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Confidence Intervals01:21

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An unbiased point estimate is often insufficient to predict a population estimate, such as population mean or population proportion. In this scenario, a confidence interval is used. A confidence interval is an estimate similar to a  sample proportion. However, unlike the point estimate which is a single value, the confidence interval  contains a range of values. These values have lower and upper limits, known as confidence limits, and can be designated as L1 and L2, respectively.
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A point estimate of the population mean is obtained from a single sample. Such a point estimate does not represent a population well because it needs to account for variability in the population. Single point estimate can also be biased despite the sample being selected randomly. Thus, a point estimate is often unreliable. A confidence interval is needed to reduce this unreliability.
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A confidence interval is a better estimate of the population than a point estimate, as it uses a range of values from a sample instead of a single value.
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The confidence coefficient is also known as the confidence level or degree of confidence. It is the percent expression for the probability, 1-α, that the confidence interval contains the true population parameter assuming that the confidence interval is obtained after sufficient unbiased sampling; for example, if the CL = 90%, then in 90 out of 100 samples the interval estimate will enclose the true population parameter. Here α is the area under the curve, distributed equally under...
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Confidence sets for dynamic poverty indexes.

Guglielmo D'Amico1, Riccardo De Blasis2

  • 1Department of Economics, Università 'G. D'Annunzio', Chieti, Italy.

Journal of Applied Statistics
|November 3, 2022
PubMed
Summary
This summary is machine-generated.

This study introduces a dynamic model for poverty measurement, showing how to accurately approximate poverty indexes using statistical laws. The research provides a method to track poverty and inequality evolution over time.

Keywords:
Markov processU-statisticsdynamic poverty measuresnonparametric estimationpopulation dynamic

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Area of Science:

  • Economics
  • Statistics
  • Econometrics

Background:

  • Poverty indexes are crucial for economic analysis but often lack dynamic considerations.
  • Modeling individual income fluctuations is essential for accurate poverty assessment.

Purpose of the Study:

  • To develop and validate a dynamic framework for poverty measurement.
  • To assess the accuracy of approximating poverty indexes using large numbers in economic systems.
  • To establish methods for confidence sets in dynamic poverty measures.

Main Methods:

  • Application of the strong law of large numbers to an infinite agent economic system.
  • Utilizing the theory of U-statistics to derive a multivariate central limit theorem.
  • Developing confidence sets for dynamic poverty indexes.

Main Results:

  • A multivariate central limit theorem for dynamic poverty measures was established.
  • The study demonstrates how to construct confidence sets, validating the model's appropriateness.
  • The approach effectively models the evolution of poverty and inequality.

Conclusions:

  • The dynamic framework provides a robust method for analyzing poverty and inequality.
  • The model's effectiveness is confirmed by application to Italian income data.
  • This approach enables the determination of poverty and inequality trends in real economies.