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Estimating Population Standard Deviation01:26

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When the population standard deviation is unknown and the sample size is large, the sample standard deviation s is commonly used as a point estimate of σ. However, it can sometimes under or overestimate the population standard deviation. To overcome this drawback, confidence intervals are determined to estimate population parameters and eliminate any calculation bias accurately. However, this only applies to random samples from normally distributed populations. Knowing the sample mean and...
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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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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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In practice, we rarely know the population standard deviation. In the past, when the sample size was large, this did not present a problem to statisticians. They used the sample standard deviation s as an estimate for σ and proceeded as before to calculate a confidence interval with close enough results. However, statisticians ran into problems when the sample size was small. A small sample size caused inaccuracies in the confidence interval.
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Small population sizes put a species at extreme risk of extinction due to a lack of variation, and a consequent decrease in adaptability. This weakens the chances of survival under pressures such as climate change, competition from other species, or new diseases. Large populations are more likely to survive pressures such as these, as such populations are more likely to harbor individuals that have genetic variants that are adaptive under new stresses. Small populations are much less...
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Design-based inference on Bernstein type estimators for continuous populations.

Sara Franceschi1, Marzia Marcheselli2, Stefania Naddeo2

  • 1Department of Economics, Statistics and Finance, University of Calabria, via Pietro Bucci 87036, Arcavacata di Rende, Cosenza, Italy.

Biometrical Journal. Biometrische Zeitschrift
|October 24, 2018
PubMed
Summary
This summary is machine-generated.

This study introduces Bernstein polynomial estimation for spatial variables using grid sampling. A pseudo-jackknife estimator is proposed to improve precision in soil survey data analysis.

Keywords:
Bernstein polynomialsdesign-basedjackknife estimatorsystematic grid samplingtessellation stratified sampling

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Area of Science:

  • Spatial statistics
  • Geostatistics
  • Numerical analysis

Background:

  • Spatial estimation is crucial for understanding variable distribution across study areas.
  • Traditional methods may lack precision, especially with grid-based sampling.
  • Bias is a significant factor affecting the accuracy of spatial estimates.

Purpose of the Study:

  • To estimate spatial variable values using Bernstein polynomials with grid sampling.
  • To evaluate the precision of these estimates within a design-based framework.
  • To propose and assess a pseudo-jackknife estimator for reducing bias and improving accuracy.

Main Methods:

  • Bernstein polynomial approximation for spatial data.
  • Design-based framework for precision evaluation.
  • Pseudo-jackknife estimation to address bias in mean squared error.
  • Theoretical analysis and simulation studies for performance assessment.
  • Application to a real-world soil survey dataset.

Main Results:

  • Bernstein polynomials provide a method for spatial estimation with regular grid sampling.
  • The pseudo-jackknife estimator demonstrates improved performance in reducing bias.
  • Simulation studies validate the theoretical findings on estimator precision.
  • The proposed methods are applicable to practical soil science surveys.

Conclusions:

  • Bernstein polynomial estimation is a viable technique for spatial variable estimation.
  • The pseudo-jackknife estimator offers a significant improvement in accuracy by mitigating bias.
  • The study provides a robust framework for evaluating and enhancing spatial estimation techniques.