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作者：Flegal, James M.; Jones, Galin L.
作者单位：University of California System; University of California Riverside; University of Minnesota System; University of Minnesota Twin Cities
摘要：Calculating a Monte Carlo standard error (MCSE) is an important step in the statistical analysis of the simulation output obtained from a Markov chain Monte Carlo experiment. An MCSE is usually based on an estimate of the variance of the asymptotic normal distribution. We consider spectral and batch means methods for estimating this variance. In particular, we establish conditions which guarantee that these estimators are strongly consistent as the simulation effort increases. In addition, for...
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作者：Hallin, Marc; Paindaveine, Davy; Siman, Miroslav
作者单位：Universite Libre de Bruxelles
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作者：Gine, Evarist; Nickl, Richard
作者单位：University of Connecticut; University of Cambridge
摘要：Given a sample from some unknown continuous density f : R -> R, we construct adaptive confidence bands that are honest for all densities in a generic subset of the union of t-Holder balls, 0 < t <= r, where r is a fixed but arbitrary integer. The exceptional (nongeneric) set of densities for which our results do not hold is shown to be nowhere dense in the relevant Holder-norm topologies. In the course of the proofs we also obtain limit theorems for maxima of linear wavelet and kernel density ...
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作者：Wei, Ying
作者单位：Columbia University
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作者：Wang, Weizhen
作者单位：University System of Ohio; Wright State University Dayton
摘要：For my class of one-sided 1 - alpha confidence intervals with a certain monotonicity ordering on the random confidence limit, the smallest interval, in the sense of the set inclusion for the difference of two proportions of two independent binomial random variables, is constructed based on a direct analysis of coverage probability function. A special ordering on the confidence limit is developed and the corresponding smallest confidence interval is derived. This interval is then applied to ide...
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作者：Wang, Yazhen; Zou, Jian
作者单位：University of Wisconsin System; University of Wisconsin Madison; University of Connecticut
摘要：High-frequency data observed on the prices of financial assets are commonly modeled by diffusion processes with micro-structure noise, and realized volatility-based methods are often used to estimate integrated volatility. For problems involving a large number of assets, the estimation objects we face are volatility matrices of large size. The existing volatility estimators work well for a small number of assets but perform poorly when the number of assets is very large. In fact, they are inco...
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作者：Chen, Song Xi; Qin, Ying-Li
作者单位：Iowa State University; Peking University
摘要：We propose a two-sample test for the means of high-dimensional data when the data dimension is much larger than the sample size. Hotelling's classical T(2) test does not work for this large p, small n situation. The proposed test does not require explicit conditions in the relationship between the data dimension and sample size. This offers much flexibility in analyzing high-dimensional data. An application of the proposed test is in testing significance for sets of genes which we demonstrate ...
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作者：Egloff, Daniel; Leippold, Markus
作者单位：University of Zurich
摘要：We introduce new quantile estimators with adaptive importance sampling. The adaptive estimators are based on weighted samples that are neither independent nor identically distributed. Using a new law of iterated logarithm for martingales, we prove the convergence of the adaptive quantile estimators for general distributions with nonunique quantiles thereby extending the work of Feldman and Tucker [Ann. Math. Statist. 37 (1996) 451-457]. We illustrate the algorithm with an example from credit p...
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作者：Serfling, Robert; Zuo, Yijun
作者单位：University of Texas System; University of Texas Dallas; Michigan State University
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作者：Delaigle, Aurore; Hall, Peter
作者单位：University of Melbourne; University of Bristol; University of California System; University of California San Diego
摘要：The notion of probability density for a random function is not as straightforward as in finite-dimensional cases. While a probability density function generally does not exist for functional data, we show that it is possible to develop the notion of density when functional data are considered in the space determined by the eigenfunctions of principal component analysis. This leads to a transparent and meaningful surrogate for density defined in terms of the average value of the logarithms of t...
