Ying Wei

Conditional growth charts

Growth charts are often more informative when they are customized per subject, taking into account prior measurements and possibly other covariates of the subject. We study a global semiparametric quantile regression model that has the ability to estimate conditional quantiles without the usual distributional assumptions. The model can be estimated from longitudinal reference data with irregular measurement times and with some level of robustness against outliers, and it is also flexible for including covariate information. We propose a rank score test for large sample inference on covariates, and develop a new model assessment tool for longitudinal growth data. Our research indicates that the global model has the potential to be a very useful tool in conditional growth chart analysis.

Stochastic comparisons of spacings from restricted families of distributions

Let X1:n[less-than-or-equals, slant]X2:n[less-than-or-equals, slant]...[less-than-or-equals, slant]Xn:n denote the order statistics of a random sample X1,...,Xn from a distribution F with support (0,[infinity]). Let the generalized spacings [resp. spacings, normalized spacings and dual normalized spacings] of the X-sample be defined by Uj,i:n=Xj:n-Xi:n, 0[less-than-or-equals, slant]i

LIKELIHOOD RATIO AND MEAN RESIDUAL LIFE ORDERS FOR ORDER STATISTICS OF HETEROGENEOUS RANDOM VARIABLES

Let X1:n ≤ X2:n ≤ ··· ≤ Xn:n denote the order statistics of a set of independent and not necessarily identically distributed random variables X1,..., Xn. Under mild assumptions, it is shown that Xk−1:n−1 ≤lr Xk:n for k = 2,..., n if X1 ≤lr X2 ≤lr ··· ≤lr Xn and that Xk:n ≤lr Xk:n−1 for k = 1,..., n − 1 if X1 ≥lr X2 ≥lr ··· ≥lr Xn, where ≤lr denotes the likelihood ratio order. Concerning the mean residual life order (≤mrl), it is shown that Xn−1:n−1 ≤mrl Xn:n if Xj ≤mrl Xn for j = 1,..., n − 1. Two counterexamples are also given to illustrate that Xk−1:n−1 ≤mrl Xk:n in this case is, in general, not true for k < n.

Lower Rank Approximation of Matrices Based on Fast and Robust Alternating Regression

We introduce fast and robust algorithms for lower rank approximation to given matrices based on robust alternating regression. The alternating least squares regression, also called criss-cross regression, was used for lower rank approximation of matrices, but it lacks robustness against outliers in these matrices. We use robust regression estimators and address some of the complications arising from this approach. We find it helpful to use high breakdown estimators in the initial iterations, followed by M estimators with monotone score functions in later iterations towards convergence. In addition to robustness, the computational speed is another important consideration in the development of our proposed algorithm, because alternating robust regression can be computationally intensive for large matrices. Based on a mix of the least trimmed squares (LTS) and Hubers M estimators, we demonstrate that fast and robust lower rank approximations are possible for modestly large matrices.

Discussion: Conditional growth charts

1. Overview. Wei and He are to be congratulated on an innovative and important article. The conditional approach to growth charts described in their article is important in a practical sense, and the use of quantile regression is both natural and well motivated. We look forward to further application of their idea to actual practice, because the concept of “falling behind” in one’s growth cycle has two meanings: the usual standard growth chart, and the conditional growth chart described here. We have described the Wei and He approach to pediatricians, and they all grasped the essential clever idea immediately and were enthusiastic about the idea. Our commentary will focus on three aspects of the approach used by the authors, specifically (a) the use of unpenalized B-splines as described by the authors; (b) conditional versus marginal semiparametric modeling of longitudinal data; and (c) some alternative modeling approaches to “catchup” that may get at the issue more directly and flexibly.