Mahler Flashcards

1
Q

Tests for changing risk parameters over time

A

Chi-squared

Compare correlations between years

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2
Q
A
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3
Q

Correlation between years test

A

1) For each separation in time, calculate correlation between given year value and the value t years prior
2) Take straight average of correlations for each separation in time t
3) Examine how average correlation depends on t: if correlation is greater between years closer together, risk parameters are shifting over time.

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4
Q

6 methods for estimating X for credibility

A
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5
Q

3 methods to evaluate quality of estimate X

A

Least Squared Error

Limited Fluctuation

Meyers/Dorweiler – focuses on pattern of errors vs. minimization of errors

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6
Q

Least Squared Error

A

SSE = Σ (Xest,team - Xact,team)2

MSE = SSE / # of teams

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7
Q

Limited Fluctuation

A

Small Chance of Large Errors

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8
Q

Meyers/Dorweiler

A

Confirms no evidence that large predictions lead to large errors and small predictions lead to small errors

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9
Q

Mahler final points

A

If risk parameters shift over time, older data should be given less or no credibility

Not having the most recent year of historical data significantly increases the squared error of the estimate

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10
Q

Simplifications of baseball data

A
  1. Constant set of risks
  2. Readily available, accurate, and not subject to development
  3. Each team of equal size with equal games played
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11
Q

Xest = µ

A

Every risk is average; give past data 0% credibility

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12
Q

Xest = Y1

A

Last year repeats (100% credibility to last year)

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13
Q

Xest = ZY1 + (1 - Z)µ

A

Credibility weight last year and the grand mean

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14
Q

Xest = Z/n ΣYi + (1 - Z)µ

A

Given the last n years equal weight (Z/n)

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15
Q

Xest, i + 1 = ZYi + (1 - Z)Xest, i

A

Exponential smoothing

Weighted least squares regression - weights geometrically decreasing for older data

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16
Q

Xest = Σ ZiYi + (1 - ΣZi

A

Most general formula

Each year has its own credibility

17
Q

Corr(X, Y)

A

E[(X - µX)(Y - µY)] / σXσY