34,335 research outputs found
Statistical Inference using the Morse-Smale Complex
The Morse-Smale complex of a function decomposes the sample space into
cells where is increasing or decreasing. When applied to nonparametric
density estimation and regression, it provides a way to represent, visualize,
and compare multivariate functions. In this paper, we present some statistical
results on estimating Morse-Smale complexes. This allows us to derive new
results for two existing methods: mode clustering and Morse-Smale regression.
We also develop two new methods based on the Morse-Smale complex: a
visualization technique for multivariate functions and a two-sample,
multivariate hypothesis test.Comment: 45 pages, 13 figures. Accepted to Electronic Journal of Statistic
Nonparametric inference of quantile curves for nonstationary time series
The paper considers nonparametric specification tests of quantile curves for
a general class of nonstationary processes. Using Bahadur representation and
Gaussian approximation results for nonstationary time series, simultaneous
confidence bands and integrated squared difference tests are proposed to test
various parametric forms of the quantile curves with asymptotically correct
type I error rates. A wild bootstrap procedure is implemented to alleviate the
problem of slow convergence of the asymptotic results. In particular, our
results can be used to test the trends of extremes of climate variables, an
important problem in understanding climate change. Our methodology is applied
to the analysis of the maximum speed of tropical cyclone winds. It was found
that an inhomogeneous upward trend for cyclone wind speeds is pronounced at
high quantile values. However, there is no trend in the mean lifetime-maximum
wind speed. This example shows the effectiveness of the quantile regression
technique.Comment: Published in at http://dx.doi.org/10.1214/09-AOS769 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Marginal integration for nonparametric causal inference
We consider the problem of inferring the total causal effect of a single
variable intervention on a (response) variable of interest. We propose a
certain marginal integration regression technique for a very general class of
potentially nonlinear structural equation models (SEMs) with known structure,
or at least known superset of adjustment variables: we call the procedure
S-mint regression. We easily derive that it achieves the convergence rate as
for nonparametric regression: for example, single variable intervention effects
can be estimated with convergence rate assuming smoothness with
twice differentiable functions. Our result can also be seen as a major
robustness property with respect to model misspecification which goes much
beyond the notion of double robustness. Furthermore, when the structure of the
SEM is not known, we can estimate (the equivalence class of) the directed
acyclic graph corresponding to the SEM, and then proceed by using S-mint based
on these estimates. We empirically compare the S-mint regression method with
more classical approaches and argue that the former is indeed more robust, more
reliable and substantially simpler.Comment: 40 pages, 14 figure
A selective overview of nonparametric methods in financial econometrics
This paper gives a brief overview on the nonparametric techniques that are
useful for financial econometric problems. The problems include estimation and
inferences of instantaneous returns and volatility functions of
time-homogeneous and time-dependent diffusion processes, and estimation of
transition densities and state price densities. We first briefly describe the
problems and then outline main techniques and main results. Some useful
probabilistic aspects of diffusion processes are also briefly summarized to
facilitate our presentation and applications.Comment: 32 pages include 7 figure
Recent advances in directional statistics
Mainstream statistical methodology is generally applicable to data observed
in Euclidean space. There are, however, numerous contexts of considerable
scientific interest in which the natural supports for the data under
consideration are Riemannian manifolds like the unit circle, torus, sphere and
their extensions. Typically, such data can be represented using one or more
directions, and directional statistics is the branch of statistics that deals
with their analysis. In this paper we provide a review of the many recent
developments in the field since the publication of Mardia and Jupp (1999),
still the most comprehensive text on directional statistics. Many of those
developments have been stimulated by interesting applications in fields as
diverse as astronomy, medicine, genetics, neurology, aeronautics, acoustics,
image analysis, text mining, environmetrics, and machine learning. We begin by
considering developments for the exploratory analysis of directional data
before progressing to distributional models, general approaches to inference,
hypothesis testing, regression, nonparametric curve estimation, methods for
dimension reduction, classification and clustering, and the modelling of time
series, spatial and spatio-temporal data. An overview of currently available
software for analysing directional data is also provided, and potential future
developments discussed.Comment: 61 page
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