Composite Quantile Estimation for Kink Model with Longitudinal Data

Kink model is developed to analyze the data where the regression function is two-stage piecewise linear with respect to the threshold covariate but continuous at an unknown kink point.In quantile regression for longitudinal data,kink point where the kink effect happens is often assumed to be heterogeneous across different quantiles.However,the kink point tends to be the same across different quantiles,especially in a region of neighboring quantile levels.Incorporating such homogeneity information could increase the estimation efficiency of the common kink point.In this paper,we propose a composite quantile estimation approach for the common kink point by combining information from multiple neighboring quantiles.Asymptotic normality of the proposed estimator is studied.In addition,we also develop a sup-likelihood-ratio test to check the existence of the kink effect at a given quantile level.A test-inversion confidence interval for the common kink point is also developed based on the quantile rank score test.The simulation studies show that the proposed composite kink estimator is more efficient than the single quantile regression estimator.We also illustrate the proposed method via an application to a longitudinal data set on blood pressure and body mass index.

Estimation of scale parameters of logistic distribution by linear functions of sample quantiles

The large sample estimation of standard deviation of logistic distribution employs the asymptotically best linear unbiased estimators based on sample quantiles. The sample quantiles are established from a pair of single spacing. Finally, a table of the variances and efficiencies of the estimator for 5≤n≤65 is provided and comparison is made with other linear estimators.

Sequential Confidence Bands for Quantile Densities Under Truncated and Censored Data

In this paper an asymptotic distribution is obtained for the maximaldeviation between the kernel quantile density estimator and the quantile density when the data aresubject to random left truncation and right censorship. Based on this result we propose a fullysequential procedure for constructing a fixed-width confidence band for the quantile density on afinite interval and show that the procedure has the desired coverage probability asymptotically asthe width of the band approaches zero.

BAHADUR REPRESENTATION OF THEKERNEL QUANTILE ESTIMATOR UNDER TRUNCATED AND CENSORED DATA

In this article the authors establish the Bahadur type representations for the kernel quantileestimator and the kernel estimator of the derivatives of the quantile function on the basis of lefttruncated and right censored data. Under suitable conditions, with probability one, the exactconvergence rate of the remainder term in the representations is obtained. As a by-product, theLIL, the asymptotic normality for those kernel estimators are derived.

Semiparametric fractional imputation using empirical likelihood in survey sampling

The empirical likelihood method is a powerful tool for incorporating moment conditions in statistical inference.We propose a novel application of the empirical likelihood for handling itemnonresponse in survey sampling.The proposed method takes the form of fractional imputation but it does not require parametric model assumptions.Instead,only the first moment condition based on a regression model is assumed and the empirical likelihood method is applied to the observed residuals to get the fractional weights.The resulting semiparametric fractional imputation provides√n-consistent estimates for various parameters.Variance estimation is implemented using a jackknifemethod.Two limited simulation studies are presented to compare several imputation estimators.

Efficient Robbins–Monro procedure for multivariate binary data

This paper considers the problem of jointly estimating marginal quantiles of a multivariatedistribution.A sufficient condition for an estimator that converges in probability under a multivariate version of Robbins–Monro procedure is provided.We propose an efficient procedurewhich incorporates the correlation structure of the multivariate distribution to improve the estimation especially for cases involving extreme marginal quantiles.Estimation efficiency of theproposed method is demonstrated by simulation in comparison with a general multivariate Robbins–Monro procedure and an efficient Robbins–Monro procedure that estimates the marginalquantiles separately.