【latex版】水贴

In this paper, we deal with the data-driven selection of multidimensional and possibly anisotropic bandwidths in the general framework of kernel empirical risk minimization. We propose a universal selection rule, which leads to optimal adaptive results in a large variety of statistical models such as nonparametric robust regression and statistical learning with errors in variables. These results are stated in the context of smooth loss functions, where the gradient of the risk appears as a good criterion to measure the performance of our estimators. The selection rule consists of a comparison of gradient empirical risks. It can be viewed as a nontrivial improvement of the so-called Goldenshluger–Lepski method to nonlinear estimators. Furthermore, one main advantage of our selection rule is the nondependency on the Hessian matrix of the risk, usually involved in standard adaptive procedures.

In this paper, we deal with the data-driven selection of multidimensional and possibly anisotropic bandwidths in the general framework of kernel empirical risk minimization. We propose a universal selection rule, which leads to optimal adaptive results in a large variety of statistical models such as nonparametric robust regression and statistical learning with errors in variables. These results are stated in the context of smooth loss functions, where the gradient of the risk appears as a good criterion to measure the performance of our estimators. The selection rule consists of a comparison of gradient empirical risks. It can be viewed as a nontrivial improvement of the so-called Goldenshluger–Lepski method to nonlinear estimators. Furthermore, one main advantage of our selection rule is the nondependency on the Hessian matrix of the risk, usually involved in standard adaptive procedures.

This paper considers the problem of defining distributions over graphical structures. We propose an extension of the hyper Markov properties of Dawid and Lauritzen [ Ann. Statist. 21 (1993) 1272–1317], which we term structural Markov properties , for both undirected decomposable and directed acyclic graphs, which requires that the structure of distinct components of the graph be conditionally independent given the existence of a separating component. This allows the analysis and comparison of multiple graphical structures, while being able to take advantage of the common conditional independence constraints. Moreover, we show that these properties characterise exponential families, which form conjugate priors under sampling from compatible Markov distributions.

In this article, we study a partially linear single-index model for longitudinal data under a general framework which includes both the sparse and dense longitudinal data cases. A semiparametric estimation method based on a combination of the local linear smoothing and generalized estimation equations (GEE) is introduced to estimate the two parameter vectors as well as the unknown link function. Under some mild conditions, we derive the asymptotic properties of the proposed parametric and nonparametric estimators in different scenarios, from which we find that the convergence rates and asymptotic variances of the proposed estimators for sparse longitudinal data would be substantially different from those for dense longitudinal data. We also discuss the estimation of the covariance (or weight) matrices involved in the semiparametric GEE method. Furthermore, we provide some numerical studies including Monte Carlo simulation and an empirical application to illustrate our methodology and theory.

Random forests are a learning algorithm proposed by Breiman [ Mach. Learn. 45 (2001) 5–32] that combines several randomized decision trees and aggregates their predictions by averaging. Despite its wide usage and outstanding practical performance, little is known about the mathematical properties of the procedure. This disparity between theory and practice originates in the difficulty to simultaneously analyze both the randomization process and the highly data-dependent tree structure. In the present paper, we take a step forward in forest exploration by proving a consistency result for Breiman’s [ Mach. Learn. 45 (2001) 5–32] original algorithm in the context of additive regression models. Our analysis also sheds an interesting light on how random forests can nicely adapt to sparsity.

We propose a roughness regularization approach in making nonparametric inference for generalized functional linear models. In a reproducing kernel Hilbert space framework, we construct asymptotically valid confidence intervals for regression mean, prediction intervals for future response and various statistical procedures for hypothesis testing. In particular, one procedure for testing global behaviors of the slope function is adaptive to the smoothness of the slope function and to the structure of the predictors. As a by-product, a new type of Wilks phenomenon [ Ann. Math. Stat. 9 (1938) 60–62; Ann. Statist. 29 (2001) 153–193] is discovered when testing the functional linear models. Despite the generality, our inference procedures are easy to implement. Numerical examples are provided to demonstrate the empirical advantages over the competing methods. A collection of technical tools such as integro-differential equation techniques [ Trans. Amer. Math. Soc. (1927) 29 755–800; Trans. Amer. Math. Soc. (1928) 30 453–471; Trans. Amer. Math. Soc. (1930) 32 860–868], Stein’s method [ Ann. Statist. 41 (2013) 2786–2819] [Stein, Approximate Computation of Expectations (1986) IMS] and functional Bahadur representation [ Ann. Statist. 41 (2013) 2608–2638] are employed in this paper.

加州劳工委员会(California Labor Commission)裁定，优步(Uber)司机应属于员工，而不是独立的承包商。该裁定可能会对按需经济造成重大影响。

UNHCR annual global trends survey finds a record 59.5m people were refugees, internally displaced or seeking asylum by the end of 2014

War, violence and persecution left one in every 122 humans on the planet a refugee, internally displaced or seeking asylum at the end of last year, according to a stark UN report that warns the world is failing the victims of an “age of unprecedented mass displacement”.

The annual global trends study by the UN’s refugee agency, UNHCR, finds that the level of worldwide displacement is higher than ever before, with a record 59.5 million people living exiled from their homes at the end of 2014.

From Beyoncé’s I Was Here video to #Kony2012, online campaigns are everywhere, shared in their millions. But does technology really amplify our humanity or is it all meaningless clicktivism? Warscapes reports

In the past, if you wanted to help out in times of tragedy you might travel to disaster zones or volunteer with a charity. But with the growth of online campaigning, the internet appears to offer the opportunity to change the world without leaving your lounge.

From Facebook to games and viral pop songs, digital initiatives reassure us that we don’t need to look up from our laptops or phones to help others in their time of need.

晚上，班主任查宿舍，突然发现墙角有几个烟头。

　班主任：来福，你作为宿舍长，老实告诉我，是谁偷偷抽烟了？

　来福：老师，其实，那些烟头是您这几天查宿舍时，抽完扔掉的。

　班主任脸上一红，随即镇定下来

　说：哦，我明白了，原来这几天你就没有安排打扫卫生啊！你作为宿舍长，现在罚你操场 跑 3000米！

　来福：……