7.1: Sampling Techniques and central limit theorem

Question 2

Probability sampling

Answer 2

selecting a sample when we know the probability of each sample member in the overall population.

Question 3

random sampling

Answer 3

ach item is assumed to have the same probability of being selected. If we have a population of data and select our sample by using a computer to randomly select a number of observations from the population, each data point has an equal probability of being selected

Question 4

Nonprobability sampling

Answer 4

based on either low cost and easy access to some data items, or on using the judgment of the researcher in selecting specific data items. Less randomness in selection may lead to greater sampling error.

Question 5

Stratified random sampling

Answer 5

• classification system -> seperate population into smaller groups based on one or more distinguishing characteritics
• Stratified sampling is often used in** bond indexing** because of the difficulty and cost of completely replicating the entire population of bonds
• In this case, bonds in a population are categorized (stratified) according to major bond risk factors including, but not limited to, duration, maturity, and coupon rate

Question 6

Cluster sampling

Answer 6

• also based on subsets of a population, but in this case, we are assuming that each subset (cluster) is representative of the overall population with respect to the item we are sampling.

Question 7

one-stage cluster sampling

Answer 7

a random sample of clusters is selected, and all the data in those clusters comprise the sample.

Question 8

two-stage cluster sampling

Answer 8

random samples from each of the selected clusters comprise the sample. Contrast this with stratified random sampling, in which random samples are selected from every subgroup.

Question 9

Convenience sampling

Answer 9

selecting sample data based on ease of access, using data that are readily available. Because such a sample is typically not random, sampling error will be greater.

Question 10

Judgmental sampling

Answer 10

which each observation is selected from a larger dataset by the researcher, based on one’s experience and judgment

Question 12

The standard error of the sample mean

Answer 12

the standard deviation of the distribution of the sample means

Question 13

** resampling** of the data.

Answer 13

reviously, we used the sample variance to calculate the standard error of our estimate of the mean. The standard error provides better estimates of the distribution of sample means when the sample is unbiased and the distribution of sample means is approximately normal.

Two alternative methods of estimating the standard error of the sample mean involve
**
1. Jacknkife
2. Bootstrap**

Question 14

Then the standard deviation of the population, σ, is known, the standard error of the sample mean is calculated as:
to (σ^2)/n as the sample size becomes large.

• sufficient large n ≥ 30
• µ, and the mean of the distribution of all possible sample means are equal.
• The variance of the distribution of sample means is σ^2/n , the population variance divided by the sample size.

Answer 14

Question 15

jackknife,

Answer 15

calculates multiple sample means, each with one of the observations removed from the sample. The standard deviation of these sample means can then be used as an estimate of the standard error of sample means. The jackknife is a computationally simple tool and can be used when the number of observations available is relatively small. This method can remove bias from statistical estimates.

Question 17

bootstrap

Answer 17

more computationally demanding, but it has some advantages. To estimate the standard error of the sample mean, we draw repeated samples of size n from the full dataset (replacing the sampled observations each time). We can then directly calculate the standard deviation of these sample means as our estimate of the standard error of the sample mean.

The bootstrap method can improve accuracy compared to using only the data in a single sample, and it can be used to construct confidence intervals for various statistics in addition to the mean, such as the median. This method can also be used to estimate the distributions of complex statistics, including those that do not have an analytic form.