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作者：Marion, Joe; Mathews, Joseph; Schmidler, Scott C.
作者单位：Duke University
摘要：We present bounds for the finite-sample error of sequential Monte Carlo samplers on static spaces. Our approach explicitly relates the performance of the algorithm to properties of the chosen sequence of distributions and mixing properties of the associated Markov kernels. This allows us to give the first finite-sample comparison to other Monte Carlo schemes. We obtain bounds for the complexity of sequential Monte Carlo approximations for a variety of target distributions such as finite spaces...
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作者：Roettger, Frank; Engelke, Sebastian; Zwiernik, Piotr
作者单位：University of Geneva; University of Toronto
摘要：Positive dependence is present in many real world data sets and has appealing stochastic properties that can be exploited in statistical modeling and in estimation. In particular, the notion of multivariate total positivity of order 2 (MTP2) is a convex constraint and acts as an implicit regularizer in the Gaussian case. We study positive dependence in multivariate extremes and introduce EMTP2, an extremal version of MTP2. This notion turns out to appear prominently in extremes, and in fact, i...
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作者：Ding, Xiucai; Zhou, Zhou
作者单位：University of California System; University of California Davis; University of Toronto
摘要：Understanding the time-varying structure of complex temporal systems is one of the main challenges of modern time-series analysis. In this paper, we show that every uniformly-positive-definite-in-covariance and sufficiently short-range dependent nonstationary and nonlinear time series can be well ap-proximated globally by a white-noise-driven autoregressive (AR) process of slowly diverging order. To our best knowledge, it is the first time such a struc-tural approximation result is established...
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作者：Chernozhukov, Victor; Hansen, Christian; Liao, Yuan; Zhu, Yinchu
作者单位：Massachusetts Institute of Technology (MIT); University of Chicago; Rutgers University System; Rutgers University New Brunswick; Brandeis University
摘要：This paper studies inference in linear models with a high-dimensional parameter matrix that can be well approximated by a spiked low-rank matrix. A spiked low-rank matrix has rank that grows slowly compared to its dimensions and nonzero singular values that diverge to infinity. We show that this framework covers a broad class of models of latent variables, which can accommodate matrix completion problems, factor models, varying coefficient models and heterogeneous treatment effects. For infere...
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作者：Han, Xiao; Yang, Qing; Fan, Yingying
作者单位：Chinese Academy of Sciences; University of Science & Technology of China, CAS; University of Southern California
摘要：Determining the precise rank is an important problem in many large-scale applications with matrix data exploiting low-rank plus noise models. In this paper, we suggest a universal approach to rank inference via residual sub-sampling (RIRS) for testing and estimating rank in a wide family of models, including many popularly used network models such as the degree corrected mixed membership model as a special case. Our procedure constructs a test statistic via subsampling entries of the residual ...
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作者：Weinstein, Asaf; Su, Weijie J.; Bogdan, Malgorzata; Barber, Rina Foygel; Candes, Emmanuel J.
作者单位：Hebrew University of Jerusalem; University of Pennsylvania; University of Wroclaw; University of Chicago; Stanford University; Stanford University
摘要：Variable selection properties of procedures utilizing penalized-likelihood estimates is a central topic in the study of high-dimensional linear regression problems. Existing literature emphasizes the quality of ranking of the variables by such procedures as reflected in the receiver operating characteristic curve or in prediction performance. Specifically, recent works have harnessed modern theory of approximate message-passing (AMP) to obtain, in a particular setting, exact asymptotic predict...
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作者：Li, Harrison H.; Owen, Art B.
作者单位：Stanford University
摘要：Tie-breaker designs trade off a measure of statistical efficiency against a with higher values of a running variable x. The efficiency measure can be any continuous function of the expected information matrix in a two-line regression model. The short-term gain is expressed as the covariance between the running variable and the treatment indicator. We investigate how to choose design functions p(x) specifying the probability of treating a subject with running variable x in order to optimize the...
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作者：Qiu, Jiaxin; Li, Zeng; Yao, Jianfeng
作者单位：University of Hong Kong; Southern University of Science & Technology; The Chinese University of Hong Kong, Shenzhen
摘要：The asymptotic normality for a large family of eigenvalue statistics of a general sample covariance matrix is derived under the ultrahigh-dimensional setting, that is, when the dimension to sample size ratio p/n & RARR; & INFIN;. Based on this CLT result, we extend the covariance matrix test problem to the new ultra-high-dimensional context, and apply it to test a matrix-valued white noise. Simulation experiments are conducted for the investigation of finite-sample properties of the general as...
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作者：Xu, Yuanzhe; Mukherjee, Sumit
作者单位：Columbia University
摘要：In this paper, we derive the limit of experiments for one-parameter Ising models on dense regular graphs. In particular, we show that the limiting ex-periment is Gaussian in the low temperature regime, and non-Gaussian in the critical regime. We also derive the limiting distributions of the maxi-mum likelihood and maximum pseudolikelihood estimators, and study limit-ing power for tests of hypothesis against contiguous alternatives. To the best of our knowledge, this is the first attempt at est...
