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Jugal Ghorai 《Annals of the Institute of Statistical Mathematics》1980,32(1):341-350
LetX
1,...,X
n
be i.i.d. random variable with a common densityf. Let
be an estimate off(x) based on a complete orthonormal basis {φ
k
:k≧0} ofL
2[a, b]. A Martingale central limit theorem is used to show that
, where
and
. 相似文献
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Global depth, tangent depth and simplicial depths for classical and orthogonal regression are compared in examples, and properties that are useful for calculations are derived. The robustness of the maximum simplicial depth estimates is shown in examples. Algorithms for the calculation of depths for orthogonal regression are proposed, and tests for multiple regression are transferred to orthogonal regression. These tests are distribution free in the case of bivariate observations. For a particular test problem, the powers of tests that are based on simplicial depth and tangent depth are compared by simulations. 相似文献
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Analysis Mathematica - РАссМАтРИВАЕтсь пРО... 相似文献
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For any nonlinear regression function, it is shown that the orthogonal regression procedure delivers an inconsistent estimator. A new technical approach to the proof of inconsistency based on the implicit-function theorem is presented. For small measurement errors, the leading term of the asymptotic expansion of the estimator is derived. We construct a corrected estimator, which has a smaller asymptotic deviation for small measurement errors.Published in Ukrainskyi Matematychnyi Zhurnal, Vol. 56, No. 8, pp. 1101–1118, August, 2004. 相似文献
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Stefan Paszkowski 《Numerical Algorithms》2008,47(1):35-62
The aim of this paper is to verify efficiency of two acceleration methods for orthogonal series (more strictly, for series
defined at the beginning of Section 1). These methods are quite different although they use the same transform of such a series
given there. The first method (Section 3) has some features common with Levin’s and Weniger’s methods. It may be profitably
used in numerical calculations for a vast class of series. The second one (Sections 4 and 5) is somewhat similar to the Euler–Knopp
transform of power series. Also this method is numerically realizable but more important is that for a narrower class of series,
including some ones having applications in physics, it gives explicit analytic formulae of their transform.
相似文献
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A kind of the proper orthogonal decomposition (POD) is used for data compression of rugged surface and reduction of the Navier–Stokes equations. An error estimate of the POD in model reduction and data compression is discussed. The numerical examples show that the error between the POD approximate solution and reference solution is consistent with theoretical results, and also show that the proposed algorithm is feasible and efficient. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2009 相似文献
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A. M. Gaisin 《Mathematical Notes》1996,60(6):611-621
Best possible conditions are found under which the logarithm of the absolute value of an entire Dirichlet series with real
coefficients rarely changing sign increases on the positive ray in the same way as in the whole plane. This result essentially
strengthens a similar result due to Pavlov concerning the growth of Taylor series on the positive ray.
Translated fromMatematicheskie Zametki, Vol. 60, No. 6, pp. 810–823, December, 1996.
This research was supported by the Russian Foundation for Basic Research under grant No. 93-01-00259. 相似文献
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《Statistics & probability letters》1987,5(3):219-224
In this note a class of nonparametric orthogonal series type estimators for regression function fitting is considered. Sufficient conditions are given for the estimators to attain the optimal convergence rate in the mean integrated square error sense. Using results from the theory of numerical integration, examples of estimators are given, for which the above mentioned conditions hold. 相似文献
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An overall bounded orthonormal set of functions
n
(x) is constructed for which there exists a series
m
=1 ann(x) with coefficients an=o(ln'n/n), which diverges to + almost everywhere. The bibliography contains 4 references.Translated from Matematicheskie Zametki, Vol. 2, No. 5, pp. 483–494, November, 1967. 相似文献
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Witold Bednorz 《Comptes Rendus Mathematique》2011,349(7-8):455-458
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, [0, 1], (n+1) n-. . [2]. — (. 5.4 5.6). . 6.4 2 [5]. , [4]. , , [6] [7]. [1]. 相似文献
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Summary Some sufficient conditions are found for summability of orthogonal series with speed. 相似文献
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