DESIGN-ADAPTIVE POINTWISE NONPARAMETRIC REGRESSION ESTIMATION FOR RECURRENT MARKOV TIME SERIES

A general framework is proposed for (auto)regression nonparametric estimation of recurrent time series in a class of Hilbert Markov processes with a Lipschitz conditional mean. This includes various nonstationarities by relaxing usual dependence assumptions as mixing or ergodicity, which are replaced with recurrence. The cornerstone of design-adaptation is a data-driven bandwidth choice based on an empirical bias variance tradeoff, giving rise to a random consistency rate for a uniform kernel estimator. The estimator converges with this random rate, which is the optimal minimax random rate over the considered class of recurrent time series. Extensions to general kernel estimators are investigated. For weak dependent time-series, the order of the random rate coincides with the deterministic minimax rate previously derived. New deterministic estimation rates are obtained for modified Box-Cox transformations of Random Walks.Nonparametric regression estimation, Recurrent time series, Design-adaptation, Optimalrandom estimation rate.

Data-driven rate-optimal specification testing in regression models

We propose new data-driven smooth tests for a parametric regression function. The smoothing parameter is selected through a new criterion that favors a large smoothing parameter under the null hypothesis. The resulting test is adaptive rate-optimal and consistent against Pitman local alternatives approaching the parametric model at a rate arbitrarily close to 1/\sqrtn. Asymptotic critical values come from the standard normal distribution and the bootstrap can be used in small samples. A general formalization allows one to consider a large class of linear smoothing methods, which can be tailored for detection of additive alternatives.Comment: Published at http://dx.doi.org/10.1214/009053604000001200 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Uniform Bias Study and Bahadur Representation for Local Polynomial Estimators of the Conditional Quantile Function

This paper investigates the bias and the Bahadur representation of a local polynomial estimator of the conditional quantile function and its derivatives. The bias and Bahadur remainder term are studied uniformly with respect to the quantile level, the covariates and the smoothing parameter. The order of the local polynomial estimator can be higher that the differentiability order of the conditional quantile function. Applications of the results deal with global optimal consistency rates of the local polynomial quantile estimator, performance of random bandwidths and estimation of the conditional quantile density function. The latter allows to obtain a simple estimator of the conditional quantile function of the private values in a first price sealed bids auctions under the independent private values paradigm and risk neutrality.Bahadur representation, Conditional quantile function, Local polynomial estimation, Econometrics of auctions

Uniform Bahadur Representation for Nonparametric Censored Quantile Regression: A Redistribution-of-Mass Approach

Censored quantile regressions have received a great deal of attention in the literature. In a linear setup, recent research has found that an estimator based on the idea of “redistribution-of-mass” in Efron (1967, Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability, vol. 4, pp. 831–853, University of California Press) has better numerical performance than other available methods. In this paper, this idea is combined with the local polynomial kernel smoothing for nonparametric quantile regression of censored data. We derive the uniform Bahadur representation for the estimator and, more importantly, give theoretical justification for its improved efficiency over existing estimation methods. We include an example to illustrate the usefulness of such a uniform representation in the context of sufficient dimension reduction in regression analysis. Finally, simulations are used to investigate the finite sample performance of the new estimator

Identity, enlightenment and political dissent in late colonial Spanish America

During the long crisis of the Spanish empire between 1810 and 1825, the Creole leaders of Spanish American independence asserted a new identity for the citizens of the states which they sought to establish, calling them 'Americanos'. This general title was paralleled and often supplanted by other political neologisms, as movements for independence and new polities took shape in the various territories of Spanish America. In New Spain, the insurgents who fought against royalist government during the decade after 181 o tried to rally fellow 'Mexicans' to a common cause; at independence in 1821, die Creole political leadership created a 'Mexican empire', the title of which, with its reference to the Aztec empire which had preceded Spain's conquest, was designed to evoke a 'national' history shared by all members of Mexican society. In South America, die leaders of the new republics also sought to promote patriotic feelings for territories which had been converted from administrative units of Spanish government into independent states. Thus, San Martin and O'Higgins convoked 'Chileans' to the cause of independence in the old Captaincy-General of Chile; shortly afterwards and with notably less success, San Martin called upon 'Peruvians' to throw off Spanish rule. Bolivar was, likewise, to call 'Colombians' to his banner in die erstwhile Viceroyalty of New Granada, before advancing south to liberate Peru in die name of 'Peruvians', and Upper Peru in die name of 'Bolivians', where die Republic which his military feats and political vision made possible was named after him

DATA-DRIVEN RATE-OPTIMAL SPECIFICATION TESTING IN REGRESSION MODELS

We propose new data-driven smooth tests for a parametric regression function. The smoothing parameter is selected through a new criterion that favors a large smoothing parameter under the null hypothesis. The resulting test is adaptive rate-optimal and consistent against Pitman local alternatives approaching the parametric model at a rate arbitrarily close to 1/\sqrt{n}. Asymptotic critical values come from the standard normal distribution and bootstrap can be used in small samples. A general formalization allows to consider a large class of linear smoothing methods, which can be tailored for detection of additive alternatives.Hypothesis testing, nonparametric adaptive tests, selection methods

Adaptive Rate-optimal Detection of Small Autocorrelation Coefficients

A new test is proposed for the null of absence of serial correlation. The test uses a data-driven smoothing parameter. The resulting test statistic has a standard limit distribution under the null. The smoothing parameter is calibrated to achieve rate-optimality against several classes of alternatives. The test can detect alternatives with many small correlation coefficients that can go to zero with an optimal adaptive rate which is faster than the parametric rate. The adaptive rate-optimality against smooth alternatives of the new test is established as well. The test can also detect ARMA and local Pitman alternatives converging to the null with a rate close or equal to the parametric one. A simulation experiment and an application to monthly financial square returns illustrate the usefulness of the proposed approach.Absence of serial correlation; Data-driven nonparametric tests; Adaptive rate-optimality; Small alternatives; Time series

HPLC assay of zearalenone and reduced metabolites in S9 fractions of duck liver

HPLC analysis of zearalenone (ZEA), zearalenols (-ZOL and ß-ZOL) and zearalanols (-ZAL and ß-ZAL) was developed, in order to obtain a sensitive and reproducible method to quantify ZEA and its reduced metabolites in subcellular fractions of animal livers (S9 samples). Optimal in vitro metabolism was observed by incubating 5 mg S9 proteins with 0.016 μmol. ZEA. Acetonitrile and diethylether/chloroform mixture were compared for extraction, as well as different mobile phases and two detection modes in HPLC analysis. Extracted samples were eluted with water/acetonitrile (55:45, v/v) at a flow-rate of 1.0 ml/min-1, resulting in well separated peaks between ZEA and the metabolites. The limits of detection ranged from 0.5 to 2 ng/mg S9 proteins using UV, and from 0.04 to 4 ng/mg S9 proteins, using fluorescence detection. Fluorescence showed a ten-fold higher sensitivity than UV detection for ZEA and -ZOL. Repeatability (10 assays) was 2.7% to 6.99% for zearalenols. Day-by-day coefficients of variation for zearalenone and zeranols with UV detection were 3.3 to 8.5 %, and 2.5 to 4.3 %, respectively. This analysis applied to S9 samples from ducks after 30 min of ZEA incubation allowed to demonstrate that -ZOL is the main reduced metabolite in the duck. The present method is particularly adapted for studying in vitro metabolism of ZEA and inter-species variations

Variations in zearalenone activation in avian food species

Zearalenone (ZEA), a widely distributed oestrogenic fusariotoxin, constitutes a potential risk for human and animal health. ZEA is metabolised to the main metabolites identified in vitro and in vivo: alpha-zearalenol (α-ZOL) and beta-zearalenol (β-ZOL). The efficiency to produce alpha-reduced metabolites appears of particular interest in risk assessment as alpha-reduced metabolites constitute activated forms whereas beta-reduced metabolites are less oestrogenic than ZEA. In this study ZEA activation was compared in avian food species. ZEA and its reduced metabolites were quantified in subcellular fractions of six avian species and rat livers. The α-ZOL/β-ZOL ratio in rats was 19. The various avian food species cannot be considered to be equivalent in terms of ZEA reduction (P<0.001). Quails represented high “beta reducers”, with α-ZOL/β-ZOL ratio less than two. Weak “beta reducers” included on one part ducks and chickens showing α-ZOL/β-ZOL ratio greater than 3 and up to 5.6 and on a second part geese, showing a lower production of α-ZOL than other poultry. Comparisons of enzyme kinetics in ducks and in quails show that these variations can be explained by the action of various isoforms of dehydrogenases. These results are relevant to food safety, in the context of frequently inevitable contamination of animal feed

Cooperative Power-Limited Optimal Rendezvous Between Many Spacecraft

The minimum fuel rendezvous problem between several power-limited low-thrust spacecraft neighboring either a circular or an elliptic orbit is investigated. Both cooperative and non cooperative maneuvers are studied. The maximum principle of Pontryagin is applied to the optimal control rendezvous problem of several spacecraft. The gravitational field models investigated are the Clohessy-Wiltshire field and the inverse-square gravity field. Numerical solutions using a shooting method and the finite difference method are used in order to determine the trajectories of the spacecraft. Unlike previous investigations, this work is not restricted to a rendezvous of two spacecraft around a circular orbit, but a few vehicles will be able to rendezvous in space at a fixed-final time, both about a circular orbit and about an elliptic orbit