Simple random sampling
Simple random sampling is a method of sampling in which each item in the population has an equal chance of being selected.
Systematic sampling is that in which every nth item in the population is selected to form a sample.
Stratified random sampling
Stratified random sampling is that in which a classification system is used to divide the population into smaller groups based on certain characteristics. From each sub group, also called a stratum, a sample is drawn and the results are pooled. Eg: Supposing you want to construct a portfolio of sovereign bonds. All the available sovereign bonds will be divided into sub groups based on maturity and coupon combinations. From each sub group a sample will be chosen. The sample size will correspond to the size of the sub group relative to the population. All samples drawn from each sub group will then be combined to form the portfolio of sovereign bonds.
Sampling error is the difference between the sample statistic (sample mean, sample variance, sample standard deviation) and the population parameter (population mean, population variance, population standard deviation). Eg: The sampling error of mean is given as;
Like the items in the population or sample the sample statistic is also a random variable which has a probability distribution. Sampling distribution is the distribution of the sample statistic. Eg: Sampling distribution of the mean is the distribution of sample means of equal size samples randomly drawn from the same population.
Time series data and cross sectional data:
Time series data consists of observations taken at specific and equally spaced time intervals. Eg: the monthly returns of a stock. Cross sectional data sample is a sample of observations taken at a single point in time. Eg: The reported earnings of all the shares in the BSE SENSEX as on 31stMarch 2016.
Longitudinal data and Panel data:
Longitudinal data are observations of multiple characteristics of the same entity over a long period of time. Eg: The P&L, the EBIT, the EBITDA, the NIMs of HDFC Bank over a period of 10 years. Panel data consists of observations of the same characteristic of multiple entities over a period of time. Eg: the NIMs of all public sector banks over the past 5 years.
Central Limit Theorem:
Central Limit theorem states that the mean of a random sample drawn from a population having a mean of µ and a variance of ϭ2, approaches the population mean µ and a variance of ϭ2/n, as the sample size becomes larger. Inferences can be made about the population mean from the sample mean regardless of the distribution of the population, as long as the sample size is large enough i.e., it is greater than or equal to 30 (n ≥30).
Standard error of the sample mean
It is the standard deviation of the distribution of sample means. The standard error becomes smaller as the sample size gets larger because as the samples get larger their means get closer to the population mean and hence the distribution of the sample means gets smaller and smaller thus making their standard deviation also smaller.
Point estimates and estimators:
Point estimates are the single values used to estimate the population parameters. The formula used to compute the point estimate is called the estimator. Eg: the sample mean is the estimator for the population mean. The desirable properties of an estimator are unbiasedness, efficiency and consistency.
To be continued……