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Estimation of Sampling Errors, CV, Confidence Intervals

Estimation of Sampling Errors, CV, Confidence Intervals . Arun Srivastava. Properties of a good Estimator. Unbiasedness Efficiency Variance measures precision of an estimator Mean square error measures it’s accuracy Consistency Concept of Bias

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Estimation of Sampling Errors, CV, Confidence Intervals

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  1. Estimation of Sampling Errors, CV, Confidence Intervals Arun Srivastava

  2. Properties of a good Estimator • Unbiasedness • Efficiency • Variance measures precision of an estimator • Mean square error measures it’s accuracy • Consistency • Concept of Bias • Why estimation of sampling error is so important?

  3. Simple random sampling (SRS): • Sample mean is an unbiased estimator of population mean. • ; SRSWR • SRSWOR

  4. Systematic Sampling • An approximate estimator of variance is • If population is assumed to be in random order

  5. PPSWR Sampling

  6. Varying probability sampling (without replacement): • Horvitz –Thompson estimator • For IPPS

  7. Stratified sampling • Estimator of total and estimated variance are

  8. Cluster sampling • Estimator of mean and variances are

  9. Cluster Sampling (Contd.) • Estimator of variance • Variance formula is also given by

  10. Cluster Sampling (Contd.) • Intra-class correlation • Intra-class correlation is the correlation coefficient between pair of units that are in the same cluster. It measures intra-cluster variability.

  11. Multi-stage Sampling • Estimator of total • Variance

  12. Multi-stage Sampling (Contd.) • Estimator of variance • In case of equal clusters

  13. Multi-stage Sampling (Contd.) • Estimator of variance

  14. Sample weights • Base weights • Non response adjustments • Post-stratification adjustments • Base weights are inverse of selection probabilities • Weights provided to ultimate sampling units

  15. Sample weights (Contd.) • For unequal probability wor sampling • For two-stage sampling with pps systematic selection at the first stage and equal probability selection at the second stage weights are (define notations)

  16. THANKS

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