65,240 research outputs found
Semiparametric GEE analysis in partially linear single-index models for longitudinal data
In this article, we study a partially linear single-index model for
longitudinal data under a general framework which includes both the sparse and
dense longitudinal data cases. A semiparametric estimation method based on a
combination of the local linear smoothing and generalized estimation equations
(GEE) is introduced to estimate the two parameter vectors as well as the
unknown link function. Under some mild conditions, we derive the asymptotic
properties of the proposed parametric and nonparametric estimators in different
scenarios, from which we find that the convergence rates and asymptotic
variances of the proposed estimators for sparse longitudinal data would be
substantially different from those for dense longitudinal data. We also discuss
the estimation of the covariance (or weight) matrices involved in the
semiparametric GEE method. Furthermore, we provide some numerical studies
including Monte Carlo simulation and an empirical application to illustrate our
methodology and theory.Comment: Published at http://dx.doi.org/10.1214/15-AOS1320 in the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Penalized single-index quantile regression
This article is made available through the Brunel Open Access Publishing Fund. Copyright for this article is retained by the author(s), with first publication rights granted to the journal.
This is an open-access article distributed under the terms and conditions of the Creative Commons Attribution
license (http://creativecommons.org/licenses/by/3.0/).The single-index (SI) regression and single-index quantile (SIQ) estimation methods product linear combinations of all the original predictors. However, it is possible that there are many unimportant predictors within the original predictors. Thus, the precision of parameter estimation as well as the accuracy of prediction will be effected by the existence of those unimportant predictors when the previous methods are used. In this article, an extension of the SIQ method of Wu et al. (2010) has been proposed, which considers Lasso and Adaptive Lasso for estimation and variable selection. Computational algorithms have been developed in order to calculate the penalized SIQ estimates. A simulation study and a real data application have been used to assess the performance of the methods under consideration
Functional Regression
Functional data analysis (FDA) involves the analysis of data whose ideal
units of observation are functions defined on some continuous domain, and the
observed data consist of a sample of functions taken from some population,
sampled on a discrete grid. Ramsay and Silverman's 1997 textbook sparked the
development of this field, which has accelerated in the past 10 years to become
one of the fastest growing areas of statistics, fueled by the growing number of
applications yielding this type of data. One unique characteristic of FDA is
the need to combine information both across and within functions, which Ramsay
and Silverman called replication and regularization, respectively. This article
will focus on functional regression, the area of FDA that has received the most
attention in applications and methodological development. First will be an
introduction to basis functions, key building blocks for regularization in
functional regression methods, followed by an overview of functional regression
methods, split into three types: [1] functional predictor regression
(scalar-on-function), [2] functional response regression (function-on-scalar)
and [3] function-on-function regression. For each, the role of replication and
regularization will be discussed and the methodological development described
in a roughly chronological manner, at times deviating from the historical
timeline to group together similar methods. The primary focus is on modeling
and methodology, highlighting the modeling structures that have been developed
and the various regularization approaches employed. At the end is a brief
discussion describing potential areas of future development in this field
Interaction Analysis of Repeated Measure Data
Extensive penalized variable selection methods have been developed in the past two decades for analyzing high dimensional omics data, such as gene expressions, single nucleotide polymorphisms (SNPs), copy number variations (CNVs) and others. However, lipidomics data have been rarely investigated by using high dimensional variable selection methods. This package incorporates our recently developed penalization procedures to conduct interaction analysis for high dimensional lipidomics data with repeated measurements. The core module of this package is developed in C++. The development of this software package and the associated statistical methods have been partially supported by an Innovative Research Award from Johnson Cancer Research Center, Kansas State University
Fused kernel-spline smoothing for repeatedly measured outcomes in a generalized partially linear model with functional single index
We propose a generalized partially linear functional single index risk score
model for repeatedly measured outcomes where the index itself is a function of
time. We fuse the nonparametric kernel method and regression spline method, and
modify the generalized estimating equation to facilitate estimation and
inference. We use local smoothing kernel to estimate the unspecified
coefficient functions of time, and use B-splines to estimate the unspecified
function of the single index component. The covariance structure is taken into
account via a working model, which provides valid estimation and inference
procedure whether or not it captures the true covariance. The estimation method
is applicable to both continuous and discrete outcomes. We derive large sample
properties of the estimation procedure and show a different convergence rate
for each component of the model. The asymptotic properties when the kernel and
regression spline methods are combined in a nested fashion has not been studied
prior to this work, even in the independent data case.Comment: Published at http://dx.doi.org/10.1214/15-AOS1330 in the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
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