Approximations

Explore various statistical approximation techniques in this comprehensive 2.5-hour video series. Learn about the Binomial Distribution approximating the Hypergeometric Distribution, the Poisson Distribution approximating the Binomial Distribution, and the Chi-square approximation to an F Distribution. Delve into the Delta Method, Normal Approximation to the t Distribution, and Fisher's Approximation. Utilize R for practical applications of the Delta Method in approximating function distributions of sample means. Investigate asymptotic confidence intervals, Welch's Approximation, and exact confidence intervals for comparing population means. Examine moment calculations for sample means of Bernoulli random variables and approximations for functions of sample means. Study the Multivariate Normal Distribution as an approximation to the Multinomial Distribution, Normal Approximation to the Negative Binomial, Method of Moments Estimation for Beta Distribution, and prove Pearson's Goodness of Fit Test Statistic limits to a Chi-square Distribution.

Syllabus

The Binomial Distribution as an approximation to the Hypergeometric Distribution.
The Poisson Distribution as an approximation to the Binomial Distribution.
Chi square approximation to an F Distribution.
Delta Method (univariate).
Normal Approximation to the t Distribution.
Fisher's Approximation to the square root of a chi-squared distribution.
(1/2) Using R and the Delta Method to Approximate the Distribution of a Function of the Sample Mean.
(2/2) Using R and the Delta Method to Approximate the Distribution of a Function of the Sample Mean.
Asymptotic C I for the Difference of 2 Independent Population Means.
Welch's Approximation to a Confidence Interval for 2 normal population means.
Exact C I for the difference of 2 independent normal population means.
1st 4 moments of the sample mean when x is a Bernoulli random variable.
Approximate Mean and Variance of a Function of the Sample Mean.
Multivariate Normal Distribution as an approximation to the Multinomial Distribution.
Normal Approximation to the Negative Binomial.
Method of Moments Estimation for a Beta Distribution (part 1).
Prove Pearson's Goodness of Fit Test Statistic limits to a Chi-sq Distribution.