2,044 research outputs found
Large-sample estimation and inference in multivariate single-index models
By optimizing index functions against different outcomes, we propose a multivariate single-index model (SIM) for development of medical indices that simultaneously work with multiple outcomes. Fitting of a multivariate SIM is not fundamentally different from fitting a univariate SIM, as the former can be written as a sum of multiple univariate SIMs with appropriate indicator functions. What have not been carefully studied are the theoretical properties of the parameter estimators. Because of the lack of asymptotic results, no formal inference procedure has been made available for multivariate SIMs. In this paper, we examine the asymptotic properties of the multivariate SIM parameter estimators. We show that, under mild regularity conditions, estimators for the multivariate SIM parameters are indee
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
Penalized likelihood estimation and iterative kalman smoothing for non-gaussian dynamic regression models
Dynamic regression or state space models provide a flexible framework for analyzing non-Gaussian time series and longitudinal data, covering for example models for discrete longitudinal observations. As for non-Gaussian random coefficient models, a direct Bayesian approach leads to numerical integration problems, often intractable for more complicated data sets. Recent Markov chain Monte Carlo methods avoid this by repeated sampling from approximative posterior distributions, but there are still open questions about sampling schemes and convergence. In this article we consider simpler methods of inference based on posterior modes or, equivalently, maximum penalized likelihood estimation. From the latter point of view, the approach can also be interpreted as a nonparametric method for smoothing time-varying coefficients. Efficient smoothing algorithms are obtained by iteration of common linear Kalman filtering and smoothing, in the same way as estimation in generalized linear models with fixed effects can be performed by iteratively weighted least squares estimation. The algorithm can be combined with an EM-type method or cross-validation to estimate unknown hyper- or smoothing parameters. The approach is illustrated by applications to a binary time series and a multicategorical longitudinal data set
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