Estimator and Sampling Distribution
3.2. Estimator and Sampling Distribution#
Learning Outcome
Students will be able to estimate the parameters of a model, use simulation methods to evaluate different estimators, and describe their bias and variance.
Sample Tasks
Identify the parameters of a statistical model to be estimated.
Compute one-sample summaries (estimates) of the center of a distribution – mean, median, and trimmed mean.
Simulate samples of data from a generative model, summarize the sample with an estimator, and examine the estimator’s sampling distribution (histogram / density estimate), its center and its spread.
Use the center and spread of the sampling distribution to describe the accuracy of an estimator in terms of bias and variance.
Simulate data to explore and evaluate sampling distributions of estimators in complex statistical models.
Our first readings, from Computational and Inferential Thinking [ADW21], discusses the parameter(s) of a distribution and estimating these parameters with a statistic (or several statistics).
Reading Questions
What is the difference between a parameter and a statistic?
What is the difference between the distribution of a population and the distribution of a statistic?
Our second readings, also from Computational and Inferential Thinking [ADW21], go deeply into estimating two statistics: the mean and the standard deviation.
Reading Questions
When will the mean equal the median?
What does the standard deviation tell about how spread out the data is?
What is the difference between the standard deviation of the data and the standard deviation of sample means?
Is the sample mean a biased or unbiased estimator of the population mean?