Annals of the Institute of Statistical Mathematics (Ann Inst Stat Math )

Publisher: Tōkei-Sūri-Kenkyūsho (Tōkyō), Springer Verlag


Annals of the Institute of Statistical Mathematics (AISM) provides an international forum for open communication among statisticians and researchers working with the common purpose of advancing human knowledge through the development of the science and technology of statistics. AISM will publish broadest possible coverage of statistical papers of the highest quality. The emphasis will be placed on the publication of papers related to: (a) the establishment of new areas of application; (b) the development of new procedures and algorithms; (c) the development of unifying theories; (d) the analysis and improvement of existing procedures and theories; and the communication of empirical findings supported by real data. In addition to papers by professional statisticians contributions are also published by authors working in various fields of application. Authors discussing applications are encouraged to contribute a complete set of data used in their papers to the AISM Data Library. The Institute of Statistical Mathematics will distribute it upon request from readers (see p. 405 and 606 Vol. 43 No. 3 1991). The final objective of AISM is to contribute to the advancement of statistics as the science of human handling of information to cope with uncertainties. Special emphasis will thus be placed on the publication of papers that will eventually lead to significant improvements in the practice of statistics.

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Springer Verlag

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Publications in this journal

  • [Show abstract] [Hide abstract]
    ABSTRACT: The ordinary Bayes estimator based on the posterior density can have potential problems with outliers. Using the density power divergence measure, we develop an estimation method in this paper based on the so called "R(α)-Posterior density"; this construction uses the concept of priors in Bayesian context and generates highly robust estimators with good efficiency under the true model. We develop the asymptotic properties of the proposed estimator and illustrate its performance numerically.
    Annals of the Institute of Statistical Mathematics 11/2014; Forthcoming paper....
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    ABSTRACT: We develop particle Gibbs samplers for static-parameter estimation in discretely observed piecewise deterministic process (PDPs). PDPs are stochastic processes that jump randomly at a countable number of stopping times but otherwise evolve deterministically in continuous time. A sequential Monte Carlo (SMC) sampler for filtering in PDPs has recently been proposed. We first provide new insight into the consequences of an approximation inherent within that algorithm. We then derive a new representation of the algorithm. It simplifies ensuring that the importance weights exist and also allows the use of variance-reduction techniques known as backward and ancestor sampling. Finally, we propose a novel Gibbs step that improves mixing in particle Gibbs samplers whose SMC algorithms make use of large collections of auxiliary variables, such as many instances of SMC samplers. We provide a comparison between the two particle Gibbs samplers for PDPs developed in this paper. Simulation results indicate that they can outperform reversible-jump MCMC approaches.
    Annals of the Institute of Statistical Mathematics 01/2014; 66(3):577-609.
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    ABSTRACT: Although the parameters in a finite mixture model are unidentifiable, there is a form of local identifiability guaranteeing the existence of the identifiable parameter regions. To verify its existence, practitioners use the Fisher information on the estimated parameters. However, there exist model/data situations where local identifiability based on Fisher information does not correspond to that based on the likelihood. In this paper, we propose a method to empirically measure degree of local identifiability on the estimated parameters, empirical identifiability, based on one’s ability to construct an identifiable likelihood set. From a detailed topological study of the likelihood region, we show that for any given data set and mixture model, there typically exists limited range of confidence levels where the likelihood region has a natural partition into identifiable subsets. At confidence levels that are too high, there is no natural way to use the likelihood to resolve the identifiability problem.
    Annals of the Institute of Statistical Mathematics 01/2014;
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    ABSTRACT: The majority of modelling and inference regarding Hidden Markov Models (HMMs) assumes that the number of underlying states is known a priori. However, this is often not the case and thus determining the appropriate number of underlying states for a HMM is of considerable interest. This paper proposes the use of a parallel sequential Monte Carlo samplers framework to approximate the posterior distribution of the number of states. This requires no additional computational effort if approximating parameter posteriors conditioned on the number of states is also necessary. The proposed strategy is evaluated on a comprehensive set of simulated data and shown to outperform the state of the art in this area: although the approach is simple, it provides good performance by fully exploiting the particular structure of the problem. An application to business cycle analysis is also presented.
    Annals of the Institute of Statistical Mathematics 01/2014; 66(3):553-575.
  • Annals of the Institute of Statistical Mathematics 01/2014;
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    ABSTRACT: This paper proposes a new method for constructing a sequence of infinitely exchangeable uniform random variables on the unit interval. For constructing the sequence, we utilize a Pólya urn partially. The resulting exchangeable sequence depends on the initial numbers of balls of the Pólya urn. We also derive the de Finetti measure for the exchangeable sequence. For an arbitrarily given one-dimensional distribution function, we generate sequences of exchangeable random variables with the one-dimensional marginal distribution by transforming the exchangeable uniform sequences with the inverse function of the distribution function. Among them we mainly investigate sequences of exchangeable discrete random variables. They differ from the well-known exchangeable sequence generated only by the Pólya urn scheme. Some examples are also given as applications of the results to exact distributions of some statistics based on sequences of exchangeable trials. Further, from the above exchangeable uniform sequence we construct partial or Markov exchangeable sequences. We also provide numerical examples of statistical inference based on the exchangeable and Markov exchangeable sequences.
    Annals of the Institute of Statistical Mathematics 01/2012; 64(3):633-655.
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    ABSTRACT: In this paper, we develop some coefficients which can be used to detect dependence in multivariate distributions not detected by several known measures of multivariate association. Several examples illustrate our results.
    Annals of the Institute of Statistical Mathematics 01/2012; 64(3):677-685.
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    ABSTRACT: Estimators based on the mode are introduced and shown empirically to have smaller Kullback–Leibler risk than the maximum likelihood estimator. For one of these, the midpoint modal estimator (MME), we prove the Kullback–Leibler risk is below $${\frac{1}{2}}$$ while for the MLE the risk is above $${\frac{1}{2}}$$ for a wide range of success probabilities that approaches the unit interval as the sample size grows to infinity. The MME is related to the mean of Fisher’s Fiducial estimator and to the rule of succession for Jefferey’s noninformative prior.
    Annals of the Institute of Statistical Mathematics 01/2012; 64(2):359-371.
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    ABSTRACT: Ranked-set sampling (RSS) and judgment post-stratification (JPS) are related schemes in which more efficient statistical inference is obtained by creating a stratification based on ranking information. The rankings may be completely subjective, or they may be based on values of a covariate. Recent work has shown that regardless of how the rankings are done, the in-stratum cumulative distribution functions (CDFs) must satisfy certain constraints, and we show here that if the rankings are done according to a covariate, then tighter constraints must hold. We also show that under a mild stochastic ordering assumption, still tighter constraints must hold. Taking advantage of these new constraints leads to improved small-sample estimates of the in-stratum CDFs in all RSS and JPS settings. For JPS, the new constraints also lead to improved estimates of the overall CDF and the population mean.
    Annals of the Institute of Statistical Mathematics 01/2012; 64(2):439-456.
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    ABSTRACT: Bayesian analysis for a covariance structure has been in use for decades. The commonly adopted Bayesian setup involves the conjugate inverse Wishart prior specification for the covariance matrix. Here we depart from this approach and adopt a novel prior specification by considering a multivariate normal prior for the elements of the matrix logarithm of the covariance structure. This specification allows for a richer class of prior distributions for the covariance structure with respect to strength of beliefs in prior location hyperparameters and the added ability to model potential correlation amongst the covariance structure. We provide three computational methods for calculating the posterior moment of the covariance matrix. The moments of interest are calculated based upon computational results via Importance sampling, Laplacian approximation and Markov Chain Monte Carlo/Metropolis–Hastings techniques. As a particular application of the proposed technique we investigate educational test score data from the project talent data set.
    Annals of the Institute of Statistical Mathematics 01/2012; 64(2):319-342.
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    ABSTRACT: This paper introduces a new family of local density separations for assessing robustness of finite-dimensional Bayesian posterior inferences with respect to their priors. Unlike for their global equivalents, under these novel separations posterior robustness is recovered even when the functioning posterior converges to a defective distribution, irrespectively of whether the prior densities are grossly misspecified and of the form and the validity of the assumed data sampling distribution. For exponential family models, the local density separations are shown to form the basis of a weak topology closely linked to the Euclidean metric on the natural parameters. In general, the local separations are shown to measure relative roughness of the prior distribution with respect to its corresponding posterior and provide explicit bounds for the total variation distance between an approximating posterior density to a genuine posterior. We illustrate the application of these bounds for assessing robustness of the posterior inferences for a dynamic time series model of blood glucose concentration in diabetes mellitus patients with respect to alternative prior specifications.
    Annals of the Institute of Statistical Mathematics 01/2012; 64(3):495-519.