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Related Concept Videos

Quartile01:15

Quartile

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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...
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Distributions to Estimate Population Parameter01:26

Distributions to Estimate Population Parameter

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The accurate values of population parameters such as population proportion, population mean, and population standard deviation (or variance) are usually unknown. These are fixed values that can only be estimated from the data collected from the samples. The estimates of each of these parameters are sample proportion, the sample mean, and sample standard deviation (or variance). To obtain the values of these sample statistics, data are required that have particular distribution and central...
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5-Number Summary01:04

5-Number Summary

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In a dataset, the 5-number summary includes the minimum data value, the data value of the first quartile, the median data value or data value of the second quartile, the data value of the third quartile, and the maximum data value. These 5 data values can be visualized as a box and whisker plot.
In a box plot, the minimum and maximum data values represent the lower and upper whiskers in the graph, and the median is designated as the center of the box in the chart. The first quartile and third...
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Modified Boxplots00:57

Modified Boxplots

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A standard box and whisker plot informs us about the spread of the data in a given sample. One can identify the minimum value, maximum value, first quartile value, second quartile or median value, and third quartile.
However, the box plot does not tell the reader about outliers - values that lie far from the center of the data. We can modify the standard box and whisker plot to identify the outliers and visualize the actual spread of the data in a sample.
Initially, we calculate the adjusted...
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Percentile01:18

Percentile

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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.
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Detection of Gross Error: The Q Test01:00

Detection of Gross Error: The Q Test

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When one or more data points appear far from the rest of the data, there is a need to determine whether they are outliers and whether they should be eliminated from the data set to ensure an accurate representation of the measured value. In many cases, outliers arise from gross errors (or human errors) and do not accurately reflect the underlying phenomenon. In some cases, however, these apparent outliers reflect true phenomenological differences. In these cases, we can use statistical methods...
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Quantification of Information Encoded by Gene Expression Levels During Lifespan Modulation Under Broad-range Dietary Restriction in C. elegans
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A General Framework for Quantile Estimation with Incomplete Data.

Peisong Han1, Linglong Kong2, Jiwei Zhao3

  • 1Department of Biostatistics, University of Michigan, Ann Arbor, MI 48109-2029, USA.

Journal of the Royal Statistical Society. Series B, Statistical Methodology
|October 22, 2019
PubMed
Summary
This summary is machine-generated.

This study introduces a novel framework for quantile estimation with incomplete data, combining imputation and inverse probability weighting via empirical likelihood. The method offers multiply robust estimators for various missing data scenarios.

Keywords:
Empirical likelihoodImputationInverse probability weightingMissing dataMultiple robustnessQuantile regression

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Area of Science:

  • Statistics
  • Data Science
  • Econometrics

Background:

  • Quantile estimation is crucial in statistical analysis.
  • Limited research exists for quantile estimation with incomplete data.
  • Existing methods for missing data have limitations.

Purpose of the Study:

  • To propose a general framework for quantile estimation with incomplete data.
  • To develop multiply robust estimators for various missing data settings.
  • To address limitations in current missing data analysis for quantiles.

Main Methods:

  • Combines imputation and inverse probability weighting (IPW) approaches.
  • Utilizes the empirical likelihood method.
  • Develops estimators for marginal and conditional quantiles under different missingness patterns.

Main Results:

  • The proposed method handles diverse missingness settings effectively.
  • It provides multiply robust estimators, consistent if any model is correct.
  • Asymptotic distributions are established using empirical process theory.

Conclusions:

  • The framework offers a flexible and robust solution for quantile estimation with missing data.
  • It advances the field of statistical inference in the presence of incomplete datasets.
  • The multiply robust nature enhances reliability across different modeling assumptions.