Efficient semiparametric estimation in generalized partially linear additive models for longitudinal/clustered data

We consider efficient estimation of the Euclidean parameters in a generalized partially linear additive models for longitudinal/clustered data when multiple covariates need to be modeled nonparametrically, and propose an estimation procedure based on a spline approximation of the nonparametric part of the model and the generalized estimating equations (GEE). Although the model in consideration is natural and useful in many practical applications, the literature on this model is very limited because of challenges in dealing with dependent data for nonparametric additive models. We show that the proposed estimators are consistent and asymptotically normal even if the covariance structure is misspecified. An explicit consistent estimate of the asymptotic variance is also provided. Moreover, we derive the semiparametric efficiency score and information bound under general moment conditions. By showing that our estimators achieve the semiparametric information bound, we effectively establish their efficiency in a stronger sense than what is typically considered for GEE. The derivation of our asymptotic results relies heavily on the empirical processes tools that we develop for the longitudinal/clustered data. Numerical results are used to illustrate the finite sample performance of the proposed estimators.Comment: Published in at http://dx.doi.org/10.3150/12-BEJ479 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

Modelling and interpreting the dependence of clustering on the spectral energy distributions of galaxies

We extend our previous physically-based halo occupation distribution models to include the dependence of clustering on the spectral energy distributions of galaxies. The high resolution Millennium Simulation is used to specify the positions and the velocities of the model galaxies. The stellar mass of a galaxy is assumed to depend only on M_{infall}, the halo mass when the galaxy was last the central dominant object of its halo. Star formation histories are parametrized using two additional quantities that are measured from the simulation for each galaxy: its formation time (t_{form}), and the time when it first becomes a satellite (t_{infall}). Central galaxies begin forming stars at time t_{form} with an exponential time scale tau_c. If the galaxy becomes a satellite, its star formation declines thereafter with a new time scale tau_s. We compute 4000 \AA break strengths for our model galaxies using stellar population synthesis models. By fitting these models to the observed abundances and projected correlations of galaxies as a function of break strength in the Sloan Digital Sky Survey, we constrain tau_c and tau_s as functions of galaxy stellar mass. We find that central galaxies with large stellar masses have ceased forming stars. At low stellar masses, central galaxies display a wide range of different star formation histories, with a significant fraction experiencing recent starbursts. Satellite galaxies of all masses have declining star formation rates, with similar e-folding times, tau_s ~ 2.5Gyr. One consequence of this long e-folding time is that the colour-density relation is predicted to flatten at redshifts > 1.5, because star formation in the majority of satellites has not yet declined by a significant factor. This is consistent with recent observational results from the DEEP and VVDS surveys.Comment: 14 pages, 11 figures, submitted to MNRA

Synthesis of a ditopic homooxacalix[3]arene for fluorescence enhanced detection of heavy and transition metal ions

A pyrene-appended ratiometric fluorescent chemosensor L based on a synthetic approach of insulating the fluorophore from the ionophore by a specific molecular spacer has been synthesised and characterised. The fluorescence spectra changes of L suggested that the chemosensor can detect heavy and transition metal (HTM) ions ratiometrically and with variable sensitivity according to the substituents present. ¹H NMR titration experiments indicated that the three triazole ligands prefer binding with Hg²⁺, Pb²⁺ and Zn²⁺, resulting in a conformational change that produces monomer emission of the pyrene accompanied by the excimer quenching. However, the addition of Fe³⁺, which may be accommodated by the cavity of L, makes the pyrene units move closer to each other, and a discernible increase in the emission intensity of the static excimer is observed. Therefore, it is believed that the ditopic scaffold of the calix[3]arene as a specific molecular spacer here plays an important role in the blocking of the heavy atom effect of HTM ions by insulating the fluorophore from the ionophore given the long distance between the metal cation and the pyrene moiety