10,892 research outputs found
Pruning and Nonparametric Multiple Change Point Detection
Change point analysis is a statistical tool to identify homogeneity within
time series data. We propose a pruning approach for approximate nonparametric
estimation of multiple change points. This general purpose change point
detection procedure `cp3o' applies a pruning routine within a dynamic program
to greatly reduce the search space and computational costs. Existing
goodness-of-fit change point objectives can immediately be utilized within the
framework. We further propose novel change point algorithms by applying cp3o to
two popular nonparametric goodness of fit measures: `e-cp3o' uses E-statistics,
and `ks-cp3o' uses Kolmogorov-Smirnov statistics. Simulation studies highlight
the performance of these algorithms in comparison with parametric and other
nonparametric change point methods. Finally, we illustrate these approaches
with climatological and financial applications.Comment: 9 pages. arXiv admin note: text overlap with arXiv:1505.0430
Writing on Dirty Paper with Resizing and its Application to Quasi-Static Fading Broadcast Channels
This paper studies a variant of the classical problem of ``writing on dirty
paper'' in which the sum of the input and the interference, or dirt, is
multiplied by a random variable that models resizing, known to the decoder but
not to the encoder. The achievable rate of Costa's dirty paper coding (DPC)
scheme is calculated and compared to the case of the decoder's also knowing the
dirt. In the ergodic case, the corresponding rate loss vanishes asymptotically
in the limits of both high and low signal-to-noise ratio (SNR), and is small at
all finite SNR for typical distributions like Rayleigh, Rician, and Nakagami.
In the quasi-static case, the DPC scheme is lossless at all SNR in terms of
outage probability. Quasi-static fading broadcast channels (BC) without
transmit channel state information (CSI) are investigated as an application of
the robustness properties. It is shown that the DPC scheme leads to an outage
achievable rate region that strictly dominates that of time division.Comment: To appear in IEEE International Symposium on Information Theory 200
Scalar, Vector and Tensor Harmonics on the Three-Sphere
Scalar, vector and tensor harmonics on the three-sphere were introduced
originally to facilitate the study of various problems in gravitational
physics. These harmonics are defined as eigenfunctions of the covariant Laplace
operator which satisfy certain divergence and trace identities, and
ortho-normality conditions. This paper provides a summary of these properties,
along with a new notation that simplifies and clarifies some of the key
expressions. Practical methods are described for accurately and efficiently
computing these harmonics numerically, and test results are given that
illustrate how well the analytical identities are satisfied by the harmonics
computed numerically in this way.Comment: 14 pages, 9 figures, to appear in General Relativity and Gravitatio
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