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Related Concept Videos

Sampling Plans01:23

Sampling Plans

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Sampling is a crucial step in analytical chemistry, allowing researchers to collect representative data from a large population. Common sampling methods include random, judgmental, systematic, stratified, and cluster sampling.
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Sampling is a technique to select a portion (or subset) of the larger population and study that portion (the sample) to gain information about the population. The sampling method ensures that samples are drawn without bias and accurately represent the population. Because measuring the entire population in a study is not practical, researchers use samples to represent the population of interest.
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Appropriate sampling methods ensure that samples are drawn without bias and accurately represent the population. Because measuring the entire population in a study is not practical, researchers use samples to represent the population of interest.
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Sampling is a technique to select a portion (or subset) of the larger population and study that portion (the sample) to gain information about the population. Data are the result of sampling from a population. The sampling method ensures that samples are drawn without bias and accurately represent the population. Because measuring the entire population in a study is not practical, researchers use samples to represent the population of interest. Among the various sampling methods used by...
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Sampling Methods: Overview01:06

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A sample refers to a smaller subset representative of a larger population. In analytical chemistry, studying or analyzing an entire population is often impractical or impossible. Therefore, samples are used to draw inferences and generalize the whole population. The sampling method selects individuals or items from a population to create a sample. Standard sampling methods include random, judgemental, systematic, stratified, and cluster sampling. 
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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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WEIGHTED LIKELIHOOD ESTIMATION UNDER TWO-PHASE SAMPLING.

Takumi Saegusa1, Jon A Wellner1

  • 1Department of Biostatistics, University of Washington, Seattle, Washington 98195-7232, USA, tsaegusa@uw.edu.

Annals of Statistics
|February 25, 2014
PubMed
Summary
This summary is machine-generated.

We developed statistical theory for weighted likelihood estimators (WLE) in complex two-phase sampling. This research provides tools for analyzing estimators with estimated weights and calibration, improving statistical inference in stratified sampling without replacement.

Keywords:
Calibrationestimated weightsnonregularregularsemiparametric modelweighted likelihood

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Area of Science:

  • Statistics
  • Statistical Inference
  • Survey Methodology

Background:

  • Weighted Likelihood Estimators (WLE) are crucial for analyzing complex survey data.
  • Existing methods often assume simpler sampling designs, like Bernoulli sampling.
  • Two-phase stratified sampling without replacement presents unique analytical challenges.

Purpose of the Study:

  • To develop asymptotic theory for Weighted Likelihood Estimators (WLE) under two-phase stratified sampling without replacement.
  • To provide a robust framework for statistical inference in complex survey designs.
  • To compare WLE performance under different second-phase sampling assumptions.

Main Methods:

  • Development of empirical process tools, including Glivenko-Cantelli, M-estimator convergence rates, and Donsker theorems.
  • Application of these tools to derive asymptotic distributions for WLE in semiparametric models.
  • Analysis of WLE with estimated weights and calibration techniques.

Main Results:

  • Established asymptotic theory for WLE under two-phase stratified sampling without replacement.
  • Derived asymptotic distributions for WLE in general semiparametric models, accommodating various nuisance parameter estimation rates.
  • Demonstrated the utility of the developed methods in Cox models with right and interval censoring.

Conclusions:

  • The developed asymptotic theory provides a rigorous foundation for WLE in complex sampling scenarios.
  • The empirical process tools offer general applicability for analyzing estimators in two-phase sampling.
  • The study highlights the importance of accounting for sampling design in statistical inference, with implications for survey data analysis.