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Lernmaterialien für Applied Statistics and Econometrics (TUM) an der TU München

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Definitions: What is meant by the term "census"?

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A survey that incorporates all individuals in a given population.

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What does "i.i.d." mean? Give an example that violates this requirement.

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- independent and identically distributed

- example: mit der Gabel zufällig in einen Kuchen Löcher stechen => assumption is violated, da die Löcher teilweise voneinander abhängen

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When is an estimator consistent?

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A consistent estimator converges in probability to the true value, when sample size is increased infinitely.

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What are drawbacks of simple regression and why? 

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It is difficult to make ceteris paribus statements about how x affects y because Assumption 4 (E(u|x)) is mostly unrealistic as the possibility is high that we have omitted variables which then enter the error term

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Definitions: What is meant by the term "sample"?

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A subset of individuals out of the population chosen to represent the population. An important condition for valid results from the sample is its representativeness

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What is the difference between probability mass function (pmf)  and cumulative distribution function (cdf)  and probability density function (pdf) ?

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  • probability mass function (pmf) is a function that gives the probability that a discrete random variable is exactly equal to some value
  • a cumulative distribution function (cdf) describes the probability that a variable X is less than or equal to x:𝐹(𝑥) = 𝑃 (𝑋 ≤ 𝑥) for all x. It can be applied to discrete and continuous random variables
  • If the random variable X is continuous, we cannot assign a probability mass with any specific value of X (because this would mean dividing a probability of 1 between an infinite number of values); instead of pmf, we therefore calculate probability density function (pdf) by taking the first derivative of cdf
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What is the definition of the p-value?

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Given the observed value of the t statistic,
what is the smallest level of significance at which the null hypothesis, 𝐻0, would still be
rejected?

=> probability of rejecting H0 if it is true

=> a small p-value is evidence against H0 because one would reject Hß even at small significance levels

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When is an estimator unbiased?

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An estimator is unbiased if its expected value is equal to the population parameter we want to estimate.

E.g. we explain wage with experience, but we omit tenure and ability -> experience is biased and its effect is overestimated

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What is the difference between cross-sectional data, pooled cross-sections, time series and panel (or longitudinal) data?

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  • Cross-sectional data: 1 point in time, many individuals (random sample)
  • Pooled cross-sections: repeated cross-sections over time, each being a random sample -> no identification of individuals between the different survey waves
  • Time series: one/several variables over time, e.g. GDP over 10 years
  • Panel Data: pooled cross sections with the same individuals
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Definition: What is the standard error?

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The estimated standard deviation of an estimation

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When is a random variable classified as discrete? When is it classified as continuous?

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  • If the range of the random variable consists of a finite number or countable infinitude of values, the random variable is classified as discrete.
  • If the range consists of a non-countable infinitude of values, the random variable is classified as continuous.
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What is covariance (in contrast to correlation)?

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  • Covariance only measures how two variables change together, not the dependency of one variable on another one
  • It can take on values between - inf and + inf
  • Covariance is about the direction of the linear relationship: Increasing the value of one variable might have a positive or a negative impact on the value of the other variable
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Q:

Definitions: What is meant by the term "census"?

A:

A survey that incorporates all individuals in a given population.

Q:

What does "i.i.d." mean? Give an example that violates this requirement.

A:

- independent and identically distributed

- example: mit der Gabel zufällig in einen Kuchen Löcher stechen => assumption is violated, da die Löcher teilweise voneinander abhängen

Q:

When is an estimator consistent?

A:

A consistent estimator converges in probability to the true value, when sample size is increased infinitely.

Q:

What are drawbacks of simple regression and why? 

A:

It is difficult to make ceteris paribus statements about how x affects y because Assumption 4 (E(u|x)) is mostly unrealistic as the possibility is high that we have omitted variables which then enter the error term

Q:

Definitions: What is meant by the term "sample"?

A:

A subset of individuals out of the population chosen to represent the population. An important condition for valid results from the sample is its representativeness

Mehr Karteikarten anzeigen
Q:

What is the difference between probability mass function (pmf)  and cumulative distribution function (cdf)  and probability density function (pdf) ?

A:
  • probability mass function (pmf) is a function that gives the probability that a discrete random variable is exactly equal to some value
  • a cumulative distribution function (cdf) describes the probability that a variable X is less than or equal to x:𝐹(𝑥) = 𝑃 (𝑋 ≤ 𝑥) for all x. It can be applied to discrete and continuous random variables
  • If the random variable X is continuous, we cannot assign a probability mass with any specific value of X (because this would mean dividing a probability of 1 between an infinite number of values); instead of pmf, we therefore calculate probability density function (pdf) by taking the first derivative of cdf
Q:

What is the definition of the p-value?

A:

Given the observed value of the t statistic,
what is the smallest level of significance at which the null hypothesis, 𝐻0, would still be
rejected?

=> probability of rejecting H0 if it is true

=> a small p-value is evidence against H0 because one would reject Hß even at small significance levels

Q:

When is an estimator unbiased?

A:

An estimator is unbiased if its expected value is equal to the population parameter we want to estimate.

E.g. we explain wage with experience, but we omit tenure and ability -> experience is biased and its effect is overestimated

Q:

What is the difference between cross-sectional data, pooled cross-sections, time series and panel (or longitudinal) data?

A:
  • Cross-sectional data: 1 point in time, many individuals (random sample)
  • Pooled cross-sections: repeated cross-sections over time, each being a random sample -> no identification of individuals between the different survey waves
  • Time series: one/several variables over time, e.g. GDP over 10 years
  • Panel Data: pooled cross sections with the same individuals
Q:

Definition: What is the standard error?

A:

The estimated standard deviation of an estimation

Q:

When is a random variable classified as discrete? When is it classified as continuous?

A:
  • If the range of the random variable consists of a finite number or countable infinitude of values, the random variable is classified as discrete.
  • If the range consists of a non-countable infinitude of values, the random variable is classified as continuous.
Q:

What is covariance (in contrast to correlation)?

A:
  • Covariance only measures how two variables change together, not the dependency of one variable on another one
  • It can take on values between - inf and + inf
  • Covariance is about the direction of the linear relationship: Increasing the value of one variable might have a positive or a negative impact on the value of the other variable
Applied Statistics and Econometrics (TUM)

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