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作者：Bai, Zhidong; Choi, Kwok Pui; Fujikoshi, Yasunori
作者单位：Northeast Normal University - China; Northeast Normal University - China; National University of Singapore; Hiroshima University
摘要：In this paper, we derive the asymptotic joint distributions of the eigenvalues under the null case and the local alternative cases in the MANOVA model and multiple discriminant analysis when both the dimension and the sample size are large. Our results are obtained by random matrix theory (RMT) without assuming normality in the populations. It is worth pointing out that the null and nonnull distributions of the eigenvalues and invariant test statistics are asymptotically robust against departu...
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作者：Paparoditis, Efstathios
作者单位：University of Cyprus
摘要：A bootstrap procedure for functional time series is proposed which exploits a general vector autoregressive representation of the time series of Fourier coefficients appearing in the Karhunen Loeve expansion of the functional process. A double sieve-type bootstrap method is developed, which avoids the estimation of process operators and generates functional pseudo time series that appropriately mimics the dependence structure of the functional time series at hand. The method uses a finite set ...
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作者：Berghaus, Betina; Buecher, Axel
作者单位：Ruhr University Bochum
摘要：The extremes of a stationary time series typically occur in clusters. A primary measure for this phenomenon is the extremal index, representing the reciprocal of the expected cluster size. Both disjoint and sliding blocks estimator for the extremal index are analyzed in detail. In contrast to many competitors, the estimators only depend on the choice of one parameter sequence. We derive an asymptotic expansion, prove asymptotic normality and show consistency of an estimator for the asymptotic ...
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作者：Molina, Isabel; Martin, Nirian
作者单位：Universidad Carlos III de Madrid; Complutense University of Madrid
摘要：In regression models involving economic variables such as income, log transformation is typically taken to achieve approximate normality and stabilize the variance. However, often the interest is predicting individual values or means of the variable in the original scale. Under a nested error model for the log transformation of the target variable, we show that the usual approach of back transforming the predicted values may introduce a substantial bias. We obtain the optimal (or best) predict...
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作者：Shi, Chengchun; Fan, Ailin; Song, Rui; Lu, Wenbin
作者单位：North Carolina State University
摘要：Precision medicine is a medical paradigm that focuses on finding the most effective treatment decision based on individual patient information. For many complex diseases, such as cancer, treatment decisions need to be tailored over time according to patients' responses to previous treatments. Such an adaptive strategy is referred as a dynamic treatment regime. A major challenge in deriving an optimal dynamic treatment regime arises when an extraordinary large number of prognostic factors, such...
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作者：Chan, Kwun Chuen Gary; Ling, Hok Kan; Sit, Tony; Yam, Sheung Chi Phillip
作者单位：University of Washington; University of Washington Seattle; Columbia University; Chinese University of Hong Kong
摘要：We study the nonparametric estimation of a decreasing density function go in a general s-sample biased sampling model with weight (or bias) functions w(i )for i = 1, ...,s. The determination of the monotone maximum likelihood estimator (g) over cap (n) and its asymptotic distribution, except for the case when s = 1, has been long missing in the literature due to certain nonstandard structures of the likelihood function, such as nonseparability and a lack of strictly positive second order deriv...
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作者：Gao, Chao; Ma, Zongming; Zhang, Anderson Y.; Zhou, Harrison H.
作者单位：University of Chicago; University of Pennsylvania; Yale University
摘要：Community detection is a central problem of network data analysis. Given a network, the goal of community detection is to partition the network nodes into a small number of clusters, which could often help reveal interesting structures. The present paper studies community detection in Degree-Corrected Block Models (DCBMs). We first derive asymptotic minimax risks of the problem for a misclassification proportion loss under appropriate conditions. The minimax risks are shown to depend on degree...
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作者：Chakrabortty, Abhishek; Cai, Tianxi
作者单位：University of Pennsylvania; Harvard University
摘要：We consider the linear regression problem under semi-supervised settings wherein the available data typically consists of: (i) a small or moderate sized labeled data, and (ii) a much larger sized unlabeled data. Such data arises naturally from settings where the outcome, unlike the covariates, is expensive to obtain, a frequent scenario in modern studies involving large databases like electronic medical records (EMR). Supervised estimators like the ordinary least squares (OLS) estimator utiliz...
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作者：Gao, Fuqing; Xiong, Jie; Zhao, Xingqiu
作者单位：Wuhan University; University of Macau; Hong Kong Polytechnic University
摘要：This paper considers self-normalized limits and moderate deviations of nonparametric maximum likelihood estimators for monotone functions. We obtain their self-normalized Cramer-type moderate deviations and limit distribution theorems for the nonparametric maximum likelihood estimator in the current status model and the Grenander-type estimator. As applications of the results, we present a new procedure to construct asymptotical confidence intervals and asymptotical rejection regions of hypoth...
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作者：Wu, Weichi; Zhou, Zhou
作者单位：University of London; University College London; University of Toronto
摘要：We consider structural change testing for a wide class of time series M-estimation with nonstationary predictors and errors. Flexible predictor-error relationships, including exogenous, state-heteroscedastic and autoregressive regressions and their mixtures, are allowed. New uniform Bahadur representations are established with nearly optimal approximation rates. A CUSUMtype test statistic based on the gradient vectors of the regression is considered. In this paper, a simple bootstrap method is...
