HYD 11/03/2024 Statistics and Introductory Econometrics

Recap: Sample investigation is to estimate the situation of population.

1. The two weapons we can use form sample investigation to estimate the population: original data of sample; indicators/estimators

*Indicators/Estimators: calculated from the original data of sample, like mean, median, mode, variance, standard deviation …

*There are two types of estimators, which measure the location of random variables and which measure the dispersion of random variables.

*Estimate: the value of a estimator.

For example: estimator is the mean of the grades of 1000 kids, and the estimate is the value of the mean which is 75/100.

2. Bias

In statistics, bias has different meaning from its meaning in everyday life.

When a sample estimator’s expectation equals the “population estimator” , then the sample estimator is not biased.

For example, sample mean’s expectation always equals to the population mean (given that sample is randomly taken), so even though there is 10 billion situations in population and we only take one as sample, the sample mean is still not biased.

*Attention: unbiased estimator does not mean the estimator has a high accuracy!

*This is why the denominator of sample variance can not be N. When you take only one sample from the population, if the denominator is N, then the sample variance is 0. No matter how many time you repeat the same trail, the expectation is always 0, which is different from population variance. Fo the denominator of sample variance cannot be N.

Precision:

Precision is the opposite of dispersion. The more a random variable’s PD is dispersed, the less precision it has.

When we have more than one unbiased estimators, we need to choose the one with the smallest precision to estimate the population’s situation.