not possible to distinguish their models on the basis of simple measures of goodness-of-fit. Global analyses that evaluate models on the basis of how well they generalize are conducted. The models are examined in terms of three constructs that all bear on generalization: cross-validity, flexibility, and representativeness. Quantitative assessment of a large ensemble of data suggests that the correlations decay over time as a power law. The conclusion is that human residual fluctuation is a correlated fractal. [ABSTRACT FROM AUTHOR]

A nonlinear geometric combination of statistical models is proposed as an alternative approach to the usual linear combination or mixture. Contrary to the linear, the geometric model is closed under the regular exponential family of distributions, as we show. As a consequence, the distribution which results from the combination is unimodal and a single location parameter can be chosen for decision making. In the case of Student t-distributions (of particular interest in forecasting) the geometric combination can be unimodal under a sufficient condition we have established. A comparative analysis between the geometric and linear combinations of predictive distributions from three Bayesian regression dynamic linear models, in a case of beer sales forecasting in Zimbabwe, shows the geometric model to consistently outperform its linear counterpart as well as its component models. Copyright © 2008 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

There has been a growing interest regarding generalized classes of distributions in statistical theory and practice because of their flexibility in model formation. Multiple imputation under such distributions that span a broader area in the symmetry–kurtosis plane appears to have the potential of better capturing real incomplete data trends. In this article, we impute continuous univariate data that exhibit varying characteristics under two well-known distributions, assess the extent to which this procedure works properly, make comparisons with normal imputation models in terms of commonly accepted bias and precision measures, and discuss possible generalizations to the multivariate case and to larger families of distributions. [ABSTRACT FROM AUTHOR]

The local specification of priors in non-decomposable graphical models does not necessarily yield a proper joint prior for all the parameters of the model. Using results concerning general exponential families with cuts, we derive specific results for the multivariate Gamma distribution (conjugate prior for Poisson counts) and the Wishart distribution (conjugate prior for Gaussian models). These results link the existence of a locally specified joint prior to the solvability of a related marginal problem over the cliques of the graph. [ABSTRACT FROM AUTHOR]

A semiparametric mixture model is characterized by a non-parametric mixing distribution (with respect to a parameter θ) and a structural parameter β common to all components. Much of the literature on mixture models has focused on fixing β and estimating . However, this can lead to inconsistent estimation of both and the order of the model m. Creating a framework for consistent estimation remains an open problem and is the focus of this article. We formulate a class of generalized exponential family (GEF) models and establish sufficient conditions for the identifiability of finite mixtures formed from a GEF along with sufficient conditions for a nesting structure. Finite identifiability and nesting structure lead to the central result that semiparametric maximum likelihood estimation of and β fails. However, consistent estimation is possible if we restrict the class of mixing distributions and employ an information-theoretic approach. This article provides a foundation for inference in semiparametric mixture models, in which GEFs and their structural properties play an instrumental role. [ABSTRACT FROM AUTHOR]

We examine robust estimators and tests using the family of generalized negative exponential disparities, which contains the Pearson's chi-square and the ordinary negative exponential disparity as special cases. The influence function and α-influence function of the proposed estimators are discussed and their breakdown points derived. Under the model, the estimators are asymptotically efficient, and are shown to have an asymptotic breakdown point of 50%. The proposed tests are shown to be equivalent to the likelihood ratio test under the null hypothesis, and their breakdown points are obtained. The competitive performance of the proposed estimators and tests relative to those based on the Hellinger distance is illustrated through examples and simulation results. Unlike the Hellinger distance, several members of this family of generalized negative exponential disparities generate estimators which also possess excellent inlier-controlling capability. The corresponding tests of hypothesis are shown to have better power breakdown than the Hellinger deviance test in the cases examined. [ABSTRACT FROM AUTHOR]

L'utilisation de la vraisemblance pondérée dans les familles exponentielles naturelles à variance quadratique Les auteurs proposent un concept de vraisemblance pondérée pour l'estimation des paramètres dans les familles exponentielles naturelles à variance quadratique. Ils appliquent leurs résultats à des données réelles et simulées. [ABSTRACT FROM AUTHOR]

It is well known that Jeffreys’ prior is asymptotically least favorable under the entropy risk, i.e. it asymptotically maximizes the mutual information between the sample and the parameter. However, in this paper we show that the prior that minimizes (subject to certain constraints) the mutual information between the sample and the parameter is natural conjugate when the model belongs to a natural exponential family. A conjugate prior can thus be regarded as maximally informative in the sense that it minimizes the weight of the observations on inferences about the parameter; in other words, the expected relative entropy between prior and posterior is minimized when a conjugate prior is used. [ABSTRACT FROM AUTHOR]

Abstract We explore the structure of one-parameter exponential families admitting an unbiased estimator for a positive integral power of the natural parameter. It is seen that only exponential families dominated by Lebesgue measure can have this property. It is outlined that similar results can be obtained for other functions of the natural parameter. [ABSTRACT FROM AUTHOR]

Les auteurs s'intéressent a une formulation de la régression par la vraisemblance pénalisée qui est suffisamment générate pour englober à la fois les liens canoniques et non-canoniques pour les families ex-ponentielles, de měme que les modèles de vie accélérée avec durées de vie sujettes è censure, Ils présentent une analyse asymptotique des taux de convergence qui permet de justifier une approche simple d'approxi-mation des estimations dans des espaces de petite dimension. Une telle approximation permet d'accélérer les calculs, pavantla voie au développementd'algorithmes qui se component bien lorsqu'ils sont appliqués èa de grands jeux de données. [ABSTRACT FROM AUTHOR]

Presents a method for building parametric-functional families of Lorenz curves, generated from an initial Lorenz curve (which satisfies some regularity conditions). Application to the exponential family; Analysis of properties, including the population function, inequality measures and Lorenz orderings; Presentation of an application for data from various countries.

RÉSUMÉ Les auteurs traitent un cas particulier d'inférence en présence de paramètres nuisibles. Ils montrent que si la fonction score orthogonalisée ne dépend que d'une statistique S, l'analyse peut s'appuyer sur la loi marginale de S plutǒt que sur celle des observations sans occasionner une perte d'information de Fisher pour le paramètre d'intérět. Le fait de conditionner par rapport à une statistique libre n'apporte donc au-cune information relative à ce paramètre, alors que le conditionnement par rapport à une statistique ap-proximativement libre entraǐne une perte d'information. Tel est le cas pour les families exponentielles multivariées rétgulières lorsque le paramètre d'intérět est un sous-vecteurde l'espérance et que la statistique est l'estimation à vraisemblance maximale du paramètre d'intérět. Plusieurs exemples sont discutés, dont celui du tableau 2 × 2. [ABSTRACT FROM AUTHOR]

Uses a maximim argument based on information theory to derive a new approach to density approximation from summary statistics which is not restircted by the assumption of validity of an underlying exponential family. Assessment of loss of predictive power of summary statistics under such minimal knowledge; Conditions for existence of optimal density approximations.

Summary When two-component parallel systems are tested, the data consist of Type-II censored data X(I), I = 1 ..... n, from one component, and their concomitants Y[sub I] randomly censored at X(,.), the stopping time of the experiment. Marshall & Olkin's (1967) bivariate exponential distribution is used to illustrate statistical inference procedures developed for this data type. Although this data type is motivated practically, the likelihood is complicated, and maximum likelihood estimation is difficult, especially in the case where the parameter space is a non-open set. An iterative algorithm is proposed for finding maximum likelihood estimates. This article derives several properties of the maximum likelihood estimator (MLE) including existence, uniqueness, strong consistency and asymptotic distribution. It also develops an alternative estimation method with closed-from expressions based on marginal distributions, and derives its asymptotic properties. Compared with variances of the MLEs in the finite and large sample situations, the alternative estimator performs very well, especially when the correlation between X and Y is small. [ABSTRACT FROM AUTHOR]

Analyzes the use of independence structure of natural conjugate densities to exponential families in designing a Gibbs' sampler with block updates. Focus on Bayesian inference problems for exponential families; Utilization of the Monte Carlo Markov chain algorithms; Consideration of the sampler as an Iterative Proportional Fitting algorithm with random inputs.

Summary Qualitative robustness of the beta-trimmed mean has already been observed in terms of relative efficiency and weak continuity of that estimator in neighbourhoods of the exponential distribution. Two more robustness considerations are given here in favour of the beta-trimmed mean: the statistical functional representing this estimator is Frechet differentiable; and it is a special case of the trimmed likelihood estimator. Further, simulations suggest that a fixed proportion of trimming is preferable to adaptive estimation in this case. [ABSTRACT FROM AUTHOR]

It has been shown that there exist monotonic relations between the elements of the normalized Fisher information matrix (correlation coefficients) and the natural parameters, if a certain inclusion relation is satisfied in a binary exponential family which is defined on n probability variables taking a binary value of either 1 or 0, and if their higher- order mutual interactions are taken into account. Due to this property, changes of correlation coefficients can be approximately predicted from the changes in the values of the parameters alone. In this paper, we study the way in which changes of the expectation parameters are related to changes in the elements of the Fisher information matrix and the normalized Fisher information matrix (negative partial correlation coefficients) in the expectation coordinate system that is dual to the natural parameter coordinate system in terms of the Fisher metric in the binary exponential family. Specifically, it can be shown that there exist monotonic properties of these statistical measures, the sufficient conditions for which are inclusion relations, in contrast to the similar relations between the correlation coefficients and natural parameters. By using this property, increases, decreases, and changes of the statistical measures can be predicted from the changes of the parameters without directly calculating the change of the measure itself. The properties of monotonic increase and decrease are also shown to be dual to each other. These properties are not direct conclusions derived from the properties in the natural coordinate system, but are newly obtained by analysis of the mixture family corresponding to the binary exponential family. © 1999 Scripta Technica, Electron Comm Jpn Pt 3, 82(12): 88–97, 1999 [ABSTRACT FROM AUTHOR]

Les auteurs abordent l'estimation bayésienne empirique, sous fonction de perte quadratique, de la durée de vie moyenne, de la variance et de la fiabilité de distributions de temps de panne appartenant à une famille exponentielle, comme e'est le cas pour les lois gamma ou de Weibull par exemple. lls proposent des estimateurs de Bayes empiriques pour les situations où la loi a priori du paramètre de durée de vie est complètement inconnue, sauf pour le fait qu'elle possède un support compact (précisé ou non). lls étudient I'optimalité asymptotique et les taux de convergence de tels estimateurs. Les taux qu'ils obtiennent en postulant la compacité du support sont meilleurs que les taux de convergence polynomiaux déj à connus. [ABSTRACT FROM AUTHOR]

SUMMARY This paper characterizes the family of Normal distributions within the class of exponential families of distributions, via the structure of the bias of the maximum likelihood estimator theta[sub n] of the canonical parameter theta. More specifically, when E[sub theta](theta[sub n]) - theta = (1/n)Q(theta) + o(1/n), the equality Q(theta) = 0 proves to be a property of the Normal distribution only. The same conclusion is obtained for the one-dimensional case by assuming that Q(O) is a polynomial of theta. [ABSTRACT FROM AUTHOR]

Summary The three-parameter gamma and three-parameter Weibull distributions are commonly used for analysing any lifetime data or skewed data. Both distributions have several desirable properties, and nice physical interpretations. Because of the scale and shape parameters, both have quite a bit of flexibility for analysing different types of lifetime data. They have increasing as well as decreasing hazard rate depending on the shape parameter. Unfortunately both distributions also have certain drawbacks. This paper considers a three-parameter distribution which is a particular case of the exponentiated Weibull distribution originally proposed by Mudholkar, Srivastava & Freimer (1995) when the location parameter is not present. The study examines different properties of this model and observes that this family has some interesting features which are quite similar to those of the gamma family and the Weibull family, and certain distinct properties also. It appears this model can be used as an alternative to the gamma model or the Weibull model in many situations. One dataset is provided where the three-parameter generalized exponential distribution fits better than the three-parameter Weibull distribution or the three-parameter gamma distribution. [ABSTRACT FROM AUTHOR]

ABSTRACT. For curved (k + 1, k)-exponential families of stochastic processes a natural and often studied sequential procedure is to stop observation when a linear combination of the coordinates of the canonical process crosses a prescribed level. For such procedures the model is, approximately or exactly, a non-curved exponential family. Subfamilies of these stopping rules defined by having the same Fisher (expected) information are considered. Within a subfamily the Bartlett correction for a point hypothesis is also constant. Methods for comparing the durations of the sampling periods for the stopping rules in such a subfamily are discussed. It turns out that some stopping times tend to be smaller than others. For exponential families of diffusions and of counting processes the probability that one such stopping time is smaller than another can be given explicity. More generally, an Edgeworth expansion of this probability is given. [ABSTRACT FROM AUTHOR]

ABSTRACT. The maximum-likelihood estimator for the curved exponential family given by continuous branching processes with immigration is investigated. These processes originated from population biology but also model the dynamics of interest rates and development of the state of technology in economics. It is proved that in contrast to branching processes with discrete space and/or time the MLE gives a unified approach to the inference. In order to include singular subdomains of the parameter space we modify the MLE slightly. Consistency and asymptotic normality for the MLE are considered. Concerning the asymptotic theory of the experiments, all three properties LAQ, LAN, and LAMN occur for different submodels. [ABSTRACT FROM AUTHOR]

ABSTRACT. Standard and fully exponential form Laplace approximations to marginal densities are described and conditions under which these give exact answers are investigated. A general result is obtained and is subsequently applied in the case of natural exponential families with cuts, in order to derive the marginal posterior density of the mean parameter corresponding to the cut, the canonical parameter corresponding to the complement of the cut and transformations of these. Important cases of families for which a cut exists and the approximations are exact are presented as examples. [ABSTRACT FROM AUTHOR]

On considère le problème d'estimer le quantile d'un distribution exponentielle, avec paramètres de position et d'échelle inconnus, à l'aide de la mesure de précision de Pitman (PMC). La fonction de perte est nécessaire à la satisfaction de quelques conditions faibles, mais est autrement arbitraire. Un estimateur optimal est obtenu de la catégorie des estimateurs équivariants de position-échelle et son admissibilité selon la PMC est examinée. [ABSTRACT FROM AUTHOR]

Soit μ une mesure positive concentrée sur R [ABSTRACT FROM AUTHOR]

Plusieurs auteurs ont remarqué que lors de ľajustement ďun modèle linéaire généralisé, les données peuvent présenter plus de variabilité résiduelle que celle prédite sous un modèle exponentiel. Deux approches sont utilisées pour représenter cette dispersion excédentaire. La première utilise une densité échantillonnale qui est un mélange conjugé de densités de la famille exponentielle. La deuxième approche utilise une fonction de quasi-vraisemblance qui ajoute un nouveau paramètre de dispersion à la fonction de vraisemblance exponentielle. Les deux approches sont comparées en faisant une analyse bayesienne avec des lois a priori non informatives. Des exemples illustrent que les deux approches peuvent mener à des analyses a posteriori différentes. [ABSTRACT FROM AUTHOR]

Dans le contexte de tests pour la corrélation intra-classe, utiles pour l'analyse de données relatives aux familles, on évalue deux approximations de la loi F. L'évaluation est basée sur le calcul de seuils empiriques et sur la comparaison entre les probabilités de dépassement exactes et celles associées aux approximations. On trouve que les méthodes approximatives peuvent conduire à des résultats très insatisfaisants et que, par conséquent, les méthodes exactes sont recommandées. [ABSTRACT FROM AUTHOR]