Inference about the slope in linear regression: an empirical likelihood approach

We present a new, efficient maximum empirical likelihood estimator for the slope in linear regression with independent errors and covariates. The estimator does not require estimation of the influence function, in contrast to other approaches, and is easy to obtain numerically. Our approach can also be used in the model with responses missing at random, for which we recommend a complete case analysis. This suffices thanks to results by Müller and Schick (Bernoulli 23:2693–2719, 2017), which demonstrate that efficiency is preserved. We provide confidence intervals and tests for the slope, based on the limiting Chi-square distribution of the empirical likelihood, and a uniform expansion for the empirical likelihood ratio. The article concludes with a small simulation study

Efficient prediction for linear and nonlinear autoregressive models

Conditional expectations given past observations in stationary time series are usually estimated directly by kernel estimators, or by plugging in kernel estimators for transition densities. We show that, for linear and nonlinear autoregressive models driven by independent innovations, appropriate smoothed and weighted von Mises statistics of residuals estimate conditional expectations at better parametric rates and are asymptotically efficient. The proof is based on a uniform stochastic expansion for smoothed and weighted von Mises processes of residuals. We consider, in particular, estimation of conditional distribution functions and of conditional quantile functions.Comment: Published at http://dx.doi.org/10.1214/009053606000000812 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Optimality of estimators for misspecified semi-Markov models

Suppose we observe a geometrically ergodic semi-Markov process and have a parametric model for the transition distribution of the embedded Markov chain, for the conditional distribution of the inter-arrival times, or for both. The first two models for the process are semiparametric, and the parameters can be estimated by conditional maximum likelihood estimators. The third model for the process is parametric, and the parameter can be estimated by an unconditional maximum likelihood estimator. We determine heuristically the asymptotic distributions of these estimators and show that they are asymptotically efficient. If the parametric models are not correct, the (conditional) maximum likelihood estimators estimate the parameter that maximizes the Kullback--Leibler information. We show that they remain asymptotically efficient in a nonparametric sense.Comment: To appear in a Special Volume of Stochastics: An International Journal of Probability and Stochastic Processes (http://www.informaworld.com/openurl?genre=journal%26issn=1744-2508) edited by N.H. Bingham and I.V. Evstigneev which will be reprinted as Volume 57 of the IMS Lecture Notes Monograph Series (http://imstat.org/publications/lecnotes.htm

The transfer principle: A tool for complete case analysis

This paper gives a general method for deriving limiting distributions of complete case statistics for missing data models from corresponding results for the model where all data are observed. This provides a convenient tool for obtaining the asymptotic behavior of complete case versions of established full data methods without lengthy proofs. The methodology is illustrated by analyzing three inference procedures for partially linear regression models with responses missing at random. We first show that complete case versions of asymptotically efficient estimators of the slope parameter for the full model are efficient, thereby solving the problem of constructing efficient estimators of the slope parameter for this model. Second, we derive an asymptotically distribution free test for fitting a normal distribution to the errors. Finally, we obtain an asymptotically distribution free test for linearity, that is, for testing that the nonparametric component of these models is a constant. This test is new both when data are fully observed and when data are missing at random.Comment: Published in at http://dx.doi.org/10.1214/12-AOS1061 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Genome-wide association of white blood cell counts in Hispanic/Latino Americans: the Hispanic Community Health Study/Study of Latinos

Circulating white blood cell (WBC) counts (neutrophils, monocytes, lymphocytes, eosinophils, basophils) differ by ethnicity. The genetic factors underlying basal WBC traits in Hispanics/Latinos are unknown. We performed a genome-wide association study of total WBC and differential counts in a large, ethnically diverse US population sample of Hispanics/Latinos ascertained by the Hispanic Community Health Study and Study of Latinos (HCHS/SOL). We demonstrate that several previously known WBC-associated genetic loci (e.g. the African Duffy antigen receptor for chemokines null variant for neutrophil count) are generalizable to WBC traits in Hispanics/Latinos. We identified and replicated common and rare germ-line variants at FLT3 (a gene often somatically mutated in leukemia) associated with monocyte count. The common FLT3 variant rs76428106 has a large allele frequency differential between African and non-African populations. We also identified several novel genetic loci involving or regulating hematopoietic transcription factors (CEBPE-SLC7A7, CEBPA and CRBN-TRNT1) associated with basophil count. The minor allele of the CEBPE variant associated with lower basophil count has been previously associated with Amerindian ancestry and higher risk of acute lymphoblastic leukemia in Hispanics. Together, these data suggest that germline genetic variation affecting transcriptional and signaling pathways that underlie WBC development and lineage specification can contribute to inter-individual as well as ethnic differences in peripheral blood cell counts (normal hematopoiesis) in addition to susceptibility to leukemia (malignant hematopoiesis)