Lect14_2700_s09

Lect14_2700_s09 - ENGRD 2700 Basic Engineering Probability...

Info iconThis preview shows pages 1–7. Sign up to view the full content.

View Full Document Right Arrow Icon
Statistical Inference Point Estimation Desirable Properties Standard Error Title Page JJ II J I Page 1 of 33 Go Back Full Screen Close Quit ENGRD 2700 Basic Engineering Probability and Statistics Lecture 14: Point Estimation: Concepts David S. Matteson School of Operations Research and Information Engineering Rhodes Hall, Cornell University Ithaca NY 14853 USA [email protected] March 11, 2009
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Statistical Inference Point Estimation Desirable Properties Standard Error Title Page JJ II J I Page 2 of 33 Go Back Full Screen Close Quit 1. Statistical Inference Given data x 1 ,...,x n , we want to Test a hypothesis, for example: Is data random sample from normal distribution? The model for the data can be represented as a linear model. Design specifications for the dam will not be ex- ceeded in the next 10,000 years. Estimate parameters in an assumed statistical model. Assuming data is normal (based on histograms, QQ-plots), what values of μ,σ should we use? Various methods are possible for estimation of pa- rameters. How do we compare different methods? Which method is best? What does best mean?
Background image of page 2
Statistical Inference Point Estimation Desirable Properties Standard Error Title Page JJ II J I Page 3 of 33 Go Back Full Screen Close Quit 2. Point Estimation What is a statistical model? A Probability Model is a triple S = sample space A =[ events; subsets of S ] P = rule for assigning probabilities to events. A Statistical Model is a family S = sample space A =[ events ] { P θ Θ } = parametric family of probabilties. Note θ could be multidimensional.
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Statistical Inference Point Estimation Desirable Properties Standard Error Title Page JJ II J I Page 4 of 33 Go Back Full Screen Close Quit Example: Suppose we have a normally distributed exper- iment with S = R , P μ,σ where P μ,σ ( -∞ ,x ] = Φ( x ; μ,σ 2 ) . Then what is θ ? What is Θ ? We could define a random variable X N ( μ,σ 2 ) by X ( s ) = s, s S = R , which would make X a normally distributed rv.
Background image of page 4
Statistical Inference Point Estimation Desirable Properties Standard Error Title Page JJ II J I Page 5 of 33 Go Back Full Screen Close Quit Example: Suppose we have an experiment where we want the outcome exponentially distributed: S =[0 , ) A = subsets of positive numbers { P λ ,λ > 0 } = probabilitiy assignments. Here P λ ([0 ,x ]) = 1 - e - λx , x > 0 , and θ = , Θ = We can define an exponential random variable by X ( s ) = s, s S = [0 , ) .
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Statistical Inference Point Estimation Desirable Properties Standard Error Title Page JJ II J I Page 6 of 33 Go Back Full Screen Close Quit Example: Build a statistical model for the experiment: Randomly sample a normal variable n times . S
Background image of page 6
Image of page 7
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 04/05/2009 for the course ENGRD 2700 taught by Professor Staff during the Spring '05 term at Cornell.

Page1 / 33

Lect14_2700_s09 - ENGRD 2700 Basic Engineering Probability...

This preview shows document pages 1 - 7. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online