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作者：Lee, Young K.; Mammen, Enno; Nielsen, Jens P.; Park, Byeong U.
作者单位：Kangwon National University; Ruprecht Karls University Heidelberg; City St Georges, University of London; Seoul National University (SNU)
摘要：In this paper, we consider a new structural model for in-sample density forecasting. In-sample density forecasting is to estimate a structured density on a region where data are observed and then reuse the estimated structured density on some region where data are not observed. Our structural assumption is that the density is a product of one-dimensional functions with one function sitting on the scale of a transformed space of observations. The transformation involves another unknown one-dime...
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作者：Wang, Y. X. Rachel; Bickel, Peter J.
作者单位：Stanford University; University of California System; University of California Berkeley
摘要：The stochastic block model (SBM) provides a popular framework for modeling community structures in networks. However, more attention has been devoted to problems concerning estimating the latent node labels and the model parameters than the issue of choosing the number of blocks. We consider an approach based on the log likelihood ratio statistic and analyze its asymptotic properties under model misspecification. We show the limiting distribution of the statistic in the case of underfitting is...
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作者：Xu, Gongjun
作者单位：University of Minnesota System; University of Minnesota Twin Cities
摘要：Statistical latent class models are widely used in social and psychological researches, yet it is often difficult to establish the identifiability of the model parameters. In this paper, we consider the identifiability issue of a family of restricted latent class models, where the restriction structures are needed to reflect pre-specified assumptions on the related assessment. We establish the identifiability results in the strict sense and specify which types of restriction structure would gi...
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作者：Anevski, Dragi; Gill, Richard D.; Zohren, Stefan
作者单位：Lund University; Leiden University - Excl LUMC; Leiden University; University of Oxford
摘要：In the context of a species sampling problem, we discuss a nonparametric maximum likelihood estimator for the underlying probability mass function. The estimator is known in the computer science literature as the high profile estimator. We prove strong consistency and derive the rates of convergence, for an extended model version of the estimator. We also study a sieved estimator for which similar consistency results are derived. Numerical computation of the sieved estimator is of great intere...
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作者：Bai, Shuyang; Taqqu, Murad S.
作者单位：University System of Georgia; University of Georgia; Boston University
摘要：For long-memory time series, inference based on resampling is of crucial importance, since the asymptotic distribution can often be non-Gaussian and is difficult to determine statistically. However, due to the strong dependence, establishing the asymptotic validity of resampling methods is nontrivial. In this paper, we derive an efficient bound for the canonical correlation between two finite blocks of a long-memory time series. We show how this bound can be applied to establish the asymptotic...
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作者：Tang, Chuan-Fa; Wang, Dewei; Tebbs, Joshua M.
作者单位：University of South Carolina System; University of South Carolina Columbia
摘要：We propose L-p distance-based goodness-of-fit (GOF) tests for uniform stochastic ordering with two continuous distributions F and G, both of which are unknown. Our tests are motivated by the fact that when F and G are uniformly stochastically ordered, the ordinal dominance curve R = FG(-1) is star-shaped. We derive asymptotic distributions and prove that our testing procedure has a unique least favorable configuration of F and G for p is an element of [1, infinity]. We use simulation to assess...
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作者：Cai, T. Tony; Guo, Zijian
作者单位：University of Pennsylvania
摘要：Confidence sets play a fundamental role in statistical inference. In this paper, we consider confidence intervals for high-dimensional linear regression with random design. We first establish the convergence rates of the minimax expected length for confidence intervals in the oracle setting where the sparsity parameter is given. The focus is then on the problem of adaptation to sparsity for the construction of confidence intervals. Ideally, an adaptive confidence interval should have its lengt...
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作者：Dobriban, Edgar
作者单位：Stanford University
摘要：Principal component analysis (PCA) is a widely used method for dimension reduction. In high-dimensional data, the signal eigenvalues corresponding to weak principal components (PCs) do not necessarily separate from the bulk of the noise eigenvalues. Therefore, popular tests based on the largest eigenvalue have little power to detect weak PCs. In the special case of the spiked model, certain tests asymptotically equivalent to linear spectral statistics (LSS)-averaging effects over all eigenvalu...
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作者：Klopp, Olga; Tsybakov, Alexandre B.; Verzelen, Nicolas
作者单位：Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS); CNRS - Institute for Humanities & Social Sciences (INSHS); Institut Polytechnique de Paris; ENSAE Paris; INRAE
摘要：Inhomogeneous random graph models encompass many network models such as stochastic block models and latent position models. We consider the problem of statistical estimation of the matrix of connection probabilities based on the observations of the adjacency matrix of the network. Taking the stochastic block model as an approximation, we construct estimators of network connection probabilities the ordinary block constant least squares estimator, and its restricted version. We show that they sa...
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作者：Loh, Po-Ling; Wainwright, Martin J.
作者单位：University of Wisconsin System; University of Wisconsin Madison; University of Wisconsin System; University of Wisconsin Madison; University of California System; University of California Berkeley; University of California System; University of California Berkeley
摘要：We develop a new primal-dual witness proof framework that may be used to establish variable selection consistency and l(infinity)-bounds for sparse regression problems, even when the loss function and regularizer are nonconvex. We use this method to prove two theorems concerning support recovery and l(infinity)-guarantees for a regression estimator in a general setting. Notably, our theory applies to all potential stationary points of the objective and certifies that the stationary point is un...
