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Related Concept Videos

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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Collecting samples or responses from an entire population takes significant time and effort, so a researcher collects responses from only a sample of that population. Suppose a study needs to collect information about a specific mobile application. After sample collection, the researcher analyzes the data and discovers that most individuals in the sample use that specific mobile application. The sample proportion measures the number of individuals in a sample who either use or don't use the...
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A complete procedure for testing a claim about a population proportion is provided here.
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Parametric survival analysis models survival data by assuming a specific probability distribution for the time until an event occurs. The Weibull and exponential distributions are two of the most commonly used methods in this context, due to their versatility and relatively straightforward application.
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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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Given simple random samples of size n from a given population with a measured characteristic such as mean, proportion, or standard deviation for each sample, the probability distribution of all the measured characteristics is called a sampling distribution. How much the statistic varies from one sample to another is known as the sampling variability of a statistic. You typically measure the sampling variability of a statistic by its standard error. The standard error of the mean is an example...
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Related Experiment Video

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Inverse Probability of Treatment Weighting Propensity Score using the Military Health System Data Repository and National Death Index
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Bayesian penalized spline model-based inference for finite population proportion in unequal probability sampling.

Qixuan Chen1, Michael R Elliott2, Roderick J A Little2

  • 1Department of Biostatistics, Columbia University, 722 West 168 Street, New York, NY 10032.

Survey Methodology
|December 5, 2017
PubMed
Summary

We developed a new Bayesian Penalized Spline Predictive (BPSP) estimator for finite population proportions. This method improves estimation efficiency and interval coverage in unequal probability sampling, outperforming existing estimators.

Keywords:
Bayesian analysisBinary dataPenalized spline regressionProbability proportional to sizeSurvey samples

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Area of Science:

  • Statistics
  • Survey Methodology

Background:

  • Finite population proportion estimation is crucial in various fields.
  • Unequal probability sampling presents unique estimation challenges.
  • Existing methods like Hájek (HK) and Generalized Regression (GR) have limitations.

Purpose of the Study:

  • To introduce a novel Bayesian Penalized Spline Predictive (BPSP) estimator.
  • To incorporate inclusion probabilities directly into proportion estimation.
  • To evaluate the BPSP estimator's performance against established methods.

Main Methods:

  • Developed a probit regression model linking binary outcomes to penalized splines of inclusion probabilities.
  • Utilized Gibbs sampling to derive the posterior predictive distribution of the population proportion.
  • Conducted simulation studies and analyzed a real tax auditing dataset.

Main Results:

  • The BPSP estimator demonstrated superior efficiency compared to HK and GR estimators.
  • BPSP's 95% credible intervals offered better confidence coverage and shorter widths, particularly for extreme proportions or small samples.
  • BPSP estimators showed robustness against model misspecification and outliers.

Conclusions:

  • The BPSP estimator is a more efficient and reliable method for finite population proportion estimation in unequal probability sampling.
  • Its robustness and improved interval properties make it a valuable alternative to traditional estimators.
  • The BPSP approach offers enhanced accuracy, especially in challenging sampling scenarios.