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Distributions to Estimate Population Parameter01:26

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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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It isn't easy to measure a parameter such as the mean height or the mean weight of a population. So, we draw samples from the population and calculate the mean height or mean weight of the individuals in the sample. This sample data acts as a representative measure of the population parameter. These sample statistics are known as estimates. 
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On many occasions, physicists, other scientists, and engineers need to make estimates of a particular quantity. These are sometimes referred to as guesstimates, order-of-magnitude approximations, back-of-the-envelope calculations, or Fermi calculations. The physicist Enrico Fermi was famous for his ability to estimate various kinds of data with surprising precision. Estimating does not mean guessing a number or a formula at random. Instead, estimation means using prior experience and sound...
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This lesson introduces two critical methods in pharmacokinetics, the Wagner-Nelson and Loo-Riegelman methods, used for estimating the absorption rate constant (ka) for drugs administered via non-intravenous routes. The Wagner-Nelson method relates ka to the plasma concentration derived from the slope of a semilog percent unabsorbed time plot. However, it is limited to drugs with one-compartment kinetics and can be impacted by factors like gastrointestinal motility or enzymatic degradation.
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The interval estimate of any variable is known as the prediction interval. It helps decide if a point estimate is dependable.
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Communication-efficient estimation and inference for high-dimensional quantile regression based on smoothed

Fengrui Di1, Lei Wang1, Heng Lian2

  • 1School of Statistics and Data Science & LPMC, Nankai University, Tianjin, China.

Statistics in Medicine
|October 20, 2022
PubMed
Summary

This study introduces novel distributed estimation methods for high-dimensional quantile regression with small local sample sizes. These communication-efficient techniques improve estimation accuracy and performance in complex datasets.

Keywords:
distributed inferencehigh-dimensional nuisance parameterkernel smoothingmultiround algorithmsnonsmooth losssurrogate likelihood

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Area of Science:

  • Statistical Learning
  • High-Dimensional Data Analysis
  • Distributed Systems

Background:

  • Distributed estimation is crucial in modern statistical learning, but faces challenges with small local sample sizes and high-dimensional covariates.
  • Existing methods struggle with slow convergence rates for nuisance parameter estimation in such distributed settings.

Purpose of the Study:

  • To develop communication-efficient distributed estimators for a low-dimensional parameter vector in high-dimensional quantile regression.
  • To address the challenges posed by small local sample sizes and large covariate dimensions in distributed data settings.

Main Methods:

  • Generalizing the decorrelated score approach to improve nuisance parameter estimation.
  • Employing smoothing techniques within multiround algorithms for enhanced efficiency.
  • Proposing two novel communication-efficient distributed estimators.

Main Results:

  • Theoretical risk bounds and limiting distributions for the proposed estimators are derived.
  • The estimators demonstrate effective performance in finite sample simulations.
  • The methods are validated through an application to a gene expression dataset.

Conclusions:

  • The proposed distributed estimation methods effectively handle high-dimensional quantile regression with small local sample sizes.
  • These techniques offer improved accuracy and efficiency for distributed statistical learning.
  • The study provides practical tools for analyzing complex, distributed datasets.