This course introduces statistical inference, sampling distributions, and confidence intervals. Students will learn how to define and construct good estimators, method of moments estimation, maximum likelihood estimation, and methods of constructing confidence intervals that will extend to more general settings.
課程信息
Sequence in calculus up through Calculus II (preferably multivariate calculus) and some programming experience in R.
您將學到的內容有
Identify characteristics of “good” estimators and be able to compare competing estimators.
Construct sound estimators using the techniques of maximum likelihood and method of moments estimation.
Construct and interpret confidence intervals for one and two population means, one and two population proportions, and a population variance.
Sequence in calculus up through Calculus II (preferably multivariate calculus) and some programming experience in R.
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科罗拉多大学波德分校
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授課大綱 - 您將從這門課程中學到什麼
Point Estimation
In this module you will learn how to estimate parameters from a large population based only on information from a small sample. You will learn about desirable properties that can be used to help you to differentiate between good and bad estimators. We will review the concepts of expectation, variance, and covariance, and you will be introduced to a formal, yet intuitive, method of estimation known as the "method of moments".
Maximum Likelihood Estimation
Large Sample Properties of Maximum Likelihood Estimators
In this module we will explore large sample properties of maximum likelihood estimators including asymptotic unbiasedness and asymptotic normality. We will learn how to compute the “Cramér–Rao lower bound” which gives us a benchmark for the smallest possible variance for an unbiased estimator.
Confidence Intervals Involving the Normal Distribution
關於 Data Science Foundations: Statistical Inference 專項課程
This program is designed to provide the learner with a solid foundation in probability theory to prepare for the broader study of statistics. It will also introduce the learner to the fundamentals of statistics and statistical theory and will equip the learner with the skills required to perform fundamental statistical analysis of a data set in the R programming language.

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