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slides_Ch5_W[1] - Econometrics Textbook Reference Chapter 5...

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Econometrics Textbook Reference: Chapter 5, Wooldridge Melissa Tartari Yale Melissa Tartari (Yale) Econometrics 1 / 27
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Large Sample Theory: A Premise In addition to °nite sample properties it is important to know the asymptotic or large sample properties of estimators and test statistics. These properties are not de°ned for a particular sample size; rather, they are de°ned as the sample size grows without bound . Melissa Tartari (Yale) Econometrics 2 / 27
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Large Sample Theory: A Premise In addition to °nite sample properties it is important to know the asymptotic or large sample properties of estimators and test statistics. These properties are not de°ned for a particular sample size; rather, they are de°ned as the sample size grows without bound . We will see that: Melissa Tartari (Yale) Econometrics 2 / 27
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Large Sample Theory: A Premise In addition to °nite sample properties it is important to know the asymptotic or large sample properties of estimators and test statistics. These properties are not de°ned for a particular sample size; rather, they are de°ned as the sample size grows without bound . We will see that: The OLS estimator of β j has satisfactory large sample properties under assumptions LR.1-LR.4. Melissa Tartari (Yale) Econometrics 2 / 27
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Large Sample Theory: A Premise In addition to °nite sample properties it is important to know the asymptotic or large sample properties of estimators and test statistics. These properties are not de°ned for a particular sample size; rather, they are de°ned as the sample size grows without bound . We will see that: The OLS estimator of β j has satisfactory large sample properties under assumptions LR.1-LR.4. Even without normality (namely, LR.6), the t and F statistics have approximately t and F distributions in large sample. Melissa Tartari (Yale) Econometrics 2 / 27
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A Review of Finite sample properties Finite sample properties of estimators are properties that hold for a sample of any size, no matter how large or small. Melissa Tartari (Yale) Econometrics 3 / 27
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A Review of Finite sample properties Finite sample properties of estimators are properties that hold for a sample of any size, no matter how large or small. EXAMPLE: Unbiasedness Melissa Tartari (Yale) Econometrics 3 / 27
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A Review of Finite sample properties Finite sample properties of estimators are properties that hold for a sample of any size, no matter how large or small. EXAMPLE: Unbiasedness De°nition: An estimator W of θ is unbiased if, for all possible values of θ , E [ W ] = θ Melissa Tartari (Yale) Econometrics 3 / 27
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A Review of Finite sample properties Finite sample properties of estimators are properties that hold for a sample of any size, no matter how large or small. EXAMPLE: Unbiasedness De°nition: An estimator W of θ is unbiased if, for all possible values of θ , E [ W ] = θ Meaning: if we could inde°nitely draw random (°nite) samples on Y from the population, compute an estimate each time, and then average them over all samples, we would obtain θ . Unbiasedness does
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