Semiparametric models are often considered for analyzing longitudinal data
for a good balance between flexibility and parsimony. In this paper, we study a
class of marginal partially linear quantile models with possibly varying
coefficients. The functional coefficients are estimated by basis function
approximations. The estimation procedure is easy to implement, and it requires
no specification of the error distributions. The asymptotic properties of the
proposed estimators are established for the varying coefficients as well as for
the constant coefficients. We develop rank score tests for hypotheses on the
coefficients, including the hypotheses on the constancy of a subset of the
varying coefficients. Hypothesis testing of this type is theoretically
challenging, as the dimensions of the parameter spaces under both the null and
the alternative hypotheses are growing with the sample size. We assess the
finite sample performance of the proposed method by Monte Carlo simulation
studies, and demonstrate its value by the analysis of an AIDS data set, where
the modeling of quantiles provides more comprehensive information than the
usual least squares approach.Comment: Published in at http://dx.doi.org/10.1214/09-AOS695 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
We study estimation in quantile regression when covariates are measured with errors. Existing methods require stringent assumptions, such as spherically symmetric joint distribution of the regression and measurement error variables, or linearity of all quantile functions, which restrict model flexibility and complicate computation. In this paper, we develop a new estimation approach based on corrected scores to account for a class of covariate measurement errors in quantile regression. The proposed method is simple to implement. Its validity requires only linearity of the particular quantile function of interest, and it requires no parametric assumptions on the regression error distributions. Finite-sample results demonstrate that the proposed estimators are more efficient than the existing methods in various models considered.
Microfluidic technologies for cell separation were reported frequently in recent years. However, a compact microfluidic instrument enabling thoroughly automated cell separation is still rarely reported until today due to the difficult hybrid between the macrosized fluidic control system and the microsized microfluidic device. In this work, we propose a novel and automated microfluidic instrument to realize size-based separation of cancer cells in a label-free and high-throughput manner. Briefly, the instrument is equipped with a fully integrated microfluidic device and a set of robust fluid-driven and control units, and the instrument functions of precise fluid infusion and high-throughput cell separation are guaranteed by a flow regulatory chip and two cell separation chips which are the key components of the microfluidic device. With optimized control programs, the instrument is successfully applied to automatically sort human breast adenocarcinoma cell line MCF-7 from 5 mL of diluted human blood with a high recovery ratio of ∼85% within a rapid processing time of ∼23 min. We envision that our microfluidic instrument will be potentially useful in many biomedical applications, especially cell separation, enrichment, and concentration for the purpose of cell culture and analysis.
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