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作者：Yan, Ting; Leng, Chenlei; Zhu, Ji
作者单位：Central China Normal University; University of Warwick; University of Michigan System; University of Michigan
摘要：Although asymptotic analyses of undirected network models based on degree sequences have started to appear in recent literature, it remains an open problem to study statistical properties of directed network models. In this paper, we provide for the first time a rigorous analysis of directed exponential random graph models using the in-degrees and out-degrees as sufficient statistics with binary as well as continuous weighted edges. We establish the uniform consistency and the asymptotic norma...
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作者：Petersen, Alexander; Mueller, Hans-Georg
作者单位：University of California System; University of California Davis
摘要：Functional data that are nonnegative and have a constrained integral can be considered as samples of one-dimensional density functions. Such data are ubiquitous. Due to the inherent constraints, densities do not live in a vector space and, therefore, commonly used Hilbert space based methods of functional data analysis are not applicable. To address this problem, we introduce a transformation approach, mapping probability densities to a Hilbert space of functions through a continuous and inver...
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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：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：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...
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作者：Patschkowski, Tim; Rohde, Angelika
作者单位：Ruhr University Bochum
摘要：A scheme for locally adaptive bandwidth selection is proposed which sensitively shrinks the bandwidth of a kernel estimator at lowest density regions such as the support boundary which are unknown to the statistician. In case of a Holder continuous density, this locally minimax-optimal bandwidth is shown to be smaller than the usual rate, even in case of homogeneous smoothness. Some new type of risk bound with respect to a density-dependent standardized loss of this estimator is established. T...
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作者：Song, Rui; Banerjee, Moulinath; Kosorok, Michael R.
作者单位：North Carolina State University; University of Michigan System; University of Michigan; University of North Carolina; University of North Carolina Chapel Hill; University of North Carolina; University of North Carolina Chapel Hill
摘要：Change-point models are widely used by statisticians to model drastic changes in the pattern of observed data. Least squares/maximum likelihood based estimation of change-points leads to curious asymptotic phenomena. When the change-point model is correctly specified, such estimates generally converge at a fast rate (n) and are asymptotically described by minimizers of a jump process. Under complete mis-specification by a smooth curve, that is, when a change-point model is fitted to data descr...
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作者：Kneip, Alois; Poss, Dominik; Sarda, Pascal
作者单位：University of Bonn; University of Bonn; University of Bonn; Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Universite Federale Toulouse Midi-Pyrenees (ComUE); Institut National des Sciences Appliquees de Toulouse; Centre National de la Recherche Scientifique (CNRS)
摘要：The paper considers functional linear regression, where scalar responses Y1,..., Yn are modeled in dependence of i.i.d. random functions X1,..., Xn. We study a generalization of the classical functional linear regression model. It is assumed that there exists an unknown number of points of impact, that is, discrete observation times where the corresponding functional values possess significant influences on the response variable. In addition to estimating a functional slope parameter, the prob...
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作者：Sherwood, Ben; Wang, Lan
作者单位：Johns Hopkins University; University of Minnesota System; University of Minnesota Twin Cities
摘要：We consider a flexible semiparametric quantile regression model for analyzing high dimensional heterogeneous data. This model has several appealing features: (1) By considering different conditional quantiles, we may obtain a more complete picture of the conditional distribution of a response variable given high dimensional covariates. (2) The sparsity level is allowed to be different at different quantile levels. (3) The partially linear additive structure accommodates nonlinearity and circum...
