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MathematicsThis study investigates the Bt-transformation of probability measures within the framework of free probability. A primary focus is the invariance under this transformation of two fundamental families: the free Meixner family and the free analog of the ...
Abdulmajeed Albarrak +2 more
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Wavelet estimations of the derivatives of variance function in heteroscedastic model
AIMS Mathematics, 2023 This paper studies nonparametric estimations of the derivatives $ r^{(m)}(x) $ of the variance function in a heteroscedastic model. Using a wavelet method, a linear estimator and an adaptive nonlinear estimator are constructed.
Junke Kou, Hao Zhang
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r-Free Convolution and Variance Function
AxiomsThe concept of r-free convolution (which is represented by r) was introduced for 0≤r≤1. It is equal to the Boolean additive convolution ⊎ if r=0 and reduced to the free additive convolution ⊞ when r=1.
Shokrya S. Alshqaq +2 more
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Variance Function Estimation [PDF]
Journal of the American Statistical Association, 1987 We develops a general theory for variance function estimation in regression. Most methods in common use are included in our development. The general qualitative conclusions are these. First, most variance function estimation procedures can be looked upon as regressions with responses' being transformations of absolute residuals from a preliminary fit ...
Davidian, M., Carroll, R.J.
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On the Notion of Reproducibility and Its Full Implementation to Natural Exponential Families
Mathematics, 2021 Let F=Fθ:θ∈Θ⊂R be a family of probability distributions indexed by a parameter θ and let X1,⋯,Xn be i.i.d. r.v.’s with L(X1)=Fθ∈F. Then, F is said to be reproducible if for all θ∈Θ and n∈N, there exists a sequence (αn)n≥1 and a mapping gn:Θ→Θ,θ⟼gn(θ ...
Shaul K. Bar-Lev
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Local Polynomial Variance-Function Estimation [PDF]
Technometrics, 1997 The conditional variance function in a heteroscedastic, nonparametric regression model is estimated by linear smoothing of squared residuals. Attention is focussed on local polynomial smoothers. Both the mean and variance functions are assumed to be smooth, but neither is assumed to be in a parametric family. The effect of preliminary estimation of the
D. Ruppert +3 more
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Mathematics, 2022 The large arcsine exponential dispersion model (LAEDM) is a class of three-parameter distributions on the non-negative integers. These distributions show the specific characteristics of being leptokurtic, zero-inflated, overdispersed, and skewed to the ...
Shaul K. Bar-Lev, Ad Ridder
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Warped functional analysis of variance [PDF]
Biometrics, 2014 SummaryThis article presents an Analysis of Variance model for functional data that explicitly incorporates phase variability through a time‐warping component, allowing for a unified approach to estimation and inference in presence of amplitude and time variability.
Gervini, Daniel, Carter, Patrick A.
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Remote Sensing, 2022 Accurately estimating forest aboveground biomass (AGB) based on remote sensing (RS) images at the regional level is challenging due to the uncertainty of the modeling sample size.
Qingtai Shu +5 more
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Interval Kepercayaan Untuk Fungsi Nilai Harapan dan Fungsi Ragam Proses Poisson Periodik Majemuk
Jambura Journal of Mathematics, 2022 Compound cyclic Poisson process have the mean and variance functions. The objective of this paper is to construct confidence intervals for respectively the mean and variance functions of a compound cyclic Poisson process with significance level 0alpha1 ...
Auliya Fithry +2 more
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