# NCSU ST 522 - Principles of Data Reduction (37 pages)

Previewing pages*1, 2, 17, 18, 19, 36, 37*of 37 page document

**View the full content.**## Principles of Data Reduction

Previewing pages *1, 2, 17, 18, 19, 36, 37*
of
actual document.

**View the full content.**View Full Document

## Principles of Data Reduction

0 0 69 views

Lecture Notes

- Pages:
- 37
- School:
- North Carolina State University
- Course:
- St 522 - Statistical Theory II

**Unformatted text preview: **

Chapter 6 Principles of Data Reduction 1 Statistical Inference Data X X1 Xn from a probability distribution f x with unknown Our task is Examples to estimate to estimate to estimate to estimate based on data the success probability p in a Bernoulli trial the supporting rate p of a president candidate the average SAT score of the freshmen at a national level Three types of methods to estimate point estimation Chapter 7 hypothesis testing Chapter 8 interval estimation Chapter 9 Two Steps for Statistical Inference Step 1 Data reduction summarizing information about in data with one or a few statistics T T X Data X1 Xn contains much information some are relevant for and some are not Dropping irrelevant information is desirable but dropping relevant information is undesirable the dimension of T is generally smaller than the sample size n Step 2 Estimator construction using T to construct point estimators test statistics upper lower confidence limit 8 2 Statistics and Partition Def A statistic T X is a function of the sample X1 Xn Examples sample mean X sample variance S 2 the largest order statistic X n the smallest order statistic X 1 Partition of Sample Space by T X Consider the discrete case For any possible value t of T there is a corresponding set At x T x t The set collection At all t makes a partition on the sample space of X Note X P X x P T X t x At The event X x is the subset of T X T x i e X x T X T x Example Toss a coin n 3 times and let X1 X3 be respectively the outcome of each toss Let T the total number of heads obtained i e P T 3i 1 Xi Write down the partition of the sample space given by T Remark Often T has a simpler data structure and distribution than the original sample X X1 Xn so it would be nice if we can use T X to summarize and then replace the entire data 9 Important Issues in Data Reduction We should think about the following questions carefully before the simplification process Is there any loss of information due to summarization How to

View Full Document