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Chapter 3

# Chapter 3 - Chapter 3 Estimator An estimator is a function...

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Chapter- 3 Estimator- An estimator is a function of the sample data. An estimator is a RV,what makes it random? Because the sample data is Random as well. An estimator is a procedure for using the sample data to have an educated guess for the population parameter such as population mean. Different methods for different guesses those diff guesses are estimators. Median- Height of the person that is in the middle. What makes one estimator better than the other. In other words, what are the desirable characteristics of the sampling distribution of an estimator? In general, we would like an estimator that gets as close as possible to the unknown true value, at least in some average sense; in other words, we would like the sampling distribution of an estimator to be as tightly centered on the unknown true value as possible. This observation leads to three specific desirable characteristics of an estimator 1) unbiasedness ( a lack of bias), consistency, and efficiency. An estimate is the numerical value of the estimator in a given sample. METHOD- ESTIMATOR NUMBERICAL VALUE- ESTIMATE Estimate unlike the estimator Is NOT a RV it is a number. Unbiasedness- The desirable property of an estimator is that the mean of its sampling distribution equals uy, if so estimator is said to be unbiased. Uy—is a number. ^Uy is an estimator it is a RV, it is a method. ^Uy is an unbiased estimator if E(^Uy)= Uy

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Consistency- The larger the sample size, the smaller the uncertainity . The probability that it is within a small interval of the true values Uy approaches 1 as the sample size increases, that is ^uy is consistent for uy. The larger the sample the more consistent it is. Efficiency - If both the estimators are unbiased chose the estimator with the tightest sampling distribution, chose the estimator with the smallest variance. Efficiency- smaller variance. Properties of Y – Sampling distribution Y has already been examined. E(Y) = uy Best Linear Unbiased Estimator (BLUE)---? – Choose the one with the most efficiency? Least squares estimator - The estimator m that minimizes the sum of squared gaps Yi --- m in expressions is called the least squares estimator.
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