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Related Concept Videos

Variance01:15

Variance

The deviations show how spread out the data are about the mean. A positive deviation occurs when the data value exceeds the mean, whereas a negative deviation occurs when the data value is less than the mean. If the deviations are added, the sum is always zero. So one cannot simply add the deviations to get the data spread. By squaring the deviations, the numbers are made positive; thus, their sum will also be positive.The standard deviation measures the spread in the same units as the data.
Estimating Population Standard Deviation01:26

Estimating Population Standard Deviation

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...
Estimating Population Mean with Unknown Standard Deviation01:22

Estimating Population Mean with Unknown Standard Deviation

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.
William S. Gosset (1876–1937) of the Guinness...
Estimating Population Mean with Known Standard Deviation01:16

Estimating Population Mean with Known Standard Deviation

To construct a confidence interval for a single unknown population mean μ, where the population standard deviation is known, we need sample mean as an estimate for μ and we need the margin of error. Here, the margin of error (EBM) is called the error bound for a population mean (abbreviated EBM). The sample mean is the point estimate of the unknown population mean μ.
The confidence interval estimate will have the form as follows:
(point estimate - error bound, point estimate + error bound)
The...
Sampling Distribution01:12

Sampling Distribution

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...
Random Error01:04

Random Error

Random or indeterminate errors originate from various uncontrollable variables, such as variations in environmental conditions, instrument imperfections, or the inherent variability of the phenomena being measured. Usually, these errors cannot be predicted, estimated, or characterized because their direction and magnitude often vary in magnitude and direction even during consecutive measurements. As a result, they are difficult to eliminate. However, the aggregate effect of these errors can be...

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A Method of Trigonometric Modelling of Seasonal Variation Demonstrated with Multiple Sclerosis Relapse Data
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Variance estimation for statistics computed from single recurrent event processes.

Yongtao Guan1, Jun Yan, Rajita Sinha

  • 1Division of Biostatistics, Yale University, New Haven, Connecticut 06520, USA. yongtao.guan@yale.edu

Biometrics
|March 3, 2011
PubMed
Summary
This summary is machine-generated.

This study introduces a new variance estimator for recurrent event processes, improving diagnostic accuracy in semiparametric rate regression analysis. The method offers consistent estimation under mild conditions, enhancing outlier detection and robust regression applications.

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Area of Science:

  • Statistics
  • Biostatistics
  • Survival Analysis

Background:

  • Recurrent event processes are common in various fields, including healthcare and reliability engineering.
  • Accurate variance estimation is crucial for reliable statistical inference and diagnosis in these processes.
  • Existing methods often require strong assumptions about the dependence structure of recurrent events.

Purpose of the Study:

  • To develop a novel variance estimator for statistics derived from single recurrent event processes.
  • To provide a method that requires only semiparametric assumptions on the first-order structure, not the second-order (dependence) structure.
  • To demonstrate the utility of the proposed estimator in semiparametric rate regression analysis.

Main Methods:

  • Proposed a new variance estimation technique for recurrent event data.
  • The method assumes a semiparametric form for the first-order structure of the processes.
  • No assumptions are made regarding the second-order (dependence) structure of the processes.

Main Results:

  • The proposed variance estimator is shown to be consistent for the target parameter under very mild conditions.
  • The estimator's performance is validated through a simulation study.
  • The method is successfully applied to two real-world datasets.

Conclusions:

  • The developed variance estimator offers a robust and flexible tool for analyzing recurrent event data.
  • It is suitable for various applications including outlier detection, residual diagnosis, and robust regression in semiparametric rate regression.
  • The method provides reliable statistical inference even with limited information about the dependence structure.