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Related Concept Videos

Bootstrapping01:24

Bootstrapping

The term "bootstrap" originated in the 19th century as a metaphor for self-improvement or achieving something independently, without external assistance. This concept extends to statistical bootstrapping, a self-contained method for estimating population parameters through resampling, even though it can be computationally intensive. Developed by the American statistician Dr. Bradley Efron in 1979, bootstrapping provides a robust way to perform inference when the original sample size is small or...
Quantifying and Rejecting Outliers: The Grubbs Test01:02

Quantifying and Rejecting Outliers: The Grubbs Test

Sometimes, a data set can have a recorded numerical observation that greatly  deviates from the rest of the data. Assuming that the data is normally distributed, a statistical method called the Grubbs test can be used to determine whether the observation is truly an outlier.  To perform a two-tailed Grubbs test, first, calculate the absolute difference between the outlier and the mean. Then, calculate the ratio between this difference and the standard deviation of the sample. This number is...
Quantitative Analysis01:12

Quantitative Analysis

Quantitative analysis is a technique for measuring the amount of specific constituents in a sample. When the sample's composition is unknown, qualitative analysis is performed first to identify its components, which ensures that the correct substances are measured during the quantitative phase.
In quantitative analysis, two key measurements are made: the sample quantity and a property proportional to the amount of the analyte (the substance being analyzed). This forms the basis of the method...
Percentile01:18

Percentile

A percentile indicates the relative standing of a data value when data are sorted into numerical order from smallest to largest. It represents the percentages of data values that are less than or equal to the pth percentile. For example, 15% of data values are less than or equal to the 15th percentile. Low percentiles always correspond to lower data values. High percentiles always correspond to higher data values.Percentiles divide ordered data into hundredths. To score in the...
Quartile01:15

Quartile

Quartiles are numbers that separate the data into quarters. Quartiles may or may not be part of the data. To find the quartiles, first, find the median or second quartile. The first quartile, Q1, is the middle value of the lower half of the data, and the third quartile, Q3, is the middle value, or median, of the upper half of the data. To get the idea, consider the same data set:
1; 1; 2; 2; 4; 6; 6.8; 7.2; 8; 8.3; 9; 10; 10; 11.5
The median or second quartile is seven. The lower half of the...
Regression Analysis01:11

Regression Analysis

Regression analysis is a statistical tool that describes a mathematical relationship between a dependent variable and one or more independent variables.
In regression analysis, a regression equation is determined based on the line of best fit– a line that best fits the data points plotted in a graph. This line is also called the regression line. The algebraic equation for the regression line is called the regression equation. It is represented as:

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Related Experiment Video

Updated: May 17, 2026

An R-Based Landscape Validation of a Competing Risk Model
05:37

An R-Based Landscape Validation of a Competing Risk Model

Published on: September 16, 2022

Wild bootstrap for quantile regression.

Xingdong Feng1, Xuming He, Jianhua Hu

  • 1School of Statistics and Management, Shanghai University of Finance and Economics, 777 Guoding Road, Shanghai 200433, China, xd.feng@mail.shufe.edu.cn.

Biometrika
|October 11, 2012
PubMed
Summary
This summary is machine-generated.

This study extends the wild bootstrap method to quantile regression, offering a robust way to estimate variance for nonlinear estimators. The modified wild bootstrap effectively handles heteroscedasticity in regression models.

Related Experiment Videos

Last Updated: May 17, 2026

An R-Based Landscape Validation of a Competing Risk Model
05:37

An R-Based Landscape Validation of a Competing Risk Model

Published on: September 16, 2022

Area of Science:

  • Statistics
  • Econometrics

Background:

  • The wild bootstrap is a statistical method primarily used for linear estimators.
  • Existing methods often yield biased variance estimates for nonlinear estimators in regression models.

Purpose of the Study:

  • To extend the validity of the wild bootstrap to quantile regression estimators.
  • To propose a modified wild bootstrap method accommodating a broader class of weight distributions for quantile regression.

Main Methods:

  • Developing a class of weight distributions asymptotically valid for quantile regression.
  • Modifying the wild bootstrap to address biased variance estimates in nonlinear settings.
  • Conducting a simulation study on median regression to compare bootstrap methods.

Main Results:

  • The proposed wild bootstrap modification is asymptotically valid for quantile regression.
  • Most existing weight distributions lead to biased variance estimates for nonlinear estimators.
  • A finite-sample correction enhances the wild bootstrap's ability to handle heteroscedasticity.

Conclusions:

  • The modified wild bootstrap provides a reliable method for variance estimation in quantile regression.
  • This approach accounts for general forms of heteroscedasticity in regression models with fixed designs.
  • The study broadens the applicability of the wild bootstrap in statistical inference.