The Annals of Statistics

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• Interactions and outliers in the two-way analysis of variance AI翻译
  作者：Terbeck, W; Davies, PL
  作者单位：University of Duisburg Essen
  摘要：The two-way analysis of variance with interactions is a well established and integral part of statistics. In spite of its long standing, it is shown that the standard definition of interactions is counterintuitive and obfuscates rather than clarifies. A different definition of interaction is given which among other advantages allows the detection of interactions even in the case of one observation per cell. A characterization of unconditionally identifiable interaction patterns is given and it...
• Estimation and testing for lattice conditional independence models on Euclidean Jordan algebras AI翻译
  作者：Massam, H; Neher, E
  作者单位：York University - Canada; University of Virginia; University of Ottawa
  摘要：In this paper we generalize the major results of Andersson and Perlman on LCI models to the setting of symmetric cones and give an explicit closed form formula for the estimate of the covariance matrix in the generalized LCI models that we define. To this end, we replace the cone H-I(+)(R) sitting inside the Jordan algebra of symmetric real I x I-matrices by the symmetric cone Omega of an Euclidean Jordan algebra V. We introduce the Andersson-Perlman cone Omega(K) subset of or equal to Omega w...
• On the construction of Bayes minimax estimators AI翻译
  作者：Fourdrinier, D; Strawderman, WE; Wells, MT
  作者单位：Universite de Rouen Normandie; Centre National de la Recherche Scientifique (CNRS); Rutgers University System; Rutgers University New Brunswick; Cornell University
  摘要：Bayes estimation of the mean of a multivariate normal distribution is considered under quadratic loss. We show that, when particular spherical priors are used, the superharmonicity of the square root of the marginal density provides a viable method for constructing (possibly proper) Bayes (and admissible) minimax estimators. Examples illustrate the theory; most notably it is shown that a multivariate Student-t prior yields a proper Bayes minimax estimate.
• Optimal discrimination designs for multifactor experiments (vol 25, pg 1161, 1997) AI翻译
  作者：Dette, H; Röder, I
  作者单位：Ruhr University Bochum; Ruhr University Bochum; Leipzig University
• New goodness-of-fit tests and their application to nonparametric confidence sets AI翻译
  作者：Dümbgen, L
  作者单位：Ruprecht Karls University Heidelberg; University of Lubeck
  摘要：Suppose one observes a process V on the unit interval, where dV = f(o)+ dW with an unknown parameter f(o) epsilon L-1[0, 1] and standard Brownian motion W. We propose a particular test of one-point hypotheses about f(o) which is based on suitably standardized increments of V. This test is shown to have desirable consistency properties if, for instance, f(o) is restricted to various Holder classes of functions. The test is mimicked in the context of nonparametric density estimation, nonparametr...
• Limiting distributions of maximum likelihood estimators for unstable autoregressive moving-average time series with general autoregressive heteroscedastic errors AI翻译
  作者：Ling, SQ; Li, WK
  作者单位：University of Hong Kong
  摘要：This paper investigates the maximum likelihood estimator (MLE) for unstable autoregressive moving-average (ARMA) time series with the noise sequence satisfying a general autoregressive heteroscedastic (GARCH) process. Under some mild conditions, it is shown that the MLE satisfying the likelihood equation exists and is consistent. The limiting distribution of the RILE is derived in a unified manner for all types of characteristic roots on or outside the unit circle and is expressed as a functio...
• Bayesian bootstrap credible sets for multidimensional mean functional AI翻译
  作者：Choudhuri, N
  作者单位：University of Michigan System; University of Michigan
  摘要：This paper shows that the Bayesian bootstrap (BB) distribution of a multidimensional mean functional based on i.i.d. observations has a strongly unimodal Lebesgue density provided the convex hull of the data has a nonempty interior. This result is then used to construct the finite sample BE credible sets. The influence of an outlier on these credible sets is studied in detail and a comparison is made with the empirical likelihood ratio confidence sets in this context.
• Arcing classifiers - Discussion AI翻译
  作者：Amit, Y; Geman, D
  作者单位：University of Chicago; University of Massachusetts System; University of Massachusetts Amherst
• Asymptotic nonequivalence of nonparametric experiments when the smoothness index is 1/2 AI翻译
  作者：Brown, LD; Zhang, CH
  作者单位：University of Pennsylvania; Rutgers University System; Rutgers University New Brunswick
  摘要：An example is provided to show that the natural asymptotic equivalence does not hold between any pairs of three nonparametric experiments: density problem, white noise with drift and nonparametric regression, when the smoothness index of the unknown nonparametric function class is 1/2.
• The silhouette, concentration functions and ML-density estimation under order restrictions AI翻译
  作者：Polonik, W
  作者单位：Ruprecht Karls University Heidelberg
  摘要：Based on empirical Levy-type concentration functions, a new graphical representation of the ML-density estimator under order restrictions is given. This representation generalizes the well-known representation of the Grenander estimator of a monotone density as the slope of the least concave majorant of the empirical distribution function to higher dimensions and arbitrary order restrictions. From the given representation it follows that a density estimator called silhouette, which arises natu...