Analysis of Double Single Index Models

ABSTRACT. Motivated from problems in canonical correlation analysis, reduced rank regression
and sufficient dimension reduction, we introduce a double dimension reduction model where a single
index of the multivariate response is linked to the multivariate covariate through a single index of
these covariates, hence the name double single index model. Because nonlinear association between
two sets of multivariate variables can be arbitrarily complex and even intractable in general, we
aim at seeking a principal one-dimensional association structure where a response index is fully
characterized by a single predictor index. The functional relation between the two single-indices is
left unspecified, allowing flexible exploration of any potential nonlinear association. We argue that
such double single index association is meaningful and easy to interpret, and the rest of the multidimensional
dependence structure can be treated as nuisance in model estimation. We investigate
the estimation and inference of both indices and the regression function, and derive the asymptotic
properties of our procedure. We illustrate the numerical performance in finite samples and demonstrate
the usefulness of the modelling and estimation procedure in a multi-covariate multi-response
problem concerning concrete.

Motivated from problems in canonical correlation analysis, reduced rank regression
and sufficient dimension reduction, we introduce a double dimension reduction model where a single
index of the multivariate response is linked to the multivariate covariate through a single index of
these covariates, hence the name double single index model.

Motivated from problems in canonical correlation analysis, reduced rank regression
and sufficient dimension reduction, we introduce a double dimension reduction model where a single
index of the multivariate response is linked to the multivariate covariate through a single index of
these covariates, hence the name double single index model.

Motivated from problems in canonical correlation analysis, reduced rank regression
and sufficient dimension reduction, we introduce a double dimension reduction model where a single
index of the multivariate response is linked to the multivariate covariate through a single index of
these covariates, hence the name double single index model.

This paper proposes an easy-to-use nonparametric indicator for club convergence, or convergence within clusters of countries: it measures whether the modes of the gross domestic product (GDP) per capita distribution become more pronounced over time. Relying on changes in the critical bandwidth for unimodality, the indicator is a dynamic extension of concepts from often-used multimodality tests. Its evolution suggests the new empirical result of a ‘millennium peak’ in club convergence in the worldwide GDP per capita distribution. The club convergence movements of the 1980s and 1990s, when groups of poor and rich countries converged to two separate points, was followed by a de-clubbing movement after the turn of the millennium. Copyright © 2016 John Wiley & Sons, Ltd.

This paper proposes an easy-to-use nonparametric indicator for club convergence, or convergence within clusters of countries: it measures whether the modes of the gross domestic product (GDP) per capita distribution become more pronounced over time. Relying on changes in the critical bandwidth for unimodality, the indicator is a dynamic extension of concepts from often-used multimodality tests. I

proposes an easy-to-use nonparametric indicator

8月26日：

1768年英國探險家詹姆斯·庫克率領皇家努力號帆船在英國普利茅斯起航，開始首次遠征。 1972年第20屆夏季奧林匹克運動會在聯邦德國慕尼黑奧林匹克體育場開幕。 1978年教宗選舉後正式選出的若望·保祿一世繼任保祿六世的教宗一職。 1999年美國運動員麥可·詹森（圖）在西班牙塞維亞舉行的世界田徑錦標賽上以43秒18打破男子400米世界紀錄。 2008年在南奧塞提亞戰爭達成停火協議1個多禮拜後，俄羅斯承認阿布哈茲與南奧塞提亞已經獲得獨立。

"山有木兮木有枝，心悦君兮君不知？" —— 说的是暗恋中的你，辗转反侧，求而不得。

"君生我未生，我生君已老。" —— 动了情，才会觉得委屈和遗憾。

"巧笑倩兮，美目盼兮。" —— 热恋中的你，眼中她的模样。

"人生若只如初见，何事秋风悲画扇？" —— 失恋的你，因弃起怨。

成瘾 = 一种重复性的强迫行为 = 生理上的依赖症 或 心理上的依赖症

拥有人类学背景的海伦·费雪（Helen Fisher）教授，坚信爱情作为世上最有力的感情，一定在大脑中有所表征。在2008年的TED演讲中，她说起了当年决定从事大脑和爱情关系的研究的心路历程。（此处有传送门：Helen Fisher studies the brain in love)）

在她团队发表的磁共振脑成像研究中，第一次定位了大脑的“爱情区” —— 腹侧背盖区 (Ventral Tegmental Area)。腹侧背盖区中活跃的ApEn细胞制造了多巴胺—— 脑中的神经递质，使人快乐 —— 并将它散发到大脑的众多区域。　

一个抄袭者，就不能称其为作者。抄袭者是整个行业的耻辱。
撇开这第一条，我们才能认真说一下基本品质。

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"Do not speak of your happiness to one less fortunate than yourself."

"You have a choice in this world, I believe, about how to tell sad stories."

"Works of imagination should be written in very plain language; the more purely imaginative they are the more necessary it is to be plain."

"I don't know how to have casual conversation. You think you're talking about one thing, and either you are and it's incredibly boring, or you're not because it's subtext and you need a decoder ring."

"For me, words are a form of action, capable of influencing change."

"I've always tried to go a step past wherever people expected me to end up."

"Always bear in mind that your own resolution to succeed is more important than any one thing."

"Blaze with the fire that is never extinguished."

"The only good is knowledge and the only evil is ignorance."

畅Ｔｈｅ ｂｕｒｄｅｎ ｏｆ ａｉｒ ｐｏｌｌｕｔｉｏｎ ｏｎ ｙｅａｒｓ ｏｆ ｌｉｆｅ ｌｏｓｔ ｉｎ Ｂｅｉｊｉｎｇ

Spatial and temporal variability of PM 2.5 and PM 10 over the North China Plain and the Yangtze River Delta, China

"Results! Why, man, I have gotten a lot of results. I know several thousand things that won't work."