Quant - Estimation & Inference

Question 1

What is a “parameter”?

Answer 1

a quantity computed from or used to describe a population of data.

Question 2

What is “sampling error”?

Answer 2

Sampling error is the difference between the observed value of a statistic and the quantity it is intended to estimate as a result of using subsets of the population.

Question 3

What is “Non-Probability Sampling”?

Answer 3

Non-probability sampling is a method of selecting units from a population using a subjective (i.e. non-random) method.

Non-probability sampling methods rely not on a fixed selection process but instead on a researcher’s sample selection capabilities. Its advantages include quick and low-cost data collection, and can apply expert judgment for efficient sample selection.

Question 4

What is the main idea behind the Central Limit Theorem?

Answer 4

The Central Limit Theorem (CLT) is a fundamental principle in statistics that explains why many distributions tend to look like a normal distribution as the sample size increases, even if the original data itself is not normally distributed.

The key to the CLT is the size of each sample. The theorem holds better when the samples are larger. Generally, a sample size of 30 or more is considered sufficient for the CLT to hold, although this can vary based on how the original data is distributed.

Question 5

How do. you calculate the “standard error of the sample mean”

Answer 5

It is typically estimated using the square root of the sample variance

Question 6

Why is Bootstrapping used in finance?

Answer 6

(1) Advantage of accuracy
(2) Easy of use

Question 7

What is Jacknife sampling and how does it compare to bootstraping?

What is its benefit?

Answer 7

Same as bootstrapping, except it does not have replacement.

Benefit:
Jackknife is often used to reduce the bias of an estimator

Question 8

What is “Probability Sampling”?

Answer 8

Probability sampling gives every member of the population an equal chance of being selected. Hence it can create a sample that is representative of the population.

Question 9

What is a “Sampling Plan”

Answer 9

A sampling plan is the set of rules used to select a sample.

Question 10

What is a “Simple Random Sample”?

Answer 10

A simple random sample is 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 11

What is “Simple Random Sampling”?

Answer 11

The procedure of drawing a sample to satisfy the definition of a simple random sample.

Question 12

What is “Systematic Sampling”?

Answer 12

A procedure of selecting every kth member until reaching a sample of the desired size. The sample that results from this procedure should be approximately random.

Question 13

What is “Stratified Random Sampling”?

Answer 13

a procedure that first divides a population into subpopulations (strata) based on classification criteria and then randomly draws samples from each stratum in sizes proportional to that of each stratum in the population.

Question 14

Why is “Stratified Random Sampling” often preferred to “Simple Random Sampling”?

Answer 14

In contrast to simple random sampling, stratified random sampling guarantees that population subdivisions of interest are represented in the sample. Another advantage is that estimates of parameters produced from stratified sampling have greater precision—that is, smaller variance or dispersion—than estimates obtained from simple random sampling.

Question 15

What type of sampling does a Bond Index use?

Answer 15

Stratified Random Sampling

Question 16

What is “Cluster Sampling”?

Answer 16

cluster sampling, also requires the division or classification of the population into subpopulation groups, called clusters. In this method, the population is divided into clusters, each of which is essentially a mini-representation of the entire populations. Then certain clusters are chosen as a whole using simple random sampling.

Question 17

What are differences between “Stratified Random Sampling” and “Cluster Sampling”?

Answer 17

Stratified sampling divides the population into different subgroups based on specific characteristics before sampling, aiming to represent all major subgroups in the sample. In contrast, cluster sampling divides the population into internally diverse groups and then samples a few of these groups entirely.

Objective: Stratified sampling aims to ensure each subgroup is proportionally represented in the sample to increase the statistical efficiency and reduce the bias. Cluster sampling aims to reduce costs and logistical difficulties by studying entire groups, accepting that this may increase the sampling error.

Selection of Units: In stratified sampling, individual members are selected from each stratum. In cluster sampling, entire clusters are selected, and then either all members of each selected cluster are studied, or further sampling occurs within each cluster.

Question 18

What is “Convenience Sampling”?

Answer 18

Non-probability sampling methods rely not on a fixed selection process but instead on a researcher’s sample selection capabilities. We introduce two major types of non-probability sampling methods here.

Convenience Sampling:
In this method, an element is selected from the population based on whether or not it is accessible to a researcher or on how easy it is for a researcher to access the element. The samples are not necessarily representative of the entire population, and hence the level of sampling accuracy could be limited.