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We derive a Gaussian approximation result for the maximum of a sum of high dimensional random vectors. Specifically, we establish conditions under which the distribution of the maximum is approximated by that of the maximum of a sum of the Gaussian random vectors with the same covariance matrices as the original vectors. This result applies when the(More)
We develop a new direct approach to approximating suprema of general empirical processes by a sequence of suprema of Gaussian processes, without taking the route of approximating whole empirical processes in the supremum norm. We prove an abstract approximation theorem that is applicable to a wide variety of problems, primarily in statistics. In particular,(More)
Slepian and Sudakov-Fernique type inequalities, which compare expectations of maxima of Gaussian random vectors under certain restrictions on the covariance matrices, play an important role in probability theory, especially in empirical process and extreme value theories. Here we give explicit comparisons of expectations of smooth functions and distribution(More)
Many economic models yield conditional moment inequalities that can be used for inference on parameters of these models. In this paper, I construct a new test of conditional moment inequalities based on studentized kernel estimates of moment functions. The test automatically adapts to the unknown smoothness of the moment functions, has uniformly correct(More)
We study the degrees of freedom in shrinkage estimation of the regression coefficients. Generalizing the idea of the Lasso, we consider the problem of estimating the coefficients by the projection of the ordinary least squares estimator onto a closed convex set. Then an unbiased estimator of the degrees of freedom is derived in terms of geometric quantities(More)
Modern construction of uniform confidence bands for nonparametric densities (and other functions) often relies on the the classical Smirnov-Bickel-Rosenblatt (SBR) condition; see, for example, Giné and Nickl (2010). This condition requires the existence of a limit distribution of an extreme value type for the supremum of a studentized empirical process(More)
This work proposes new inference methods for the estimation of a regression coefficient<lb>of interest in quantile regression models. We consider high-dimensional models where the number of<lb>regressors potentially exceeds the sample size but a subset of them suffice to construct a reasonable<lb>approximation of the unknown quantile regression function in(More)
This paper develops a uniform test of linearity against thresholds effects in the quantile regression framework. The test is based on the supremum of the Wald process over the space of quantile and threshold parameters. We establish the asymptotic null distribution of the test statistic for stationary weakly dependent processes, and propose a simulation(More)
To investigate the effect of an antioxidant edaravone on the apoptotic process, we examined Bax and Bcl-2 immunohistochemical expression and terminal deoxynucleotidyl transferase-mediated dUTP-biotin nick end labeling (TUNEL) reactivity. Rat focal ischemia models were prepared by 2 h transient middle cerebral artery occlusion. Edaravone or physiological(More)
We have found previously that human plasma-membrane-associated sialidase (NEU3), a key glycosidase for ganglioside degradation, was markedly up-regulated in human colon cancers, with an involvement in suppression of apoptosis. To elucidate the molecular mechanisms underlying increased NEU3 expression, in the present study we investigated its role in cell(More)