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Sampling Distribution of the Mean
Published in Marcello Pagano, Kimberlee Gauvreau, Heather Mattie, Principles of Biostatistics, 2022
Marcello Pagano, Kimberlee Gauvreau, Heather Mattie
Suppose that we are interested in estimating the mean value of a continuous random variable. For example, we might wish to make a statement about the mean serum cholesterol level of all males residing in the United States, based on a sample drawn from this population. The obvious approach would be to use the mean of the sample as an estimate of the unknown population mean μ. The sample mean is called an estimator of the parameter There are many different approaches to the process of estimation; in this case, because the population is assumed to be normally distributed, the sample mean is something called a maximum likelihood estimator[173]. The method of maximum likelihood finds the value of the parameter that is most likely to have produced the observed sample data. This method can usually be relied on to yield reasonable estimators. Note, however, that two different samples are likely to result in different sample means; consequently, there is some degree of uncertainty involved. Before we apply this estimation procedure, therefore, we first examine some of the properties of the sample mean and the ways in which it can vary.
Bayesian Estimation of Sample Size and Power
Published in Harry Yang, Steven J. Novick, Bayesian Analysis with R for Drug Development, 2019
where is the sample mean of the ith trial and . Using the data from Table 3.1, it follows that the weighted sample mean
Probability and Statistics
Published in Richard L. Morin, Monte Carlo Simulation in the Radiological Sciences, 2019
where X and Y are independent random variables for which xj is one of n observed values of x and yk is one of n observed values of y. Define the X sample mean, , by
A geometric approach for computing tolerance bounds for elastic functional data
Published in Journal of Applied Statistics, 2020
J. Derek Tucker, John R. Lewis, Caleb King, Sebastian Kurtek
Let k-variate Gaussian distribution with mean vector μ and covariance matrix Σ. The sample mean vector A are defined as: p proportion of the data from a β confidence is given by b is known as the tolerance factor, and is determined by the probability condition b is known to be extremely difficult and there are multiple approximations that have been proposed in the literature (see [11] for multiple methods). In this work, we use the approach of Krishnamoorthy and Mondal [12] due to its known accuracy and precision. Note that in the fPCA coefficient space 10).
A generalized BLUE approach for combining location and scale information in a meta-analysis
Published in Journal of Applied Statistics, 2022
Xin Yang, Alan D. Hutson, Dongliang Wang
In meta-analyses of continuous outcomes, the sample mean and standard deviation are two commonly used summary statistics in order to pool data, but many trials report other summary statistics instead. Researchers need to transform those quantities back to the sample mean and standard deviation. We propose a generalized BLUE methodology for estimating individual and global mean and standard deviation based on summary statistics in published studies. We conduct a simulation study to compare the proposed BLUE with the existing methods of Luo et al. [17] and Wan et al. [23] for the individual case and inverse variance weights for the global case.
A semi-analytical solution to the maximum-likelihood fit of Poisson data to a linear model using the Cash statistic
Published in Journal of Applied Statistics, 2022
Massimiliano Bonamente, David Spence
The asymptotic value of 10), and it is negative if 18) is the sample mean of the variable