Exact mean integrated squared error and bandwidth selection for kernel distribution function estimators

Oryshchenko, Vitaliy

doi:10.1080/03610926.2018.1563182

Cited by 6 publications

(4 citation statements)

References 29 publications

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“…The MISE expression ( P m ( E )) is given by Oryshchenko 24 as

P_{m} false(E false) = true {true\int}_{0}^{\infty} P_{m} false(E false/ γ false) P_{R i c i a n} false(γ false) d γ,

where P m ( E / γ ) denotes the conditional error probability, E stands for signal error per symbol, γ is the received SNR while P Rician ( γ ) is the PDF of the output SNR. If Equation (17) is substituted into Equation (18), then this expression is obtained

\begin{matrix} right P_{m} (E) = & left {falsefalse}_{\int}^{0} 2 P_{m} (E / γ) ({falsefalse}_{\sum}^{l = 1} γ_{T C}) (1 + \frac{{(1 - S_{4}^{2})}^{0.5}}{1 - {(1 - S_{4}^{2})}^{0.5}}) \\ right & left \times e x p (- \frac{{(1 - S_{4}^{2})}^{0.5}}{1 - {(1 - S_{4}^{2})}^{0.5}} - {({falsefalse}_{\sum}^{l = 1} γ_{T C})}^{2} (1 + {(1 - S_{4}^{2})}^{...})) \end{matrix}

…”

Section: Methodsmentioning

confidence: 99%

Hybrid threshold combining and maximum ratio combining model for satellite communication over composite Rayleigh and Rician fading channel

Ahmed

Agbaje

et al. 2021

Satell Commun Network

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Communication through satellite is of great task and importance especially in the world of telecommunication infrastructure. It plays a leading role for future communication systems. However, the performance of the satellite communication system is dominated by the channel conditions overwhelmed by multipath fading and ionospheric scintillation effects. Maximum ratio combining (MRC) previously used to tackle this problem is characterized with hardware complexity resulted in long processing time, while threshold combining (TC) with simple hardware display poor performance. Thus, evaluation of hybrid TC-MRC, with closed-form expression over composite Rayleigh and Rician fading channel is necessary. In this paper, TC and MRC are combined to improve the signal quality and performance. The data are modulated using M-ary quadrature amplitude modulation and transmitted over the combined effects. The received signals at varying paths are scanned to select the best paths. A mathematical expression using the probability density function of composite Rayleigh and Rician fading channel for mean integrated square error (MISE) is derived. The model is efficiently simulated and the performance is estimated. The results show that the hybrid TC-MRC model achieves lower MISE and processing time compared to threshold combiner and even maximum ratio combiner, and thereby enhance the performance of the satellite communication system.

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“…The MISE expression ( P m ( E )) is given by Oryshchenko 24 as

P_{m} false(E false) = true {true\int}_{0}^{\infty} P_{m} false(E false/ γ false) P_{R i c i a n} false(γ false) d γ,

\begin{matrix} right P_{m} (E) = & left {falsefalse}_{\int}^{0} 2 P_{m} (E / γ) ({falsefalse}_{\sum}^{l = 1} γ_{T C}) (1 + \frac{{(1 - S_{4}^{2})}^{0.5}}{1 - {(1 - S_{4}^{2})}^{0.5}}) \\ right & left \times e x p (- \frac{{(1 - S_{4}^{2})}^{0.5}}{1 - {(1 - S_{4}^{2})}^{0.5}} - {({falsefalse}_{\sum}^{l = 1} γ_{T C})}^{2} (1 + {(1 - S_{4}^{2})}^{...})) \end{matrix}

…”

Section: Methodsmentioning

confidence: 99%

Hybrid threshold combining and maximum ratio combining model for satellite communication over composite Rayleigh and Rician fading channel

Ahmed

Agbaje

et al. 2021

Satell Commun Network

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“…Fourth order Gaussian-based kernels, Wand and Schucany (1990, Section 2) and Oryshchenko (2017) respectively. Thus the choices of the asymptotically optimal bandwidths (27/4 √ π) 1/9 R(f (4) ) −1/9 n −1/9 and (7/2 √ π) 1/7 R(f (3) ) −1/7 n −1/7 for p.d.f.…”

Section: Kernel Functions and Bandwidthsmentioning

confidence: 99%

“…The condition ψ(k) > 0 is satisfied if k is a symmetric second order kernel, since in this case ψ(k) = K(x)(1 − K(x))dx > 0. Although ψ(k) need not be positive in general, this property holds for certain classes of kernels, including Gaussian kernels of arbitrary order; see Oryshchenko (2017).…”

Section: Known βmentioning

confidence: 99%

Improved density and distribution function estimation

Oryshchenko¹,

Smith²

2019

Electron. J. Statist.

Self Cite

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Given additional distributional information in the form of moment restrictions, kernel density and distribution function estimators with implied generalised empirical likelihood probabilities as weights achieve a reduction in variance due to the systematic use of this extra information. The particular interest here is the estimation of densities or distributions of (generalised) residuals in semi-parametric models defined by a finite number of moment restrictions. Such estimates are of great practical interest, being potentially of use for diagnostic purposes, including tests of parametric assumptions on an error distribution, goodness-of-fit tests or tests of overidentifying moment restrictions. The paper gives conditions for the consistency and describes the asymptotic mean squared error properties of the kernel density and distribution estimators proposed in the paper. A simulation study evaluates the small sample performance of these estimators. Supplements provide analytic examples to illustrate situations where kernel weighting provides a reduction in variance together with proofs of the results in the paper.where E[·] denotes expectation taken with respect to the true population probability law of z. The true parameter value β 0 is generally unknown, but can also be fully or partially known in particular applications.Models specified in the form of unconditional moment restrictions (1.1) convey partial information about the distribution F z of z and are ubiquitous in economics; see, e.g., the monographs Hall (2005) and Mátyás (1999). Many other commonly used models lead to estimators that can be reformulated as solutions to a set of moment restrictions. Clearly, models given by conditional moment restrictions imply (1.1). Traditionally, such models are estimated by the generalised method of moments (GMM). However, the performance of GMM estimators and associated test statistics is often poor in finite samples, which has lead to the development of a number of (information-theoretic) alternatives to GMM.This paper focuses on the class of generalised (G) empirical likelihood (EL) estimators, which has attractive large sample properties; see, e.

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“…where C = ∞ −∞ t k(t) K(t)dt and σ 2 k is the variance of k(•). For further discussion, see the works by [18][19][20][21][22][23][24][25], among others. In cases where the data are censored, we refer to the works of [26,27].…”

Section: Introductionmentioning

confidence: 99%

Smooth Versions of the Mann–Whitney–Wilcoxon Statistics

Herawati

Ahmad

2022

Axioms

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The well-known Mann–Whitney–Wilcoxon (MWW) statistic is based on empirical distribution estimates. However, the data are often drawn from smooth populations. Therefore, the smoothness characteristic is not preserved. In addition, several authors have pointed out that empirical distribution is often an inadmissible estimate. Thus, in this work, we develop smooth versions of the MWW statistic based on smooth distribution function estimates. This approach preserves the data characteristics and allows the efficiency of the procedure to improve. In addition, our procedure is shown to be robust against a large class of dependent observations. Hence, by choosing a rectangular array of known distribution functions, our procedure allows the test to be a lot more reflective of the real data.

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Exact mean integrated squared error and bandwidth selection for kernel distribution function estimators

Cited by 6 publications

References 29 publications

Hybrid threshold combining and maximum ratio combining model for satellite communication over composite Rayleigh and Rician fading channel

Hybrid threshold combining and maximum ratio combining model for satellite communication over composite Rayleigh and Rician fading channel

Improved density and distribution function estimation

Smooth Versions of the Mann–Whitney–Wilcoxon Statistics

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