1 / 9

Lecture 13

Lecture 13. Chapter 6 Point Estimation. Now, we are ready to deal with some real life applications !. Real life: We do not know the exact values of 99% of the processes ! Population mean =  unknown ! Population standard deviation =  unknown !

hyunki-noh
Download Presentation

Lecture 13

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Lecture 13 Chapter 6 Point Estimation

  2. Now, we are ready to deal with some real life applications ! • Real life: We do not know the exact values of 99% of the processes ! • Population mean =  unknown ! • Population standard deviation =  unknown ! • All we have is the samples that we collect, and using the samples, we can make “good” or reasonable estimations about the population parameters.

  3. Statistical inference is almost always directed towards drawing a conclusion about one or more population parameter(s). • A point estimate of a population parameter, , is a single number that can be regarded as a sensible value for . • We calculate the value of the point estimator from the collected sample data, and the calculated statistic is called the point estimator of , denoted by . • Most well-konwn examples for point estimators are the estimators for the mean and the variance of a population. • The true mean of the population can be estimated by the sample average, sample median, sample trimmed mean etc. Note that the measures mentioned here are all measures of the centre. • The population variance can be estimated by CSS/(n-1), or CSS/(n). We know that statisticians prefer the CSS/(n-1) measure to estimate the population variance.

  4. Like any statistic we calculate using the sample, any estimator is a random variable itself and has an associated pdf. • How to choose among several possible estimators for a given population parameter? • The answer is to choose the estimator which provides the most accurate answer in the long run, i.e. whose value is closer to the real number of the estimated parameter in the long run. • Since a parameter estimator is a random variable with an associated pdf, for it to be an accurate estimator, its pdf should be closely concentrated about the real value of . • If and are the two estimators for , iff

  5. Properties of point estimators

  6. Methods of obtaining the estimators • We will cover the method of moments in the scope of this class. Students interested in the maximum likelihood method described in Devore are encouraged to read pages 267-273. • The Method of Moments: • The kth moment of a population is E(Xk) • The kth moment of a sample is (1/n)(Xik) 2nd moment of a sample: 1st moment of a sample: • The population moments are functions of the unknown parameters 1, 2,…,n. Equating the population moments to the sample moments and solving for the unknown  values will give the moment estimates of the  values.

More Related