Modeling Persistent Trends in Distributions

We present a nonparametric framework to model a short sequence of probability distributions that vary both due to underlying effects of sequential progression and confounding noise. To distinguish between these two types of variation and estimate the sequential-progression effects, our approach leverages an assumption that these effects follow a persistent trend. This work is motivated by the recent rise of single-cell RNA-sequencing experiments over a brief time course, which aim to identify genes relevant to the progression of a particular biological process across diverse cell populations. While classical statistical tools focus on scalar-response regression or order-agnostic differences between distributions, it is desirable in this setting to consider both the full distributions as well as the structure imposed by their ordering. We introduce a new regression model for ordinal covariates where responses are univariate distributions and the underlying relationship reflects consistent changes in the distributions over increasing levels of the covariate. This concept is formalized as a "trend" in distributions, which we define as an evolution that is linear under the Wasserstein metric. Implemented via a fast alternating projections algorithm, our method exhibits numerous strengths in simulations and analyses of single-cell gene expression data.Comment: To appear in: Journal of the American Statistical Associatio

Exports and sectoral financial dependence: evidence on French firms during the great global crisis

The unprecedented drop in international trade during the last quarter of 2008 and the first quarter of 2009 has mainly been analysed at the macroeconomic or sectoral level. However, exporters who are heterogeneous in terms of productivity, size or external financial dependence should be heterogeneously affected by the crisis. This issue is examined in this paper by using data on monthly exports at the product and destination level for some 100,000 individual French exporters, up to 2009M4. We show that the drop in French exports is mainly due to the intensive margin of large exporters. Small and large exporters are evenly affected when sectoral and geographical specialisations are controlled for. Lastly, exporters (small and large) in sectors structurally more dependent on external finance are the most affected by the crisis. JEL Classification: F02, F10, G01financial crisis, firms’ heterogeneity, intensive and extensive margins, international trade

Firms and the global crisis: French exports in the turmoil.

The unprecedented drop in international trade during the last quarter of 2008 and the first quarter of 2009 has mostly been analysed at the macroeconomic or sectoral level. However, heterogeneous exporters in terms of productivity, size or external finance dependence should be hit differently by the crisis. This issue is examined here using data on monthly exports at the product and destination level for some 100,000 individual French exporters, up to 2009M4. We show that the drop in French exports is mainly due to the intensive margin of large exporters. Small and large firms are evenly affected when sectoral and geographical specialisations are controlled for. Lastly, firms (small and large) in sectors structurally more dependent on external finance are the most affected by the crisis.Financial crisis , international trade , firms heterogeneity , intensive and extensive margins.