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作者：Zhou, Hang; Yao, Fang; Zhang, Huiming
作者单位：Peking University; University of Macau
摘要：Despite extensive studies on functional linear regression, there exists a fundamental gap in theory between the ideal estimation from fully observed covariate functions and the reality that one can only observe functional covariates discretely with noise. The challenge arises when deriving a sharp perturbation bound for the estimated eigenfunctions in the latter case, which renders existing techniques for functional linear regression not applicable. We use a pooling method to attain the estima...
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作者：Tudball, Matthew J.; Hughes, Rachael A.; Tilling, Kate; Bowden, Jack; Zhao, Qingyuan
作者单位：University of Bristol; University of Exeter; University of Cambridge
摘要：Many partial identification problems can be characterized by the optimal value of a function over a set where both the function and set need to be estimated by empirical data. Despite some progress for convex problems, statistical inference in this general setting remains to be developed. To address this, we derive an asymptotically valid confidence interval for the optimal value through an appropriate relaxation of the estimated set. We then apply this general result to the problem of selecti...
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作者：Kreiss, J. P.; Paparoditis, E.
作者单位：Braunschweig University of Technology; University of Cyprus
摘要：Fitting parametric models by optimizing frequency-domain objective functions is an attractive approach of parameter estimation in time series analysis. Whittle estimators are a prominent example in this context. Under weak conditions and the assumption that the true spectral density of the underlying process does not necessarily belong to the parametric class of spectral densities fitted, the distribution of Whittle estimators typically depends on difficult to estimate characteristics of the u...
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作者：Ascolani, F.; Lijoi, A.; Rebaudo, G.; Zanella, G.
作者单位：Bocconi University; Bocconi University; University of Texas System; University of Texas Austin; Bocconi University; Bocconi University
摘要：Dirichlet process mixtures are flexible nonparametric models, particularly suited to density estimation and probabilistic clustering. In this work we study the posterior distribution induced by Dirichlet process mixtures as the sample size increases, and more specifically focus on consistency for the unknown number of clusters when the observed data are generated from a finite mixture. Crucially, we consider the situation where a prior is placed on the concentration parameter of the underlying...
