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Résumé	This flashcard set covers advanced statistical methods at the university level, focusing on topics like ANOVA, missing data analysis, and copula models. It delves into key concepts such as variance, data imputation, and the trade-offs between sample size and data quality. Researchers and students in statistics or data science will find this set particularly useful for understanding complex analytical techniques and their practical applications.
Cartes-fiches	125
Utilisateurs	1
Langue	English
Catégorie	Informatique
Niveau	Université
Crée / Actualisé	04.10.2019 / 11.10.2019
Lien de web	https://card2brain.ch/cards/20191004_srai?max=40&offset=120
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Explain the tradeoff between quality and quantity.

What is given? (4)

State the final formular.

Give an example.

What can we conclude?

given
- finite population y1...yN
- g(y) = quantity of interest
- \(\mu_g=E(g(y))\)
- \(\hat\mu_g=\frac{E(R~g(y))}{E(R)}\)
\((\hat\mu_g - \mu_g) = \rho_{Rg}~\sigma_g~\sqrt{(N-n)/n}\)
- accuracy = quality (correlation between availability of data and quantity of interest) * variation (of quantity of interest) * quantity
example: 90% out of 1.000.000 with 5% correlation is equal to 3600 samples without correlation
>> quantity doesnt compensate quality (important in times of big data)

Why is the assumption X (i.e. own price) -> Y (sales) often wrong. Explain.

How to tackle this? (3)

Y depends on X but also on Z (observable, but not available) and U (unobservable)
- \(f_{Y|X,Z,U}=\int f_{Y|X,Z,U}f_{Z,U}~dZdU \neq f_{Y|X}\)
solutions
- extend dataset by Z, U (i.e. competitors price)
- X independent of Z, U (i.e. own price independent of competitor's price)
- find instrumental variable which influcences X (own price) but independent of Z, U (i.e. competitor's price)

Explain the effect of making X independent of Z,U.

How can this be done?

\(\int\frac{f_{Y,X,Z,U}}{f_{X|Z,U}}dZdU = \int\frac{f_{Y,X,Z,U}}{f_{X}}dZdU = f_{Y|X}\)
>> experiment: make X independent / randomly of other influencing effects

What is the main idea of ANOVA? (1)

Name statistics and idea of it (3)

State the F-statistics. (3)

ANOVA = analysis of variance
test in experimental setting (i.e. comparing two versions >> AB-test)
RSS_X = sum of squares residuals = sum of squared deviation of y_jk to group mean y_bar_k .
RSS_zero = sum of squared deviation to overall mean y_bar . .
idea: if RSS_X and RSS_zero are close >> low variance, low difference >> no significant difference/effect
\(F=\frac{\frac{RSS_0-RSS_X}{K-1}}{\frac{RSS_X}{n-K}}\)
- nominator: how much difference normed by number of groups
- denominator: variance of RSS_X (error in groups) bias corrected (# groups)
- >> relates difference of overall RSS_0 to groups RSS_X with the variance within the group

Name elements of the ANOVA table. (6)

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