6期

最新文章

• ROBUST BAYES-LIKE ESTIMATION: RHO-BAYES ESTIMATION AI翻译
  作者：Baraud, Yannick; Birge, Lucien
  作者单位：University of Luxembourg; Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS); Universite Paris Cite
  摘要：We observe n independent random variables with joint distribution P and pretend that they are i.i.d. with some common density s (with respect to a known measure mu) that we wish to estimate. We consider a density model (S) over bar for s that we endow with a prior distribution pi (with support in (S) over bar) and build a robust alternative to the classical Bayes posterior distribution which possesses similar concentration properties around s whenever the data are truly i.i.d. and their densit...
• DISTANCE-BASED AND RKHS-BASED DEPENDENCE METRICS IN HIGH DIMENSION AI翻译
  作者：Zhu, Changbo; Zhang, Xianyang; Yao, Shun; Shao, Xiaofeng
  作者单位：University of Illinois System; University of Illinois Urbana-Champaign; Texas A&M University System; Texas A&M University College Station
  摘要：In this paper, we study distance covariance, Hilbert-Schmidt covariance (aka Hilbert-Schmidt independence criterion [In Advances in Neural Information Processing Systems (2008) 585-592]) and related independence tests under the high dimensional scenario. We show that the sample distance/Hilbert-Schmidt covariance between two random vectors can be approximated by the sum of squared componentwise sample cross-covariances up to an asymptotically constant factor, which indicates that the standard ...
• ISOTONIC REGRESSION IN MULTI-DIMENSIONAL SPACES AND GRAPHS AI翻译
  作者：Deng, Hang; Zhang, Cun-Hui
  作者单位：Rutgers University System; Rutgers University New Brunswick
  摘要：In this paper, we study minimax and adaptation rates in general isotonic regression. For uniform deterministic and random designs in [0, 1](d) with d >= 2 and N(0, 1) noise, the minimax rate for the l(2) risk is known to be bounded from below by n(-1/d) when the unknown mean function f is non-decreasing and its range is bounded by a constant, while the least squares estimator (LSE) is known to nearly achieve the minimax rate up to a factor (log n)(gamma) where n is the sample size, gamma = 4 i...
• LIMIT DISTRIBUTION THEORY FOR BLOCK ESTIMATORS IN MULTIPLE ISOTONIC REGRESSION AI翻译
  作者：Han, Qiyang; Zhang, Cun-Hui
  作者单位：Rutgers University System; Rutgers University New Brunswick
  摘要：We study limit distributions for the tuning-free max-min block estimator originally proposed in (Fokianos, Leucht and Neumann (2017)) in the problem of multiple isotonic regression, under both fixed lattice design and random design settings. We show that, if the regression function f(0) admits vanishing derivatives up to order alpha(k) along the kth dimension (k = 1, ..., d) at a fixed point x(0) is an element of (0, 1)(d), and the errors have variance sigma(2), then the max-min block estimato...
• INFERENCE FOR CONDITIONAL VALUE-AT-RISK OF A PREDICTIVE REGRESSION AI翻译
  作者：He, Yi; Hou, Yanxi; Peng, Liang; Shen, Haipeng
  作者单位：University of Amsterdam; Fudan University; University System of Georgia; Georgia State University; University of Hong Kong
  摘要：Conditional value-at-risk is a popular risk measure in risk management. We study the inference problem of conditional value-at-risk under a linear predictive regression model. We derive the asymptotic distribution of the least squares estimator for the conditional value-at-risk. Our results relax the model assumptions made in (Oper. Res. 60 (2012) 739-756) and correct their mistake in the asymptotic variance expression. We show that the asymptotic variance depends on the quantile density funct...
• OPTIMAL ESTIMATION OF VARIANCE IN NONPARAMETRIC REGRESSION WITH RANDOM DESIGN AI翻译
  作者：Shen, Yandi; Gao, Chao; Witten, Daniela; Han, Fang
  作者单位：University of Washington; University of Washington Seattle; University of Chicago
  摘要：Consider the heteroscedastic nonparametric regression model with random design Y-i = f (X-i) + V-1/2 (X-i)epsilon(i), i = 1, 2, ..., n, with f (.) and V (.) alpha- and beta-Holder smooth, respectively. We show that the minimax rate of estimating V (.) under both local and global squared risks is of the order n( - 8 alpha beta/4 alpha beta+2 alpha+beta )boolean OR n (- 2 beta/2 beta+1), where a boolean OR b := max{a, b} for any two real numbers a, b. This result extends the fixed design rate n(...
• SINGULARITY, MISSPECIFICATION AND THE CONVERGENCE RATE OF EM AI翻译
  作者：Dwivedi, Raaz; Nhat Ho; Khamaru, Koulik; Wainwright, Martin J.; Jordan, Michael, I; Yu, Bin
  作者单位：University of California System; University of California Berkeley; University of California System; University of California Berkeley
  摘要：A line of recent work has analyzed the behavior of the Expectation-Maximization (EM) algorithm in the well-specified setting, in which the population likelihood is locally strongly concave around its maximizing argument. Examples include suitably separated Gaussian mixture models and mixtures of linear regressions. We consider over-specified settings in which the number of fitted components is larger than the number of components in the true distribution. Such mis-specified settings can lead t...
• MODEL SELECTION AND LOCAL GEOMETRY AI翻译
  作者：Evans, Robin J.
  作者单位：University of Oxford
  摘要：We consider problems in model selection caused by the geometry of models close to their points of intersection. In some cases-including common classes of causal or graphical models, as well as time series models-distinct models may nevertheless have identical tangent spaces. This has two immediate consequences: first, in order to obtain constant power to reject one model in favour of another we need local alternative hypotheses that decrease to the null at a slower rate than the usual parametr...
• OPTIMAL RATES OF ENTROPY ESTIMATION OVER LIPSCHITZ BALLS AI翻译
  作者：Han, Yanjun; Jiao, Jiantao; Weissman, Tsachy; Wu, Yihong
  作者单位：Stanford University; University of California System; University of California Berkeley; Yale University
  摘要：We consider the problem of minimax estimation of the entropy of a density over Lipschitz balls. Dropping the usual assumption that the density is bounded away from zero, we obtain the minimax rates (n ln n.)(-s/(s+d)) + n(-1/2) for 0 < s <= 2 for densities supported on [0, 1](d), where s is the smoothness parameter and n is the number of independent samples. We generalize the results to densities with unbounded support: given an Orlicz functions Psi of rapid growth (such as the subexponential ...
• ASSESSMENT OF THE EXTENT OF CORROBORATION OF AN ELABORATE THEORY OF A CAUSAL HYPOTHESIS USING PARTIAL CONJUNCTIONS OF EVIDENCE FACTORS AI翻译
  作者：Karmakar, Bikram; Small, Dylan S.
  作者单位：University of Pennsylvania
  摘要：An elaborate theory of predictions of a causal hypothesis consists of several falsifiable statements derived from the causal hypothesis. Statistical tests for the various pieces of the elaborate theory help to clarify how much the causal hypothesis is corroborated. In practice, the degree of corroboration of the causal hypothesis has been assessed by a verbal description of which of the several tests provides evidence for which of the several predictions. This verbal approach can miss quantita...