Exact and Approximate Probabilities for the Null Distribution of Bartels Randomness Test

2018 ◽  
pp. 227-240
Author(s):  
Ayana Mateus ◽  
Frederico Caeiro
Keyword(s):  
Null Distribution ◽  
Randomness Test

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 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.

scholarly journals Monitoring Persistence Change in Heavy-Tailed Observations

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 936
Author(s):  
Dan Wang
Keyword(s):  
Kernel Method ◽  
Alternative Hypothesis ◽  
Null Distribution ◽  
Real Data ◽  
Ratio Test ◽  
Finite Sample ◽  
Test Statistic ◽  
Bootstrap Approximation ◽  
Heavy Tailed ◽  
Better Than

In this paper, a ratio test based on bootstrap approximation is proposed to detect the persistence change in heavy-tailed observations. This paper focuses on the symmetry testing problems of I(1)-to-I(0) and I(0)-to-I(1). On the basis of residual CUSUM, the test statistic is constructed in a ratio form. I prove the null distribution of the test statistic. The consistency under alternative hypothesis is also discussed. However, the null distribution of the test statistic contains an unknown tail index. To address this challenge, I present a bootstrap approximation method for determining the rejection region of this test. Simulation studies of artificial data are conducted to assess the finite sample performance, which shows that our method is better than the kernel method in all listed cases. The analysis of real data also demonstrates the excellent performance of this method.

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