66 research outputs found
An alternative local polynomial estimator for the error-in-variables problem
We consider the problem of estimating a regression function when a covariate
is measured with error. Using the local polynomial estimator of Delaigle, Fan,
and Carroll (2009) as a benchmark, we propose an alternative way of solving the
problem without transforming the kernel function. The asymptotic properties of
the alternative estimator are rigorously studied. A detailed implementing
algorithm and a computationally efficient bandwidth selection procedure are
also provided. The proposed estimator is compared with the existing local
polynomial estimator via extensive simulations and an application to the
motorcycle crash data. The results show that the new estimator can be less
biased than the existing estimator and is numerically more stable
Elliptically symmetric distributions for directional data of arbitrary dimension
We formulate a class of angular Gaussian distributions that allows different
degrees of isotropy for directional random variables of arbitrary dimension.
Through a series of novel reparameterization, this distribution family is
indexed by parameters with meaningful statistical interpretations that can
range over the entire real space of an adequate dimension. The new
parameterization greatly simplifies maximum likelihood estimation of all model
parameters, which in turn leads to theoretically sound and numerically stable
inference procedures to infer key features of the distribution. Byproducts from
the likelihood-based inference are used to develop graphical and numerical
diagnostic tools for assessing goodness of fit of this distribution in a data
application. Simulation study and application to data from a hydrogeology study
are used to demonstrate implementation and performance of the inference
procedures and diagnostics methods.Comment: 22 pages, 15 figure
Parametric Modal Regression with Error in Covariates
An inference procedure is proposed to provide consistent estimators of
parameters in a modal regression model with a covariate prone to measurement
error. A score-based diagnostic tool exploiting parametric bootstrap is
developed to assess adequacy of parametric assumptions imposed on the
regression model. The proposed estimation method and diagnostic tool are
applied to synthetic data generated from simulation experiments and data from
real-world applications to demonstrate their implementation and performance.
These empirical examples illustrate the importance of adequately accounting for
measurement error in the error-prone covariate when inferring the association
between a response and covariates based on a modal regression model that is
especially suitable for skewed and heavy-tailed response data.Comment: 15 pages, 3 figure
Bayesian Modal Regression based on Mixture Distributions
Compared to mean regression and quantile regression, the literature on modal
regression is very sparse. We propose a unified framework for Bayesian modal
regression based on a family of unimodal distributions indexed by the mode
along with other parameters that allow for flexible shapes and tail behaviors.
Following prior elicitation, we carry out regression analysis of simulated data
and datasets from several real-life applications. Besides drawing inference for
covariate effects that are easy to interpret, we consider prediction and model
selection under the proposed Bayesian modal regression framework. Evidence from
these analyses suggest that the proposed inference procedures are very robust
to outliers, enabling one to discover interesting covariate effects missed by
mean or median regression, and to construct much tighter prediction intervals
than those from mean or median regression. Computer programs for implementing
the proposed Bayesian modal regression are available at
https://github.com/rh8liuqy/Bayesian_modal_regression.Comment: 34 pages, 14 figure
Bayesian registration of functions and curves
Bayesian analysis of functions and curves is considered, where warping and other geometrical transformations are often required for meaningful comparisons. The functions and curves of interest are represented using the recently introduced square root velocity function, which enables a warping invariant elastic distance to be calculated in a straightforward manner. We distinguish between various spaces of interest: the original space, the ambient space after standardizing, and the quotient space after removing a group of transformations. Using Gaussian process models in the ambient space and Dirichlet priors for the warping functions, we explore Bayesian inference for curves and functions. Markov chain Monte Carlo algorithms are introduced for simulating from the posterior. We also compare ambient and quotient space estimators for mean shape, and explain their frequent similarity in many practical problems using a Laplace approximation. Simulation studies are carried out, as well as practical alignment of growth rate functions and shape classification of mouse vertebra outlines in evolutionary biology. We also compare the performance of our Bayesian method with some alternative approaches
Editorial: Engineering probiotics for multiple interventions on intestinal diseases
No abstract available
Local polynomial regression for pooled response data
We propose local polynomial estimators for the conditional mean of a
continuous response when only pooled response data are collected under
different pooling designs. Asymptotic properties of these estimators are
investigated and compared. Extensive simulation studies are carried out to
compare finite sample performance of the proposed estimators under various
model settings and pooling strategies. We apply the proposed local polynomial
regression methods to two real-life applications to illustrate practical
implementation and performance of the estimators for the mean function
Size and shape analysis of error-prone shape data
We consider the problem of comparing sizes and shapes of objects when landmark data are prone to measurement error. We show that naive implementation of ordinary Procrustes analysis that ignores measurement error can compromise inference. To account for measurement error, we propose the conditional score method for matching configurations, which guarantees consistent inference under mild model assumptions. The effects of measurement error on inference from naive Procrustes analysis and the performance of the proposed method are illustrated via simulation and application in three real data examples. Supplementary materials for this article are available online
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