1,373 research outputs found
Multiple testing, uncertainty and realistic pictures
We study statistical detection of grayscale objects in noisy images. The
object of interest is of unknown shape and has an unknown intensity, that can
be varying over the object and can be negative. No boundary shape constraints
are imposed on the object, only a weak bulk condition for the object's interior
is required. We propose an algorithm that can be used to detect grayscale
objects of unknown shapes in the presence of nonparametric noise of unknown
level. Our algorithm is based on a nonparametric multiple testing procedure. We
establish the limit of applicability of our method via an explicit,
closed-form, non-asymptotic and nonparametric consistency bound. This bound is
valid for a wide class of nonparametric noise distributions. We achieve this by
proving an uncertainty principle for percolation on finite lattices.Comment: This paper initially appeared in January 2011 as EURANDOM Report
2011-004. Link to the abstract at EURANDOM Repository:
http://www.eurandom.tue.nl/reports/2011/004-abstract.pdf Link to the paper at
EURANDOM Repository: http://www.eurandom.tue.nl/reports/2011/004-report.pd
Segmentation of Time Series: Parameter Dependence of Blake-Zisserman and Mumford-Shah Functionals and the Transition from Discrete to Continuous
The paper deals with variational approaches to the segmentation of time
series into smooth pieces, but allowing for sharp breaks. In discrete time, the
corresponding functionals are of Blake-Zisserman type. Their natural
counterpart in continuous time are the Mumford-Shah functionals. Time series
which minimise these functionals are proper estimates or representations of the
signals behind recorded data. We focus on consistent behaviour of the
functionals and the estimates, as parameters vary or as the sampling rate
increases. For each time continuous time series
we take conditional expectations w.r.t. to -algebras generated by finer
and finer partitions of the time domain into intervals, and thereby construct a
sequence of discrete time series. As increases this
amounts to sampling the continuous time series with more and more accuracy. Our
main result is consistent behaviour of segmentations w.r.t. to variation of
parameters and increasing sampling rate
Consistencies and rates of convergence of jump-penalized least squares estimators
We study the asymptotics for jump-penalized least squares regression aiming
at approximating a regression function by piecewise constant functions. Besides
conventional consistency and convergence rates of the estimates in
our results cover other metrics like Skorokhod metric on the space of
c\`{a}dl\`{a}g functions and uniform metrics on . We will show that
these estimators are in an adaptive sense rate optimal over certain classes of
"approximation spaces." Special cases are the class of functions of bounded
variation (piecewise) H\"{o}lder continuous functions of order
and the class of step functions with a finite but arbitrary number of jumps. In
the latter setting, we will also deduce the rates known from change-point
analysis for detecting the jumps. Finally, the issue of fully automatic
selection of the smoothing parameter is addressed.Comment: Published in at http://dx.doi.org/10.1214/07-AOS558 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Robust nonparametric detection of objects in noisy images
We propose a novel statistical hypothesis testing method for detection of
objects in noisy images. The method uses results from percolation theory and
random graph theory. We present an algorithm that allows to detect objects of
unknown shapes in the presence of nonparametric noise of unknown level and of
unknown distribution. No boundary shape constraints are imposed on the object,
only a weak bulk condition for the object's interior is required. The algorithm
has linear complexity and exponential accuracy and is appropriate for real-time
systems. In this paper, we develop further the mathematical formalism of our
method and explore important connections to the mathematical theory of
percolation and statistical physics. We prove results on consistency and
algorithmic complexity of our testing procedure. In addition, we address not
only an asymptotic behavior of the method, but also a finite sample performance
of our test.Comment: This paper initially appeared in 2010 as EURANDOM Report 2010-049.
Link to the abstract at EURANDOM repository:
http://www.eurandom.tue.nl/reports/2010/049-abstract.pdf Link to the paper at
EURANDOM repository: http://www.eurandom.tue.nl/reports/2010/049-report.pd
Проектирование цеха для производства транспортировочных крышек
Объектом исследования является технология печати и установка для 3Dпечати. Предметом проектирования – транспортировочные крышки.
Целью работы является исследование и расчёт физических характеристик
напечатанных деталей. В процессе работы проведен аналитический обзор. Также изучены
основные виды технологий печати, принципы их работы и создания 3D моделей с помощью 3D принтера.The object of research is printing technology and installation for 3D printing. The subject of design is transportation covers.
The aim of the work is to study and calculate the physical characteristics of printed parts.
In the process, an analytical review was carried out. The main types of printing technologies, the principles of their work and the creation of 3D models with using a 3D printer
Optimasi Portofolio Resiko Menggunakan Model Markowitz MVO Dikaitkan dengan Keterbatasan Manusia dalam Memprediksi Masa Depan dalam Perspektif Al-Qur`an
Risk portfolio on modern finance has become increasingly technical, requiring the use of sophisticated mathematical tools in both research and practice. Since companies cannot insure themselves completely against risk, as human incompetence in predicting the future precisely that written in Al-Quran surah Luqman verse 34, they have to manage it to yield an optimal portfolio. The objective here is to minimize the variance among all portfolios, or alternatively, to maximize expected return among all portfolios that has at least a certain expected return. Furthermore, this study focuses on optimizing risk portfolio so called Markowitz MVO (Mean-Variance Optimization). Some theoretical frameworks for analysis are arithmetic mean, geometric mean, variance, covariance, linear programming, and quadratic programming. Moreover, finding a minimum variance portfolio produces a convex quadratic programming, that is minimizing the objective function ðð¥with constraintsð ð 𥠥 ðandð´ð¥ = ð. The outcome of this research is the solution of optimal risk portofolio in some investments that could be finished smoothly using MATLAB R2007b software together with its graphic analysis
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