CFA 10: Sampling and Estimation

Question 1

sampling

Sampling

Answer 1

The process of obtaining a sample.

Question 2

statistic

Sampling

Answer 2

A quantity computed from or used to describe a sample of data.

Question 3

sampling plan

Sampling

Answer 3

A set of rules used to select a sample.

Question 4

simple random sample

Sampling

Answer 4

A subset of a larger population created in such a way that each element of the population has an equal probability of being selected to the subset.

Question 5

systematic sampling

Sampling

Answer 5

With systematic sampling, we select every Kth member until we have a sample of the desired size. The sample that results from this procedure should be approximately random.

Question 6

sampling error

Sampling

Answer 6

Any difference between the sample mean and the population mean; teh difference between the observed value of astatistic and the quantity it is intended to estimate.

Question 7

sampling distribution

Sampling

Answer 7

The sampling distribution of a statistic is the distribution of all the distinct possible values that the statistc can assume when computed from samples of the same size randomly drawn from the same population.

Question 8

stratified random sampling

Sampling

Answer 8

The population is divided into subpopulations (strata) based on one or more classification criteria. Simple random samples are then drawn from each stratum in sizes proportional to the relative size of each stratum in the population. These samples are then pooled to form a stratified random sample.

Question 9

indexing

Sampling

Answer 9

An investment strategy in which an investor constructs a portfolio to mirror the performance of a specified index.

Question 10

The Central Limit Theorem

Distribution of the Sample Mean

Answer 10

The central limit theorem states that for large sample sizes, for any underlying distribution for a random variable, the sampling distribution of the sample mean for that variable will be approximately normal, with mean equal to the population mean for that random variable and variance equal to the population variance divided by sample size.

Question 11

estimators

Point and Interval Estimates of the Population Mean

Answer 11

An estimation formula; the formula used to compute the sample mean and other sample statistics are examples of estimators.

Question 12

estimate

Point and Interval Estimates of the Population Mean

Answer 12

The particular value calculated from sample observations using an estimator.

Question 13

point estimate

Point and Interval Estimates of the Population Mean

Answer 13

A single numerical estimate of an unknown quantity, such as a population parameter.

Question 14

unbiased estimator

Point and Interval Estimates of the Population Mean

Answer 14

One whose expected value (the mean of its sampling distribution) equals the parameter it is intended to estimate.

Question 15

efficiency (in an unbiased estimator)

Point and Interval Estimates of the Population Mean

Answer 15

An unbiased estimator is efficient if no other unbiased estimator of the same parameter has a sampling distribution with smaller variance.

Question 16

consistency (in an estimator)

Point and Interval Estimates of the Population Mean

Answer 16

A consistent estimator is one for which the probability of estimates close to to the value of the population parameter increases as sample size increases.

Question 17

confidence interval

Point and Interval Estimates of the Population Mean

Answer 17

A confidence interval is a range for which one can assert with a given probability 1-a, called the degree of confidence, that it will contain the parameter it is intended to estimate. This interval is often referred to as the 100(1-a)% confidence interval for the parameter.

Question 18

construction of confidence intervals

Point and Interval Estimates of the Population Mean

Answer 18

A 100(1-a)% confidence interval for a parameter has the following structure:

Point estimate (+/-) Reliability factor x standard error

where

point estimate = a point estimate of the parameter (a value of a sample statistic)

reliability factor = a number based on the assumed distribution of the point estimate and the degree of confidence (1-a) for the confidence interval.

standard error = the standard error of the sample statistic providing the point estimate

Question 19

degrees of freedom (df)

Point and Interval Estimates of the Population Mean

Answer 19

The number of independent observations used.

Question 20

data mining

More on Sampling

Answer 20

The practice of determining a model by extensive searching through a dataset for statistically significant patterns.

Question 21

out-of-sample test

More on Sampling

Answer 21

A test of a strategy or model using a sample outside the time period on which the strategy or model was developed.

Question 22

intergenerational data mining

More on Sampling

Answer 22

A form of data mining that applies information developed by previous researchers using a dataset to guide current research using the same or a related dataset.

Question 23

sample selection bias

More on Sampling

Answer 23

When data availability leads to certain assets being excluded from the analysis.

Question 24

survivorship bias

More on Sampling

Answer 24

The bias resulting from a test design that fails to account for companies that have gone bankrupt, merged, or are otherwise no longer reported in a database.

Question 25

look-ahead bias

More on Sampling

Answer 25

A bias caused by using information that was unavailable on the test date.

Question 26

time-period bias

More on Sampling

Answer 26

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.