【latex版】水贴

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。