On the Dependence between Quantiles and Dispersion Estimators

In this study, we derive the joint asymptotic distributions of functionals of quantile estimators (the non-parametric sample quantile and the parametric location-scale quantile) and functionals of measure of dispersion estimators (the sample standard deviation, sample mean absolute deviation, sample median absolute deviation) - assuming an underlying identically and independently distributed sample. Additionally, for location-scale distributions, we show that asymptotic correlations of such functionals do not depend on the mean and variance parameter of the distribution. Further, we compare the impact of the choice of the quantile estimator (sample quantile vs. parametric location-scale quantile) in terms of speed of convergence of the asymptotic covariance and correlations respectively. As application, we show in simulations a good finite sample performance of the asymptotics. Further, we show how the theoretical dependence results can be applied to the most well-known risk measures (Value-at-Risk, Expected Shortfall, expectile). Finally, we relate the theoretical results to empirical findings in the literature of the dependence between risk measure prediction (on historical samples) and the estimated volatility

Adaptation of maize source leaf metabolism to stress related disturbances in carbon, nitrogen and phosphorus balance

Schlueter U, Colmsee C, Scholz U, et al. Adaptation of maize source leaf metabolism to stress related disturbances in carbon, nitrogen and phosphorus balance. BMC Genomics. 2013;14(1): 442.Background: Abiotic stress causes disturbances in the cellular homeostasis. Re-adjustment of balance in carbon, nitrogen and phosphorus metabolism therefore plays a central role in stress adaptation. However, it is currently unknown which parts of the primary cell metabolism follow common patterns under different stress conditions and which represent specific responses. Results: To address these questions, changes in transcriptome, metabolome and ionome were analyzed in maize source leaves from plants suffering low temperature, low nitrogen (N) and low phosphorus (P) stress. The selection of maize as study object provided data directly from an important crop species and the so far underexplored C-4 metabolism. Growth retardation was comparable under all tested stress conditions. The only primary metabolic pathway responding similar to all stresses was nitrate assimilation, which was down-regulated. The largest group of commonly regulated transcripts followed the expression pattern: down under low temperature and low N, but up under low P. Several members of this transcript cluster could be connected to P metabolism and correlated negatively to different phosphate concentration in the leaf tissue. Accumulation of starch under low temperature and low N stress, but decrease in starch levels under low P conditions indicated that only low P treated leaves suffered carbon starvation. Conclusions: Maize employs very different strategies to manage N and P metabolism under stress. While nitrate assimilation was regulated depending on demand by growth processes, phosphate concentrations changed depending on availability, thus building up reserves under excess conditions. Carbon and energy metabolism of the C-4 maize leaves were particularly sensitive to P starvation

The cis-acting CTTC-P1BS module is indicative for gene function of LjVTI12, a Qb-SNARE protein gene that is required for arbuscule formation in Lotus japonicus

Lota F, Wegmueller S, Buer B, et al. The cis-acting CTTC-P1BS module is indicative for gene function of LjVTI12, a Qb-SNARE protein gene that is required for arbuscule formation in Lotus japonicus. The Plant Journal. 2013;74(2):280-293.The majority of land plants live in symbiosis with arbuscular mycorrhizal fungi from the phylum Glomeromycota. This symbiosis improves acquisition of phosphorus (P) by the host plant in exchange for carbohydrates, especially under low-P availability. The symbiosome, constituted by root cortex cells accommodating arbuscular mycorrhizal fungal hyphae, is the site at which bi-directional exchange of nutrients and metabolites takes place. Uptake of orthophosphate (Pi) in the symbiosome is facilitated by mycorrhiza-specific plant Pi transporters. Modifications of the potato Pi transporter 3 (StPT3) promoter were analysed in transgenic mycorrhizal roots, and it was found that the CTTC cis-regulatory element is necessary and sufficient for a transcriptional response to fungal colonization under low-Pi conditions. Phylogenetic foot-printing also revealed binary combination of the CTTC element with the Pi starvation response-associated PHR1-binding site (P1BS) in the promoters of several mycorrhiza-specific Pi transporter genes. Scanning of the Lotus japonicus genome for gene promoters containing both cis-regulatory elements revealed a strong over-representation of genes involved in transport processes. One of these, LjVTI12, encoding a member of the SNARE family of proteins involved in membrane transport, exhibited enhanced transcript levels in Lotus roots colonized with the arbuscular mycorrhizal fungus Glomus intraradices. Down-regulation of LjVTI12 by RNA interference resulted in a mycorrhiza-specific phenotype characterized by distorted arbuscule morphology. The results highlight cooperative cis-regulation which integrates mycorrhiza and Pi starvation signaling with vesicle trafficking in symbiosome development

Facing Up to Longevity with Old Actuarial Methods: A Comparison of Pooled Funds and Income Tontines

We compare the concepts underlying modern actuarial solutions to pension insurance and present two recently developed pension products—pooled annuity overlay funds (based on actuarial fairness) and equitable income tontines (based on equitability). These two products adopt specific approaches to the management of longevity risk by mutualising it among participants rather than transferring it completely to the insurer. As the market would appear to be ready for such innovations, our study seeks to establish a general framework for their introduction. We stress that the notion of actuarial fairness, which characterises pooled annuity overlay funds, enables participants to join and exit the fund at any time. Such freedom of action is a quite remarkable feature and one that cannot be matched by lifelong contracts

Bivariate FCLT for the Sample Quantile and Measures of Dispersion for Augmented GARCH(p, q) processes

In this note, we build upon the asymptotic theory for GARCH processes, considering the general class of augmented GARCH(p, q) processes. Our contribution is to complement the well-known univariate asymptotics by providing a bivariate functional central limit theorem between the sample quantile and the r-th absolute centred sample moment. This extends existing results in the case of identically and independently distributed random variables. We show that the conditions for the convergence of the estimators in the univariate case suffice even for the joint bivariate asymptotics. We illustrate the general results with various specific examples from the class of augmented GARCH(p, q) processes and show explicitly under which conditions on the moments and parameters of the process the joint asymptotics hold

Bivariate FCLT for the Sample Quantile and Measures of Dispersion for Augmented GARCH(p, q) processes

In this note, we build upon the asymptotic theory for GARCH processes, considering the general class of augmented GARCH(p, q) processes. Our contribution is to complement the well-known univariate asymptotics by providing a bivariate functional central limit theorem between the sample quantile and the r-th absolute centred sample moment. This extends existing results in the case of identically and independently distributed random variables. We show that the conditions for the convergence of the estimators in the univariate case suffice even for the joint bivariate asymptotics. We illustrate the general results with various specific examples from the class of augmented GARCH(p, q) processes and show explicitly under which conditions on the moments and parameters of the process the joint asymptotics hold