Exponential smoothing based on L-estimation

Přemysl Bejda; Tomáš Cipra

Displaying similar documents to “Exponential smoothing based on L-estimation”

Real closed exponential fields

Paola D&amp;amp;#039;Aquino, Julia F. Knight, Salma Kuhlmann, Karen Lange (2012)

Fundamenta Mathematicae

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Ressayre considered real closed exponential fields and “exponential” integer parts, i.e., integer parts that respect the exponential function. In 1993, he outlined a proof that every real closed exponential field has an exponential integer part. In the present paper, we give a detailed account of Ressayre’s construction and then analyze the complexity. Ressayre’s construction is canonical once we fix the real closed exponential field R, a residue field section k, and a well ordering...

Decay of correlations for nonuniformly expanding systems

Sébastien Gouëzel (2006)

Bulletin de la Société Mathématique de France

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We estimate the speed of decay of correlations for general nonuniformly expanding dynamical systems, using estimates on the time the system takes to become really expanding. Our method can deal with fast decays, such as exponential or stretched exponential. We prove in particular that the correlations of the Alves-Viana map decay in $O (e^{- c \sqrt{n}})$ .

Exponential sums of the form $\sum χ {(x)}^{a x} ζ_{m}^{b x}$

S. Gurak (2007)

Acta Arithmetica

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The sum of digits of $⌊ n^{c} ⌋$

Johannes F. Morgenbesser (2011)

Acta Arithmetica

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Elliptic functions, area integrals and the exponential square class on B₁(0) ⊆ ℝⁿ, n > 2

Caroline Sweezy (2004)

Studia Mathematica

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For two strictly elliptic operators L₀ and L₁ on the unit ball in ℝⁿ, whose coefficients have a difference function that satisfies a Carleson-type condition, it is shown that a pointwise comparison concerning Lusin area integrals is valid. This result is used to prove that if L₁u₁ = 0 in B₁(0) and $S u ₁ \in L^{\infty} (S^{n - 1})$ then ${u ₁ |}_{S^{n - 1}} = f$ lies in the exponential square class whenever L₀ is an operator so that L₀u₀ = 0 and $S u ₀ \in L^{\infty}$ implies ${u ₀ |}_{S^{n - 1}}$ is in the exponential square class; here S is the Lusin area integral. The exponential...

Polynomials associated with exponential regression

J. Bukac (2001)

Applicationes Mathematicae

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Fitting exponentials $a + b e^{c x}$ to data by the least squares method is discussed. It is shown how the polynomials associated with this problem can be factored. The closure of the set of this type of functions defined on a finite domain is characterized and an existence theorem derived.

On cumulative $^{13}$ C breath tests: An effort to improve the accuracy of test results revealed a substantial uncertainty in input data

Chleboun, Jan, Kocna, Petr

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A cumulative $^{1} 3$ C breath test can be used to detect a pancreatic disorder, for example. The test is burdened by uncertain input data. Among them, the estimation of CO $_{2}$ production rate is a key issue. An established estimate based on the body surface area could be replaced by an estimate using the basal metabolic rate. Although the latter estimate might be considered more appropriate than the former, the differences between them are large in some sex and agegroups. Such disagreements pose...

Integral representations for solutions of exponential Gauß-Manin systems

Marco Hien, Céline Roucairol (2008)

Bulletin de la Société Mathématique de France

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Let $f, g : U \to 𝔸^{1}$ be two regular functions from the smooth affine complex variety $U$ to the affine line. The associated exponential Gauß-Manin systems on the affine line are defined to be the cohomology sheaves of the direct image of the exponential differential system $𝒪_{U} e^{g}$ with respect to $f$ . We prove that its holomorphic solutions admit representations in terms of period integrals over topological chains with possibly closed support and with rapid decay condition.

The zeros of functions of finite order in $C^{n}$

Lawrence Gruman (1983)

Annales Polonici Mathematici

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Admissibly integral manifolds for semilinear evolution equations

Nguyen Thieu Huy, Vu Thi Ngoc Ha (2014)

Annales Polonici Mathematici

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We prove the existence of integral (stable, unstable, center) manifolds of admissible classes for the solutions to the semilinear integral equation $u (t) = U (t, s) u (s) + \int_{s}^{t} U (t, ξ) f (ξ, u (ξ)) d ξ$ when the evolution family ${(U (t, s))}_{t \geq s}$ has an exponential trichotomy on a half-line or on the whole line, and the nonlinear forcing term f satisfies the (local or global) φ-Lipschitz conditions, i.e., ||f(t,x)-f(t,y)|| ≤ φ(t)||x-y|| where φ(t) belongs to some classes of admissible function spaces. These manifolds are formed by trajectories of the...

The multisample version of the Lepage test

František Rublík (2005)

Kybernetika

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The two-sample Lepage test, devised for testing equality of the location and scale parameters against the alternative that at least for one of the parameters the equality does not hold, is extended to the general case of $k > 1$ sampled populations. It is shown that its limiting distribution is the chi-square distribution with $2 (k - 1)$ degrees of freedom. This $k$ -sample statistic is shown to yield consistent test and a formula for its noncentrality parameter under Pitman alternatives is derived. For...

An Elementary Proof of the Exponential Conditioning of Real Vandermonde Matrices

Stefano Serra Capizzano (2007)

Bollettino dell'Unione Matematica Italiana

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We provide and discuss an elementary proof of the exponential con- ditioning of real Vandermonde matrices which can be easily given in undergraduate courses: we exclusively use the definition of conditioning and the sup-norm formula on $[-1,1]$ for Chebyshev polynomials of first kind. The same proof idea works virtually unchanged for the famous Hilbert matrix.

Orthogonal series regression estimation under long-range dependent errors

Waldemar Popiński (2001)

Applicationes Mathematicae

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This paper is concerned with general conditions for convergence rates of nonparametric orthogonal series estimators of the regression function. The estimators are obtained by the least squares method on the basis of an observation sample $Y_{i} = f (X_{i}) + η_{i}$ , i=1,...,n, where $X_{i} \in A \subset ℝ^{d}$ are independently chosen from a distribution with density ϱ ∈ L¹(A) and $η_{i}$ are zero mean stationary errors with long-range dependence. Convergence rates of the error $n^{- 1} \sum_{i = 1}^{n} (f (X_{i}) - f ̂_{N} (X_{i})) ²$ for the estimator $f ̂_{N} (x) = \sum_{k = 1}^{N} c ̂_{k} e_{k} (x)$ , constructed using an orthonormal system...