In this paper, we provide the O() corrections to the hydrodynamic model derived by Degond and Motsch from a kinetic version of the model by Vicsek and co-authors describing flocking biological agents. The parameter stands for the ratio of the microscopic to the macroscopic scales. The O() corrected model involves diffusion terms in both the mass and velocity equations as well as terms which are quadratic functions of the first-order derivatives of the density and velocity. The derivation method is based on the standard ChapmanEnskog theory, but is significantly more complex than usual due to both the non-isotropy of the fluid and the lack of momentum conservation.

Statistical estimation and inference for marginal hazard models with varying coefficients for multivariate failure time data are important subjects in survival analysis. A local pseudo-partial likelihood procedure is proposed for estimating the unknown coefficient functions. A weighted average estimator is also proposed in an attempt to improve the efficiency of the estimator. The consistency and asymptotic normality of the proposed estimators are established and standard error formulas for the estimated coefficients are derived and empirically tested. To reduce the computational burden of the maximum local pseudo-partial likelihood estimator, a simple and useful one-step estimator is proposed. Statistical properties of the one-step estimator are established and simulation studies are conducted to compare the performance of the one-step estimator to that of the maximum local pseudo-partial likelihood estimator. The

The problem of estimating the density function and the regression function involving errors-in-variables in time series is considered. Under appropriate conditions, it is shown that the rates obtained in Fan (1991), Fan and Truong (1990) are also achievable in the context of dependent observations. Consequently, the results presented here extend our previous results for cross-sectional data to the longitudinal ones. oAbbreviated title. Measurement Errors in Time Series AMS 1980 subject classification. Primary 62G20. Secondary 62G05, 62J99.

This paper is about the propagation of the singularities in the solutions to the Cauchy problem of the spatially inhomogeneous Boltzmann equation with angular cutoff assumption. It is motivated by the work of BoudinDesvillettes on the propagation of singularities in solutions near vacuum. It shows that for the solution near a global Maxwellian, singularities in the initial data propagate like the free transportation. Precisely, the solution is the sum of two parts in which one keeps the singularities of the initial data and the other one is regular with locally bounded derivatives of fractional order in some Sobolev space. In addition, the dependence of the regularity on the cross-section is also given.

Problems of nonparametric ltering arises frequently in engineering and nancial economics. Nonparametric lters often involve some ltering parameters to choose. These parameters can be chosen to optimize the performance locally at each time point or globally over a time interval. In this article, the ltering parameters are chosen via minimizing the prediction error for a large class of lters. Under a general martingale setting, with mild conditions on the time series structure and virtually no assumption on lters, we show that the adaptive lter with ltering parameter chosen by historical data performs nearly as well as the one with the ideal lter in the class, in terms of ltering errors. The theoretical result is also veri ed via intensive simulations. Our approach is also useful for choosing the orders of parametric models such as AR or GARCH processes. It can also be applied to volatility estimation in nancial economics. We illustrate the proposed methods by estimating the volatility of the returns of the S&P500 index and the yields of the three-month Treasury bills.