Asymptotic Forms of Hermite Polynomials

The asymptotic behavior of Hermite polynomials, H_n, (z), as n → ∞ has been investigated by several authors. The results previous to 1939, among which probably the best known are those of Plancherel and Rotach [8], are summarized in G. Szegö: Orthogonal Polynomials [10]. Some of the newer results are due to J. C. P. Miller [7], L. O. Heflinger [4] and M. Wyman. Since Hermite polynomials are special parabolic cylinder functions, attention should also be called to the results obtained in the complex plane by A. Erdélyi, M. Kennedy and J. L. McGregor [2] and by N. D. Kazarinoff [5]

Relevance and Conditionals: A Synopsis of Open Pragmatic and Semantic Issues

Recently several papers have reported relevance effects on the cognitive assessments of indicative conditionals, which pose an explanatory challenge to the Suppositional Theory of conditionals advanced by David Over, which is influential in the psychology of reasoning. Some of these results concern the “Equation” (P(if A, then C) = P(C|A)), others the de Finetti truth table, and yet others the uncertain and-to-inference task. The purpose of this chapter is to take a Birdseye view on the debate and investigate some of the open theoretical issues posed by the empirical results. Central among these is whether to count these effects as belonging to pragmatics or semantics

Meta-analysis is a powerful tool to summarize variety mixture effects - exemplified by grain yield and weed suppression of spring barley

In a new project, we aim to increase the general understanding of the power of meta-analysis to combine existing experimental results on variety mixtures. In this way, explanatory power can be increased compared to separate analyses and overall measures and relationships may be revealed. We will thus pursue to uncover a number of critical issues, including the relative importance of various traits and trait combinations on mixing success. To demonstrate the methods of meta-analysis applicable for variety mixture data, we considered a data set consisting of grain yield and weed ground cover assessments in 16 field trials of six 3-component variety mixtures and their components (part of the Danish BAR-OF field trials). The effects of mixing were analysed separately for each field trial and the results used in a meta-analysis in combination with their standard errors. We also analysed the mixing effects of each mixture by fitting a linear model to the entire data set. Both methods showed an overall positive mixing effect on grain yield and a trend for less weed to be found in variety mixtures. Finally, strengths and shortcomings of the methods are highlighted

Yield of spring barley mixtures as a function of varietal and environmental characteristics

To design good variety mixtures it is important to understand the influence of varietal and environmental characteristics on mixing effect, e.g. what characteristics are more beneficial when all mixed varieties express it highly and what characteristics are more beneficial when the mixed varieties express it to varying extent. However, as it is generally impossible to manage more than a few experimental combinations in each field trial, information on general relationships and factors of importance for the successful design of variety mixtures may be overlooked. Using meta-regression (e.g. Houwelingen et al. 2002), numerous results of such trials can be combined, and the influence of varietal and environmental factors on mixing effect can be elucidated. Here, two specific hypotheses were investigated: 1. Variation in straw length among component varieties will increase mixing effect due to enhanced potential for resource utilization. 2. Mixing effect will increase with more stressful environments due to increased importance of mechanisms like complementarity and compensation. Meta-analyses with and without covariates were applied to test the hypotheses and elucidate factors of importance for mixing success. The simple meta-analysis showed significant overall increase in yield due to mixing of varieties in spite of slightly opposing results between individual trials. However, the meta-regressions were unable to support the two hypotheses: the mixing effect was not affected by component variation in straw length, and the mixing effect was slightly increasing with environmental yield potential, which was actually arguing against the hypothesis. Further analyses must be done to investigate whether these trends can be found in other data sets and whether further covariates may assist interpretation. The results also show that experimental trials with extraordinarily small experimental variation may influence the conclusions of the analysis. The excluded trial was performed at an experimental farm which is known to provide rather homogenous growing conditions. This information is not readily included in the current use of weighting. In the work to come, we will assess the appropriateness of the current application of inverse variance as weights in meta-analysis of field trial data. Other critical issues that need further investigation include the possible lack of independence between estimates due to shared environments and common component varieties of mixtures

Transformations for multivariate statistics

This paper derives transformations for multivariate statistics that eliminate asymptotic skewness, extending the results of Niki and Konishi (1986, Annals of the Institute of Statistical Mathematics 38, 371-383). Within the context of valid Edgeworth expansions for such statistics we first derive the set of equations that such a transformation must satisfy and second propose a local solution that is sufficient up to the desired order. Application of these results yields two useful corollaries. First, it is possible to eliminate the first correction term in an Edgeworth expansion, thereby accelerating convergence to the leading term normal approximation. Second, bootstrapping the transformed statistic can yield the same rate of convergence of the double, or prepivoted, bootstrap of Beran (1988, Journal of the American Statistical Association 83, 687-697), applied to the original statistic, implying a significant computational saving. The analytic results are illustrated by application to the family of exponential models, in which the transformation is seen to depend only upon the properties of the likelihood. The numerical properties are examined within a class of nonlinear regression models (logit, probit, Poisson, and exponential regressions), where the adequacy of the limiting normal and of the bootstrap (utilizing the k-step procedure of Andrews, 2002, Econometrica 70, 119-162) as distributional approximations is assessed

Effects of inter-varietal diversity, biotic stresses and environmental productivity on grain yield of spring barley variety mixtures

Varietal seed mixtures tend to increase and stabilize crop yields, yet their application is sparse. Large-scale cultivation of variety mixtures may require a better understanding of how inter-varietal interactions and their interaction with the environment may influence the grain yield of variety mixtures relative to their component varieties. For this purpose, six variety mixtures of spring barley and 14 component varieties were grown in each of 17 trial environments. A total of 28 observed and a priori plant characteristics, including grain yield, disease severity and weed competitiveness, were derived for each component variety in each trial. The relationship between inter-varietal diversity of each characteristic and the mixing effect on grain yield was analysed. Additionally, various types of yield stability were estimated and compared among mixtures and component varieties. One mixture out-yielded all of its component varieties in almost half of the trial environments. Inter-varietal diversity in grain yield potential correlated significantly with mixing effect, as did straw length diversity when weighted with weed pressure. The grain yields of most mixtures were more stable across environments than their component varieties when accounting also for the general response to environmental productivity. Hence, most mixtures adapted slightly better to environmental productivity and were less sensitive to environmental stress than their component varieties. We conclude that the efficacy of variety mixtures may be enhanced by mixing relatively high-yielding varieties differing in responsiveness to environmental productivity

Foreign Direct Investment in Times of Crisis

This paper compares the current foreign direct investment (FDI) recession with FDI responses to past economic crises. The authors find that although developed country outflows have taken an equally big hit as major developed countries have after past crises, outflows seem to be bouncing back more slowly this time. By contrast with the overall decline in recent years, inflows to emerging markets often remained stable during their past economic crises. Both patterns indicate that the global scale of the current crisis has led to a greater FDI response than after individual country crises in the past. Compared with global economic downturns since the 1970s, the current FDI recession has also been greater in magnitude. The exception is the FDI plunge in the early 2000s, despite the much smaller economic crisis at the time. The authors conclude by recommending that policymakers not just further liberalize FDI regimes--as they find was the typical pattern during earlier crises--but rather use the downturn to rethink their FDI policies with an enhanced focus on "sustainable FDI" promotion.foreign direct investment, investment policy, trade policy, protectionism, international investment agreements, economic crises, financial crises

Relevance differently affects the truth, acceptability, and probability evaluations of “and”, “but”, “therefore”, and “if–then”

In this study we investigate the influence of reason-relation readings of indicative conditionals and ‘and’/‘but’/‘therefore’ sentences on various cognitive assessments. According to the Frege-Grice tradition, a dissociation is expected. Specifically, differences in the reason-relation reading of these sentences should affect participants’ evaluations of their acceptability but not of their truth value. In two experiments we tested this assumption by introducing a relevance manipulation into the truth-table task as well as in other tasks assessing the participants’ acceptability and probability evaluations. Across the two experiments a strong dissociation was found. The reason-relation reading of all four sentences strongly affected their probability and acceptability evaluations, but hardly affected their respective truth evaluations. Implications of this result for recent work on indicative conditionals are discussed

The Influence of International Economic Institutions on Fossil Fuel Subsidy Reform

International economic institutions, particularly the G20, the OECD and the IMF, have been vocal in advocating reform of fossil fuel subsidies. The question that the paper seeks to answer is how influential the institutions have been in inducing countries to reform their fossil fuel subsidies? Although studies of individual fossil fuel subsidy reforms point to the role of international economic institutions as one factor among many, no overarching study has studied their influence across countries. This gap deserves to be addressed, particularly given the power of these institutions. More specifically, the paper focuses on pathways of influence which go beyond legally binding multilateral agreements. Such influences include learning, ideational change such as socialisation, and commitments which have to be adhered to. Concerning fossil subsidy reform, these pathways may consist of adherence to the (non-binding) G20 commitment, learning about fossil fuel subsidies and the possibilities to reform them, or socialisation into the norm that such subsidies should be reformed. Case studies of the US, India, the UK, Indonesia, Sweden and Denmark showed that ideational change stemming from the G20 and the OECD helped move fossil fuel subsidies up the agenda in industrialised countries, IMF was decisive in one case of Indonesian fossil fuel reform, and that learning processes mattered in terms of workshops organised by the OECD and the World Bank