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作者：Nickl, Richard; van de Geer, Sara
作者单位：University of Cambridge; Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：The problem of constructing confidence sets in the high-dimensional linear model with n response variables and p parameters, possibly p >= n, is considered. Full honest adaptive inference is possible if the rate of sparse estimation does not exceed n(-1/4), otherwise sparse adaptive confidence sets exist only over strict subsets of the parameter spaces for which sparse estimators exist. Necessary and sufficient conditions for the existence of confidence sets that adapt to a fixed sparsity leve...
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作者：Khmaladze, Estate
作者单位：Victoria University Wellington
摘要：The paper proposes one-to-one transformation of the vector of components {Y-in}(i=1)(m) of Pearson's chi-square statistic, Y-in = nu(in)-npi/root np(i,) i = l, ... , m, into another vector {Z(in)}(i=1)(m), which, therefore, contains the same statistical information, but is asymptotically distribution free. Hence any functional/test statistic based on {Z(in)}(i=1)(m) is also asymptotically distribution free. Natural examples of such test statistics are traditional goodness-of-fit statistics fro...
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作者：Nordman, Daniel J.; Bunzel, Helle; Lahiri, Soumendra N.
作者单位：Iowa State University; Iowa State University; Aarhus University; CREATES; North Carolina State University
摘要：Standard blockwise empirical likelihood (BEL) for stationary, weakly dependent time series requires specifying a fixed block length as a tuning parameter for setting confidence regions. This aspect can be difficult and impacts coverage accuracy. As an alternative, this paper proposes a new version of BEL based on a simple, though nonstandard, data-blocking rule which uses a data block of every possible length. Consequently, the method does not involve the usual block selection issues and is al...
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作者：Chan, Hock Peng; Lai, Tze Leung
作者单位：National University of Singapore; Stanford University
摘要：By making use of martingale representations, we derive the asymptotic normality of particle filters in hidden Markov models and a relatively simple formula for their asymptotic variances. Although repeated resamplings result in complicated dependence among the sample paths, the asymptotic variance formula and martingale representations lead to consistent estimates of the standard errors of the particle filter estimates of the hidden states.
