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Financial_Econometrics(Ch3)

# Financial_Econometrics(Ch3) - Chapter 3 Review of...

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1 Chapter 3 Review of Statistics Zhu Tao Dept. of Finance, Jinan University

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2 Statistics h Statistics is the science of using data to learn about unknown characteristics of distributions in populations of interest. Z The cost of 2000 U.S. census Z \$10 billion Z The process takes ten years Z The key insight of statistics Z We could have a random sample from the population. Z We draw inferences from the sample
3 Z Three types of statistics methods Z Estimation Z To compute a “best guess” numerical value for an unknown characteristic of a population Z Hypothesis Testing Z First, to formulate a specific hypothesis about the population. e.g. E(heights of all the people)=1.7m Z Second, to develop a procedure to decide whether the hypothesis is true based on a sample of evidence Z Confidence intervals Z To estimate an interval or range for an unknown population characteristic, using a sample.

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4 3.1 estimation of the population mean h Key Concept Z Estimator Z a function of a randomly selected sample. Z Random variable Z Estimate Z the numerical value of the estimator when the sample is selected Z a number, non-randomness Z Suppose we want to learn about the mean of a population, Y. Z Naturally, the sample average, Y bar, is a estimator of the mean of Y. Of course, Y bar is one of the many possible estimators.
5 Z Criteria for estimator selection Z Unbiasedness Z Consistency Z Efficiency Z Linearity

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6 Z Unbiasedness Z We could evaluate an estimator many times over repeated randomly selected samples Z It is reasonable to hope that, on average, you would get the right answer. Z Definition Z P68 Key concept 3.2
7 Z Consistency Z Associated with sample size Z When the sample size is large, the variance of the estimator is very small Z Definition Z P68 Key concept 3.2

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8 Z Efficiency Z We hope the distribution of an estimator is tightly centered on the true value of the characteristic of the population Z For two possible unbiased estimator, Y1 and Y2, if var(Y1)<var(Y2), Y1 is said to be more efficient than Y2. Z Definition Z P68 Key concept 3.2
9 Z Linearity Z If the estimator is a linear function of the a sample drawn from the population Z The property of linearity helps to estimate the distribution of the estimator

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10 Z Properties of Z unbiasedness: Z consistency: (Law of large numbers) Z Efficiency: It can be proved that Y bar is efficient Z Example: Z P70 Key Concept 3.3 Z Linearity: is an obvious linear function of a random selected sample Z BLUE (Best Linear Unbiased Estimator) Y μ Y E = ) ( Y p μ Y Y Y Y Y Y and Y vs Y ~ .
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