30,407 research outputs found
An asymptotic analysis of distributed nonparametric methods
We investigate and compare the fundamental performance of several distributed learning methods that have been proposed recently. We do this in the context of a distributed version of the classical signal-in-Gaussian-white-noise model, which serves as a benchmark model for studying performance in this setting. The results show how the design and tuning of a distributed method can have great impact on convergence rates and validity of uncertainty quantification. Moreover, we highlight the difficulty of designing nonparametric distributed procedures that automatically adapt to smoothness
MATS: Inference for potentially Singular and Heteroscedastic MANOVA
In many experiments in the life sciences, several endpoints are recorded per
subject. The analysis of such multivariate data is usually based on MANOVA
models assuming multivariate normality and covariance homogeneity. These
assumptions, however, are often not met in practice. Furthermore, test
statistics should be invariant under scale transformations of the data, since
the endpoints may be measured on different scales. In the context of
high-dimensional data, Srivastava and Kubokawa (2013) proposed such a test
statistic for a specific one-way model, which, however, relies on the
assumption of a common non-singular covariance matrix. We modify and extend
this test statistic to factorial MANOVA designs, incorporating general
heteroscedastic models. In particular, our only distributional assumption is
the existence of the group-wise covariance matrices, which may even be
singular. We base inference on quantiles of resampling distributions, and
derive confidence regions and ellipsoids based on these quantiles. In a
simulation study, we extensively analyze the behavior of these procedures.
Finally, the methods are applied to a data set containing information on the
2016 presidential elections in the USA with unequal and singular empirical
covariance matrices
Nonparametric and Varying Coefficient Modal Regression
In this article, we propose a new nonparametric data analysis tool, which we
call nonparametric modal regression, to investigate the relationship among
interested variables based on estimating the mode of the conditional density of
a response variable Y given predictors X. The nonparametric modal regression is
distinguished from the conventional nonparametric regression in that, instead
of the conditional average or median, it uses the "most likely" conditional
values to measures the center. Better prediction performance and robustness are
two important characteristics of nonparametric modal regression compared to
traditional nonparametric mean regression and nonparametric median regression.
We propose to use local polynomial regression to estimate the nonparametric
modal regression. The asymptotic properties of the resulting estimator are
investigated. To broaden the applicability of the nonparametric modal
regression to high dimensional data or functional/longitudinal data, we further
develop a nonparametric varying coefficient modal regression. A Monte Carlo
simulation study and an analysis of health care expenditure data demonstrate
some superior performance of the proposed nonparametric modal regression model
to the traditional nonparametric mean regression and nonparametric median
regression in terms of the prediction performance.Comment: 33 page
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