Smoothed Quantiles for χ 2 Type Test Statistics with Applications

2021 ◽  
pp. 1-30
Author(s):  
Ke-Hai Yuan ◽  
Brenna Gomer ◽  
Katerina M. Marcoulides
Keyword(s):  
Test Statistics ◽  
Type Test

scholarly journals Robust Statistical Inference in Generalized Linear Models Based on Minimum Renyi’s Pseudodistance Estimators

Entropy ◽  
2022 ◽  
Vol 24 (1) ◽  
pp. 123
Author(s):  
María Jaenada ◽  
Leandro Pardo
Keyword(s):  
Generalized Linear Models ◽  
Influence Function ◽  
Regression Models ◽  
Linear Models ◽  
Asymptotic Properties ◽  
Significant Loss ◽  
Superior Performance ◽  
Test Statistics ◽  
Linear Regression Models ◽  
Type Test

Minimum Renyi’s pseudodistance estimators (MRPEs) enjoy good robustness properties without a significant loss of efficiency in general statistical models, and, in particular, for linear regression models (LRMs). In this line, Castilla et al. considered robust Wald-type test statistics in LRMs based on these MRPEs. In this paper, we extend the theory of MRPEs to Generalized Linear Models (GLMs) using independent and nonidentically distributed observations (INIDO). We derive asymptotic properties of the proposed estimators and analyze their influence function to asses their robustness properties. Additionally, we define robust Wald-type test statistics for testing linear hypothesis and theoretically study their asymptotic distribution, as well as their influence function. The performance of the proposed MRPEs and Wald-type test statistics are empirically examined for the Poisson Regression models through a simulation study, focusing on their robustness properties. We finally test the proposed methods in a real dataset related to the treatment of epilepsy, illustrating the superior performance of the robust MRPEs as well as Wald-type tests.

scholarly journals Prostate cancer survival estimates: An application with piecewise hazard function derivation

2019 ◽  
Vol 08 (03) ◽  
pp. 150-159
Author(s):  
Atanu Bhattacharjee ◽  
Atul Budukh ◽  
Rajesh Dikshit
Keyword(s):  
Prostate Cancer ◽  
Hazard Rate ◽  
Hazard Function ◽  
Cancer Survival ◽  
Test Statistics ◽  
Aged Patients ◽  
Time Points ◽  
Maximum Duration ◽  
Type Test

Abstract Background: The hazard function is defined as time-dependent. However, it is an overlooked area of research about the estimation of hazard function within the frame of time. The possible explanation could be carried by estimating function through the changes of time points. It is expected that it will provide us the overall idea of survival trend. This work is dedicated to propose a method to work with piecewise hazard rate. It is a data-driven method and provides us the estimates of hazard function with different time points. Methods: The proposed method is explored with prostate cancer patients, registered in the Surveillance, Epidemiology, and End Results Program and having aged at diagnosis with range 40–80 years and above. A total of 610,814 patients are included in this study. The piecewise hazard rate is formulated to serve the objective. The measurement of piecewise hazard rate is compared with Wald-type test statistics, and corresponding R function is provided. The duration of follow-ups is split into different intervals to obtain the piecewise hazard rate estimates. Results: The maximum duration of follow-up observed in this study is 40 years. The piecewise hazard rate changes at different intervals of follow-ups are observed almost same except few later intervals in the follow-up. The likelihood of hazard in earlier aged patients observed lower in comparison to older patients. The hazard rates in different grades of prostate cancer also observed separately. Conclusion: The application of piecewise hazard helps to generate statistical inference in a deeper manner. This analysis will provide us the better understanding of a requirement of effective treatment toward prolonged survival benefit for different aged patients.

scholarly journals Maximal type test statistics based on conditional processes

1996 ◽  
Vol 53 (1) ◽  
pp. 1-19
Author(s):  
Jan Beirlant ◽  
John H.J. Einmahl
Keyword(s):  
Test Statistics ◽  
Type Test

scholarly journals Generalized multivariate rank type test statistics via spatial U-quantiles

2008 ◽  
Vol 78 (4) ◽  
pp. 376-383 ◽  
Author(s):  
Weihua Zhou ◽  
Robert Serfling
Keyword(s):  
Test Statistics ◽  
Type Test

scholarly journals New Test Statistics for One and Two Mean Vectors with Two-step Monotone Missing Data

2020 ◽  
Vol 9 (6) ◽  
pp. 56
Author(s):  
Mizuki Onozawa ◽  
Ayaka Yagi ◽  
Takashi Seo
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Asymptotic Behavior ◽  
Missing Data ◽  
Test Statistics ◽  
Test Statistic ◽  
Type Test ◽  
Mean Vectors ◽  
Mean Vector

We consider the tests for a single mean vector and two mean vectors with two-step monotone missing data. In this paper, we propose new test statistics for one sample and two sample designs based on the simplified T^2-type test statistic. Further, we present the approximation to the upper percentiles of these statistics and propose the transformed test statistics. Finally, we investigate the accuracy and asymptotic behavior of the approximation for X^2 distribution by a Monte Carlo simulation.

scholarly journals Goodness-of-fit Test for the Bivariate Hermite Distribution

2020 ◽  
Author(s):  
Francisco Novoa-Muñoz ◽  
Pablo González-Albornoz
Keyword(s):  
Goodness Of Fit ◽  
Null Distribution ◽  
Test Statistics ◽  
Finite Sample ◽  
Goodness Of Fit Test ◽  
Bootstrap Approach ◽  
Type Test ◽  
Empirical Probability ◽  
Hermite Distribution ◽  
Von Mises

This paper studies the goodness of fit test for the bivariate Hermite distribution. Specifically, we propose and study a Cramér-von Mises-type test based on the empirical probability generation function. The bootstrap can be used to consistently estimate the null distribution of the test statistics. A simulation study investigates the goodness of the bootstrap approach for finite sample sizes.

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