ECONOMETRICS By Prof. Burak Saltoglu

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ECONOMETRICSBy Prof. Burak Saltoglu

• Lecture 5
• Statistical Inference

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Standard Normal Distribution

• Standard normal distribution is a normal
  distribution with 0 mean and 1 variance. To
  standardize a normal distribution, we define

Then
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Standard Normal Distribution
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Chi Distribution

• If denote m independent N(0,1), random
  variables, then

And
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Chi Distribution
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t-Distribution

• A t random variable is formed by dividing a
  standart normal variable by the square root of an
  independent chi-square random variable.

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t-Distribution
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F-Distribution

• An F random variable is formed by the ratio of
  two independent chi-square random variables that
  have been divided by their degrees of freedom.

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F-Distribution
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Interval Estimation on Regresion Coefficents and
Hypothesis Testing
which is an unbiased estimator of
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Interval Estimation, Hypothesis Testing

• Our focus
• The sampling variability of the estimators.
• Because of the sampling fluctuations, a single
  point estimator is likely to differ from the
  true value.
• In stead of relying on the point estimate alone,
  we may construct an interval around the point
  estimator.

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Confidence Interval of
We know
Then
which is standart normal.
We also know
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Confidence Interval of
Consider
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Confidence Interval of

• But

if
Then,
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Confidence Interval of
Then we can use this test statistic to construct
confidence intervals and for hypothesis testing.
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Hypothesis Testing

• One Sided Tests

or
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Hypothesis Testing
Choosing , the Level of Significance
is the probability of committing Type I error
the probability of rejecting the true
hypothesis . Since we dont know the costs of
making the two types of errors by convention
is set to 0.05 or 0.01. The exact level of
significance P is the exact probability of
committing Type I error.
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Hypothesis Testing

• In general,
• , where c is a constant, against the
  alternative , we compute the value of the test
  statistic
• We reject if

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Prediction Intervals
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Prediction Intervals
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END

• End of lecture