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A rich theory of production and analysis of productive eciency has developed since pioneering work by Koopmans (1951) and Debreu (1951). Farrell (1957) is the earliest published empirical study, and appeared in a statistical journal (JRSS), even though Farrell provided no statistical theory. The literature in econometrics, management sciences, operations research and mathematical statistics has since been enriched by hundreds of papers trying to develop or implement new tools for analyzing productivity and efficiency of firms. Both parametric and nonparametric approaches have been proposed. The mathematical challenge is to derive estimators of production, cost, revenue,or profit frontiers which represent, in the case of production frontiers, the optimal loci of combinations of inputs (like labor, energy, capital, etc.) and outputs (the products or services produced by the firms). Optimality is defined in terms of various economic considerations. Then the efficiency of a particular unit is measured by its distance to the estimated frontier. The statistical problem can be viewed as the problem of estimating the support of a multivariate random variable, subject to some shape constraints, in multiple dimensions. These techniques are applied in thousands of papers in the economic and business literature. This "Guided Tour" reviews the development of various nonparametric approaches since the early work of Farrell. Remaining challenges and open issues in this challenging arena are also described.

Productivity catching-up among countries has been an important topic of interest for many researchers. In particular, one is willing to see how the productivity of countries evolves over time and how exogenous factors may influence the process. Many studies have analyzed the effect of Foreign Direct Investment (FDI) on catching-up over time, many by using restrictive parametric models. We use an appropriate nonparametric two-step approach on conditional efficiencies to investigate how FDI and time affect the process. By using a dataset of 44 countries over 1970-2007, we explore the channels under which FDI fosters productivity by disentangling the impact of this factor on production process and its components: impact on the attainable production set (input-output space), and the impact on the distribution of efficiencies. We extend existing methodological tools - conditional nonparametric efficiency measures - to examine these interrelationships. We emphasize the usefulness of smoothing over time to better analyze the potential dynamic influence of FDI on efficiency. We find that both FDI and time play an important role as influencing efficiency distribution and affecting, to a smaller extend, the production set. This effect of FDI does not seem to vary much over time. By the second stage nonparametric regression of the conditional efficiencies over FDI and time we identify clearly effect of time and FDI on conditional efficiency and we determine idiosyncratic efficiency, which represents ”Solow residual”, measured by looking to the unexplained part of the conditional efficiencies. By doing so, we are able to rank the productivity of countries at each time period, or on the average, when facing different environmental conditions.

In this study, we merge results of two recent directions in efficiency analysis research-aggregation and bootstrap-applied, as an example, to one of the most popular point estimators of individual efficiency: the data envelopment analysis (DEA) estimator. A natural context of the methodology developed here is a study of efficiency of a particular economic system (e.g., an industry) as a whole, or a comparison of efficiencies of distinct groups within such a system (e.g., regulated vs. non-regulated firms or private vs. public firms). Our methodology is justified by the (neoclassical) economic theory and is supported by carefully adapted statistical methods. Copyright 2007 John Wiley & Sons, Ltd.

Using monoclonal anti-trinitrophenyl (TNP) antibodies complexed to TNP-myoglobin-coated gold particles, we analysed at the ultrastructural level the retention by follicular dendritic cells (FDC) of immune complexes containing various antibody isotypes. Gold-labelled immune complexes were injected subcutaneously or intravenously into naive mice and, after 24 h, germinal centres of draining lymph nodes or spleen were examined by electron microscopy. FDC generally retained complexes containing IgG2a and IgG2b better than those formed with IgG1 or IgG3. IgM was rarely retained. FDC isolated from lymph nodes or spleens were incubated in vitro with gold-labelled complexes in a serum-free medium. IgG2a and IgG2b complexes were also retained in vitro in large quantities by FDC; IgG1 and IgG3 complexes were retained in smaller quantities or in highly variable quantities compared with IgG2; IgM complexes were rarely seen on FDC. There was no difference between FDC isolated from lymph nodes or from spleen with respect to the Ig isotypes required for Fc-mediated retention of immune complexes.

Regression models are introduced in the framework of Bayesian cuts (see, for example, Florens and Mouchart, 1977). It is well known that once the prior distribution is not natural-conjugate or the sampling process is non-normal, the computation of the posterior distribution may rapidly become intractable. This involves the temptation of specifying simplistic models in order to keep control on the tractability. Examples of these complications are well known when introducing fat-tails distributions in order to treat outliers or when facing asymmetrically distributed residuals. When the main interest lies in the computation of the posterior expectations of the parameters, we show that Least-Squares (L.S.) approximations allows one to render tractable those nonstandard models. This suggests that approximate solutions to reasonable models may be attractive alternatives to the exact solution to simplified models. The Least-Squares approximations may be interpreted in the framework of a normal approximation to the joint distribution of parameters and observations. This suggests that their practical relevance will crucially depend on the choice of co-ordinates. This note handles that choice in the field of regression models. In this paper the main emphasis is on parameter estimation (i.e. approximation of the posterior expectations of the parameter) while Goldstein (1976) uses similar tools to concentrate on predictions and de Vylder (1982) pays particular attention to restricted covariance matrices in the context of credibility theory. In Section 2 we introduce the basic model. Then in Section 3 we present our L.S. approximations trying to take advantage of the use of unbiased estimators, while in Section 4 we consider the particular case of singular covariance matrices.

The aim of the paper is to present a statistical methodology allowing the estimation of technical performances of production units within a particular sector of activities. The approach is such that it allows the introduction of exogenous environmental factors explaining a part of the apparent inefficiency. The statistical procedure will be based on the observation of production activities of a set of firms. The method is illustrated through the analysis of technical efficiencies of railway companies.