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Related Concept Videos

Types of Hypothesis Testing01:11

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There are three types of hypothesis tests: right-tailed, left-tailed, and two-tailed.
When the null and alternative hypotheses are stated, it is observed that the null hypothesis is a neutral statement against which the alternative hypothesis is tested. The alternative hypothesis is a claim that instead has a certain direction. If the null hypothesis claims that p = 0.5, the alternative hypothesis would be an opposing statement to this and can be put either p > 0.5, p < 0.5, or p...
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Hypothesis testing is a critical statistical procedure facilitating informed, evidence-based decisions. It begins with a hypothesis, which is a tentative explanation, or a prediction about a population parameter. This hypothesis can be either a null hypothesis (H0), indicating no effect or difference, or an alternative hypothesis (Ha), suggesting an effect or difference.
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Hypothesis testing is a fundamental statistical tool that begins with the assumption that the null hypothesis H0 is true. During this process, two types of errors can occur: Type I and Type II. A Type I error refers to the incorrect rejection of a true null hypothesis, while a Type II error involves the failure to reject a false null hypothesis.
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Survival analysis is a statistical method used to analyze time-to-event data, often employed in fields such as medicine, engineering, and social sciences. One of the key challenges in survival analysis is dealing with incomplete data, a phenomenon known as "censoring." Censoring occurs when the event of interest (such as death, relapse, or system failure) has not occurred for some individuals by the end of the study period or is otherwise unobservable, and it might have many different...
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Statistical inference techniques, paramount in hypothesis testing, differentiate into two broad categories: parametric and nonparametric statistics.
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Function-based hypothesis testing in censored two-sample location-scale models.

Sundarraman Subramanian1

  • 1Department of Mathematical Sciences, Center for Applied Mathematics and Statistics, New Jersey Institute of Technology, Newark, USA. sundars@njit.edu.

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Summary
This summary is machine-generated.

This study introduces a new statistical test for censored data in two-sample location-scale models. The proposed empirical likelihood method, using bootstrap, provides a robust way to test model adequacy.

Keywords:
Functional delta methodGaussian processLagrange multiplierNelson–Aalen estimatorNonparametric maximum likelihoodQuantile function

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Area of Science:

  • Statistics
  • Biostatistics
  • Survival Analysis

Background:

  • Hypothesis testing for two-sample location-scale models is established for uncensored data.
  • A significant gap exists in testing adequacy for censored two-sample location-scale models.

Purpose of the Study:

  • To develop a novel statistical test for assessing the adequacy of censored two-sample location-scale models.
  • To address the lack of existing methods for hypothesis testing in these specific censored data scenarios.

Main Methods:

  • A plug-in empirical likelihood approach was developed to create a new test statistic.
  • Multiplier bootstrap and model-appropriate resampling were employed to approximate critical values for the null asymptotic distribution.
  • Minimum distance estimators for location and scale were utilized, though any consistent estimators are applicable.

Main Results:

  • The proposed test statistic is asymptotically not distribution-free, necessitating bootstrap for practical application.
  • Numerical studies confirmed the validity and effectiveness of the developed testing method.
  • Real-world data examples were used to illustrate the practical application of the test.

Conclusions:

  • The study successfully introduced a functional test for censored two-sample location-scale models.
  • The bootstrap-based approach provides a reliable method for hypothesis testing in these models.
  • The findings offer a valuable tool for analyzing censored data in various scientific fields.