5.2: Coincidence Intervals, Resampling, and Sampling Biases

Question 1

Definition of Confidence Interval

Answer 1

A range for which one can assert with a given probability 1 − α, called the degree of confidence, that it will contain the parameter it is intended to estimate.

Question 2

How standard normal random deviation is denoted?

Answer 2

Z

Question 3

What does Zα denote?

Answer 3

The point of the standard normal distribution such that α of the probability remains in the right tail.

Question 4

What are the considerations for Confidence Intervals for the Population Mean?

Answer 4

1) Whether it is normally distributed or not,
2)What is the sample size,
3)Whether we know the variance

Question 5

How to calculate Confidence Intervals for the Population Mean if it is normally distributed with known variance?

Answer 5

x̄ ± Za/2 * σ / √n

σ - population standard deviation

Question 6

Reliability Factors for Confidence Intervals Based on the Standard Normal Distribution:

90% confidence intervals: Use z0.05 = ?
95% confidence intervals: Use z0.025 = ?
99% confidence intervals: Use z0.005 = ?

Answer 6

= 1.65
= 1.96
= 2.58

Question 7

Formula for Confidence Intervals for the Population Mean—The z-Alternative (Large Sample, Population Variance Unknown):

Answer 7

x̄ ± Za/2 * S / √n

s - sample standard deviation

Question 8

In which cases t-distribution is appropriate for calculating Confidence Intervals for the Population Mean?

Answer 8

1)When the population variance is unknown,

2)When the variance is unknown and even in cases where the samples is large and Z reliability factor could be used from CLT,

Question 9

In which cases t-distribution can be used for calculating Confidence Intervals for the Population Mean?

Answer 9

The sample is large,

Or the sample is small, but the population is normally distributed, or approximately normally distributed.

Question 10

Confidence Intervals for the Population Mean (Population Variance Unknown) - t-Distribution formula?

Answer 10

x̄ ± ta/2 * S / √n

Question 11

The Bootstrap Resampling Method is often referred to as?

Answer 11

Model-free or non-parametric resampling.

Question 12

How does Bootstrap Resampling Method work?

Answer 12

It mimics the process by treating the randomly drawn sample as if it were the population.

Often used to find standard error or construct confidence intervals of population parameters.

Question 13

What is the bootstrap sampling distribution formula to approximate the true sampling distribution?

(To estimate the standard error of the sample mean)

Answer 13

S x̄ = √(1 / B-1)* Σ(01 – 02)^2

B denotes the number of resamples drawn from the original sample,

θˆb (O1) denotes the mean of a resample,

θbar (O2) denotes the mean across all the resample means.

Question 14

What is the Jackknife resampling method?

Answer 14

A resampling method that repeatedly draws samples by taking the original observed data sample and leaving out one observation at a time (without replacement) from the set.

Question 15

What is Data Snooping?

Answer 15

Data Snooping relates to overuse of the same or related data through extensive searching through a dataset for statistically significant patterns.

Question 16

What is Sample Selection Bias?

Answer 16

Systematically excluding some members of the population according to a particular attribute.

Example, the bias introduced when data availability leads to certain observations being excluded from the analysis.

Question 17

Definition of Survivorship Bias is…

Answer 17

The exclusion of poorly performing or defunct companies from an index or database, biasing the index or database toward financially healthy companies.

Question 18

Implicit Selection Bias is introduced through…

Answer 18

The presence of a threshold that filters out some unqualified members.

Question 19

How do you call a scenario in which the hedge funds that are added to databases and indexes only after they are initially successful create a certain type of bias?

Answer 19

Backfill Bias

Question 20

What is the name of bias that occurs when the testing used information that was unavailable at the moment?

Answer 20

Look-ahead Bias

Question 21

The possibility that when we use a time-series sample, our statistical conclusion may be sensitive to the starting and ending dates of the sample is called?

Answer 21

Time-period Bias