Algorithm AS 284: Null Distribution of a Statistic for Testing Sphericity and Additivity: A Jacobi Polynomial Expansion

1993 ◽  
Vol 42 (3) ◽  
pp. 567 ◽  
Author(s):  
Robert J. Boik
Keyword(s):  
Jacobi Polynomial ◽  
Null Distribution ◽  
Polynomial Expansion ◽  
Distribution Of A Statistic

scholarly journals An approach to NLO QCD analysis of the semi-inclusive DIS data with the modified Jacobi polynomial expansion method

JETP Letters ◽  
2005 ◽  
Vol 82 (2) ◽  
pp. 53-58 ◽  
Author(s):  
A. N. Sissakian ◽  
O. Yu. Shevchenko ◽  
O. N. Ivanov
Keyword(s):  
Jacobi Polynomial ◽  
Expansion Method ◽  
Polynomial Expansion ◽  
Polynomial Expansion Method ◽  
Qcd Analysis

scholarly journals On polynomial expansion of multivalent functions

1991 ◽  
Vol 14 (3) ◽  
pp. 443-446
Author(s):  
M. M. Elhosh
Keyword(s):  
Jacobi Polynomial ◽  
Polynomial Expansion ◽  
Coefficient Bounds ◽  
Polynomial Series

Coefficient bounds for meanp-valent functions, whose expansion in an ellipse has a Jacobi polynomial series, are given in this paper.

The Non-Null Distribution of a Statistic in Principal Components Analysis

Biometrika ◽  
1966 ◽  
Vol 53 (3/4) ◽  
pp. 590
Author(s):  
A. M. Kshirsagar
Keyword(s):  
Principal Components Analysis ◽  
Principal Components ◽  
Null Distribution ◽  
Components Analysis ◽  
Distribution Of A Statistic

Bootstrap Analysis

2017 ◽  
Author(s):  
Russell Cheng
Keyword(s):  
Goodness Of Fit ◽  
Null Distribution ◽  
Real Data ◽  
Confidence Regions ◽  
Confidence Bands ◽  
Cumulative Distribution ◽  
Attractive Alternative ◽  
Bootstrap Analysis ◽  
Parametric Bootstrapping ◽  
Anderson Darling

Parametric bootstrapping (BS) provides an attractive alternative, both theoretically and numerically, to asymptotic theory for estimating sampling distributions. This chapter summarizes its use not only for calculating confidence intervals for estimated parameters and functions of parameters, but also to obtain log-likelihood-based confidence regions from which confidence bands for cumulative distribution and regression functions can be obtained. All such BS calculations are very easy to implement. Details are also given for calculating critical values of EDF statistics used in goodness-of-fit (GoF) tests, such as the Anderson-Darling A2 statistic whose null distribution is otherwise difficult to obtain, as it varies with different null hypotheses. A simple proof is given showing that the parametric BS is probabilistically exact for location-scale models. A formal regression lack-of-fit test employing parametric BS is given that can be used even when the regression data has no replications. Two real data examples are given.

scholarly journals A fast sparse spectral method for nonlinear integro-differential Volterra equations with general kernels

2021 ◽  
Vol 47 (3) ◽  
Author(s):  
Timon S. Gutleb
Keyword(s):  
Open Source ◽  
Spectral Method ◽  
Jacobi Polynomial ◽  
Numerical Experiments ◽  
Exponential Convergence ◽  
Analytic Solutions ◽  
Convolution Type ◽  
Volterra Equations ◽  
Polynomial Bases ◽  
Sparsity Structure

AbstractWe present a sparse spectral method for nonlinear integro-differential Volterra equations based on the Volterra operator’s banded sparsity structure when acting on specific Jacobi polynomial bases. The method is not restricted to convolution-type kernels of the form K(x, y) = K(x − y) but instead works for general kernels at competitive speeds and with exponential convergence. We provide various numerical experiments based on an open-source implementation for problems with and without known analytic solutions and comparisons with other methods.

scholarly journals Coefficients of a Comprehensive Subclass of Meromorphic Bi-Univalent Functions Associated with the Faber Polynomial Expansion

Axioms ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 27
Author(s):  
Hari Mohan Srivastava ◽  
Ahmad Motamednezhad ◽  
Safa Salehian
Keyword(s):  
Unit Disk ◽  
Univalent Functions ◽  
Expansion Method ◽  
Upper Bounds ◽  
Polynomial Expansion ◽  
Open Unit ◽  
Open Unit Disk ◽  
Faber Polynomial ◽  
The Subject ◽  
Polynomial Expansion Method

In this paper, we introduce a new comprehensive subclass ΣB(λ,μ,β) of meromorphic bi-univalent functions in the open unit disk U. We also find the upper bounds for the initial Taylor-Maclaurin coefficients |b0|, |b1| and |b2| for functions in this comprehensive subclass. Moreover, we obtain estimates for the general coefficients |bn|(n≧1) for functions in the subclass ΣB(λ,μ,β) by making use of the Faber polynomial expansion method. The results presented in this paper would generalize and improve several recent works on the subject.

Corrigenda: Improved Approximation to the Non-Null Distribution of the Correlation Coefficient

1975 ◽  
Vol 70 (350) ◽  
pp. 494
Author(s):  
Helena Chmura Kraemer
Keyword(s):  
Correlation Coefficient ◽  
Null Distribution

scholarly journals Proposing a machine-learning based method to predict stillbirth before and during delivery and ranking the features: nationwide retrospective cross-sectional study

2021 ◽  
Vol 21 (1) ◽  
Author(s):  
Toktam Khatibi ◽  
Elham Hanifi ◽  
Mohammad Mehdi Sepehri ◽  
Leila Allahqoli
Keyword(s):  
Machine Learning ◽  
External Validation ◽  
Fetal Loss ◽  
Null Distribution ◽  
Training Dataset ◽  
Gradient Boosting ◽  
Support Vector ◽  
Cross Sectional ◽  
Boosting Method ◽  
Demographic Features

Abstract Background Stillbirth is defined as fetal loss in pregnancy beyond 28 weeks by WHO. In this study, a machine-learning based method is proposed to predict stillbirth from livebirth and discriminate stillbirth before and during delivery and rank the features. Method A two-step stack ensemble classifier is proposed for classifying the instances into stillbirth and livebirth at the first step and then, classifying stillbirth before delivery from stillbirth during the labor at the second step. The proposed SE has two consecutive layers including the same classifiers. The base classifiers in each layer are decision tree, Gradient boosting classifier, logistics regression, random forest and support vector machines which are trained independently and aggregated based on Vote boosting method. Moreover, a new feature ranking method is proposed in this study based on mean decrease accuracy, Gini Index and model coefficients to find high-ranked features. Results IMAN registry dataset is used in this study considering all births at or beyond 28th gestational week from 2016/04/01 to 2017/01/01 including 1,415,623 live birth and 5502 stillbirth cases. A combination of maternal demographic features, clinical history, fetal properties, delivery descriptors, environmental features, healthcare service provider descriptors and socio-demographic features are considered. The experimental results show that our proposed SE outperforms the compared classifiers with the average accuracy of 90%, sensitivity of 91%, specificity of 88%. The discrimination of the proposed SE is assessed and the average AUC of ±95%, CI of 90.51% ±1.08 and 90% ±1.12 is obtained on training dataset for model development and test dataset for external validation, respectively. The proposed SE is calibrated using isotopic nonparametric calibration method with the score of 0.07. The process is repeated 10,000 times and AUC of SE classifiers using random different training datasets as null distribution. The obtained p-value to assess the specificity of the proposed SE is 0.0126 which shows the significance of the proposed SE. Conclusions Gestational age and fetal height are two most important features for discriminating livebirth from stillbirth. Moreover, hospital, province, delivery main cause, perinatal abnormality, miscarriage number and maternal age are the most important features for classifying stillbirth before and during delivery.

A NONPARAMETRIC TEST OF SIGNIFICANT VARIABLES IN GRADIENTS

2020 ◽  
pp. 1-45
Author(s):  
Feng Yao ◽  
Taining Wang
Keyword(s):  
Null Distribution ◽  
Monte Carlo Study ◽  
Nonparametric Test ◽  
Hedonic Price ◽  
Finite Sample ◽  
Test Statistic ◽  
Bootstrap Test ◽  
Local Polynomial Estimation ◽  
Polynomial Estimation ◽  
Mean Function

We propose a nonparametric test of significant variables in the partial derivative of a regression mean function. The derivative is estimated by local polynomial estimation and the test statistic is constructed through a variation-based measure of the derivative in the direction of variables of interest. We establish the asymptotic null distribution of the test statistic and demonstrate that it is consistent. Motivated by the null distribution, we propose a wild bootstrap test, and show that it exhibits the same null distribution, whether the null is valid or not. We perform a Monte Carlo study to demonstrate its encouraging finite sample performance. An empirical application is conducted showing how the test can be applied to infer certain aspects of regression structures in a hedonic price model.

Sign in / Sign up

Export Citation Format

Share Document