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作者：Bull, Adam D.
作者单位：University of Cambridge
摘要：In quantitative finance, we often model asset prices as semimartingales, with drift, diffusion and jump components. The jump activity index measures the strength of the jumps at high frequencies, and is of interest both in model selection and fitting, and in volatility estimation. In this paper, we give a novel estimate of the jump activity, together with corresponding confidence intervals. Our estimate improves upon previous work, achieving near-optimal rates of convergence, and good finite-s...
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作者：Dong, Chaohua; Gao, Jiti; Tjostheim, Dag
作者单位：Southwestern University of Finance & Economics - China; Monash University; University of Bergen
摘要：Estimation mainly for two classes of popular models, single-index and partially linear single-index models, is studied in this paper. Such models feature nonstationarity. Orthogonal series expansion is used to approximate the unknown integrable link functions in the models and a profile approach is used to derive the estimators. The findings include the dual rate of convergence of the estimators for the single-index models and a trio of convergence rates for the partially linear single-index m...
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作者：Drees, Holger; Rootzen, Holger
作者单位：University of Hamburg; Chalmers University of Technology; University of Gothenburg
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作者：Yang, Yun; Dunson, David B.
作者单位：University of California System; University of California Berkeley; Duke University
摘要：There is increasing interest in the problem of nonparametric regression with high-dimensional predictors. When the number of predictors D is large, one encounters a daunting problem in attempting to estimate a D-dimensional surface based on limited data. Fortunately, in many applications, the support of the data is concentrated on a d-dimensional subspace with d << D. Manifold learning attempts to estimate this subspace. Our focus is on developing computationally tractable and theoretically su...
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作者：Le, Can M.; Levina, Elizaveta; Vershynin, Roman
作者单位：University of Michigan System; University of Michigan; University of Michigan System; University of Michigan
摘要：Community detection is one of the fundamental problems of network analysis, for which a number of methods have been proposed. Most model-based or criteria-based methods have to solve an optimization problem over a discrete set of labels to find communities, which is computationally infeasible. Some fast spectral algorithms have been proposed for specific methods or models, but only on a case-by-case basis. Here, we propose a general approach for maximizing a function of a network adjacency mat...
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作者：Akritas, Michael G.
作者单位：Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park
摘要：For a response variable Y, and a d dimensional vector of covariates X, the first projective direction, V, is defined as the direction that accounts for the most variability in Y. The asymptotic distribution of an estimator of a trimmed version of V has been characterized only under the assumption of the single index model (SIM). This paper proposes the use of a flexible trimming function in the objective function, which results in the consistent estimation of V. It also derives the asymptotic ...
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作者：Fissler, Tobias; Ziegel, Johanna F.
作者单位：University of Bern
摘要：A statistical functional, such as the mean or the median, is called elicitable if there is a scoring function or loss function such that the correct forecast of the functional is the unique minimizer of the expected score. Such scoring functions are called strictly consistent for the functional. The elicitability of a functional opens the possibility to compare competing forecasts and to rank them in terms of their realized scores. In this paper, we explore the notion of elicitability for mult...
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作者：Joseph, Antony; Yu, Bin
作者单位：University of California System; University of California Berkeley
摘要：The performance of spectral clustering can be considerably improved via regularization, as demonstrated empirically in Amini et al. [Ann. Statist. 41 (2013) 2097-2122]. Here, we provide an attempt at quantifying this improvement through theoretical analysis. Under the stochastic block model (SBM), and its extensions, previous results on spectral clustering relied on the minimum degree of the graph being sufficiently large for its good performance. By examining the scenario where the regulariza...
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作者：Perchet, Vianney; Rigollet, Philippe; Chassang, Sylvain; Snowberg, Erik
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris Cite; Sorbonne Universite; Inria; Massachusetts Institute of Technology (MIT); Massachusetts Institute of Technology (MIT); Princeton University; California Institute of Technology; National Bureau of Economic Research
摘要：Motivated by practical applications, chiefly clinical trials, we study the regret achievable for stochastic bandits under the constraint that the employed policy must split trials into a small number of batches. We propose a simple policy, and show that a very small number of batches gives close to minimax optimal regret bounds. As a byproduct, we derive optimal policies with low switching cost for stochastic bandits.
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作者：Fan, Jianqing; Liao, Yuan; Wang, Weichen
作者单位：Princeton University; University System of Maryland; University of Maryland College Park
摘要：This paper introduces a Projected Principal Component Analysis (Projected-PCA), which employs principal component analysis to the projected (smoothed) data matrix onto a given linear space spanned by covariates. When it applies to high-dimensional factor analysis, the projection removes noise components. We show that the unobserved latent factors can be more accurately estimated than the conventional PCA if the projection is genuine, or more precisely, when the factor loading matrices are rela...
