Stones in a box N=CR/T is called an estimator. Give me any box of stones, i can use the same "method"or procedure"or formula to estimate the number of stones. Give me a specific box of stones, I can give you an estimate of the number of stones in that box (using the estimator N=CR/T). For example, I estimate that there are 510 stones in the box 510 stones is an estimate of number of stones in the box Ka-fu Wong C2007 ECON1003: Analysis of Economic Data Lesson 1-11
Ka-fu Wong © 2007 ECON1003: Analysis of Economic Data Lesson1-11 Stones in a box N=CR/T is called an estimator. Give me any box of stones, I can use the same “method” or “procedure” or “formula” to estimate the number of stones. Give me a specific box of stones, I can give you an estimate of the number of stones in that box (using the estimator N=CR/T). For example, I estimate that there are 510 stones in the box. “510 stones” is an estimate of number of stones in the box
Simulations to see the properties of this proposed estimator How good is the proposed estimator? a To see the properties of this proposed estimator i have used maTLaB to simulate our Capture-recapture experiment with different numbers of capture(C) and different numbers of recapture(R), relative to the total number of fish in the pond. Throughout N=500 and 1000 simulations That is, I will give you 1000 boxes of stones, each having 500 stones. I am not telling you the number of stones in each box. You will have to produce 1000 estimates of stones in these 1000 boxes. I would like to see how good your estimator Method"or procedure"or formula")is Ka-fi Wong 2007 ECON1003: Analysis of Economic Data Lesson 1-12
Ka-fu Wong © 2007 ECON1003: Analysis of Economic Data Lesson1-12 Simulations to see the properties of this proposed estimator ◼ How good is the proposed estimator? ◼ To see the properties of this proposed estimator, I have used MATLAB to simulate our Capture-recapture experiment with different numbers of capture (C) and different numbers of recapture (R), relative to the total number of fish in the pond. ◼ Throughout, ◼ N=500 and ◼ 1000 simulations That is, I will give you 1000 boxes of stones, each having 500 stones. I am not telling you the number of stones in each box. You will have to produce 1000 estimates of stones in these 1000 boxes. I would like to see how good your estimator (“method” or “procedure” or “formula”) is
Definition: Estimator Estimator is a formula or a rule that takes a set of data and returns an estimate of the population guantity(also known as population parameter) we are interested in e(X1X2r- Xn) Ka-fu Wong C2007 ECON1003: Analysis of Economic Data Lesson 1-13
Ka-fu Wong © 2007 ECON1003: Analysis of Economic Data Lesson1-13 Definition: Estimator ◼ Estimator is a formula or a rule that takes a set of data and returns an estimate of the population quantity (also known as population parameter) we are interested in. θ(x1 ,x2 ,...,xn)
Example: An estimator for the population mean If we are interested in the population mean a very intuitive estimator of the population mean based on a sample(Xyx2…yxkn)is e(X1X2y Xn)=(X1+X2+atxn)/n a Suppose someone suggest e(x1X2 74 xn)=(x1+x2+…+xn+1)/n Ka-fu Wong C2007 ECON1003: Analysis of Economic Data Lesson 1-14
Ka-fu Wong © 2007 ECON1003: Analysis of Economic Data Lesson1-14 Example: An estimator for the population mean ◼ If we are interested in the population mean, a very intuitive estimator of the population mean based on a sample (x1 ,x2 ,...,xn) is θ(x1 ,x2 ,...,xn)= (x1+x2+...+xn)/n ◼ Suppose someone suggest θ(x1 ,x2 ,...,xn)= (x1+x2+...+xn+1)/n
Simulating the properties of a sample mean estimator a If we were to study the properties of the following two estimators for the population mean: e(xiX2rXn=(X,+X2+un+Xn)/n versus 8(X1x2y…Xn)=(x1+x2+…+xn+1)/n a With some basic computing skills, we may perform Monte Carlo simulations to compare their properties. Ka-fu Wong C2007 ECON1003: Analysis of Economic Data Lesson 1-15
Ka-fu Wong © 2007 ECON1003: Analysis of Economic Data Lesson1-15 Simulating the properties of a sample mean estimator ◼ If we were to study the properties of the following two estimators for the population mean: θ(x1 ,x2 ,...,xn)= (x1+x2+...+xn)/n versus θ(x1 ,x2 ,...,xn)= (x1+x2+...+xn+1)/n ◼ With some basic computing skills, we may perform Monte Carlo simulations to compare their properties