Loading...
Please wait, while we are loading the content...
Similar Documents
Intro to Statistics . Inferences for normal families . 1 Basic Concepts : Population , Sample , Parameter , Statistics
| Content Provider | Semantic Scholar |
|---|---|
| Copyright Year | 2017 |
| Abstract | In statistics we usually have a data set (or a sample), which can be described as a single draw of data from all potential realizations of that data. We may describe it as a realization x of random vector X . The distribution FX of data vector X is often referred as population. In Econometrics one encounters 3 types of data: cross-section, time series and panel. Cross-section is usually described as a set of iid (independent and identically distributed ) random vectors X1, ..., Xn (that ∏n is, X = (X1, ..., Xn), x = (x1, ..., xn)). If we assume that Xi ∼ F , then FX (x) = F (xi). Time-series i=1 data Xt, t = 1, ..., T usually allow dependency between consecutive observations and describe (X1, ..., XT ) as one realization of a path that results from a dynamic process. Panel data usually consider X = {Xit, i = 1, .., n, t = 1, ..., T } that we have a draw from n independent identically distributed dynamic processes. The object of interest here is usually some functional of the unknown distribution FX . Any such function is known as a parameter. In the case of cross-sectional data, it is usually some function of distribution of one observation F ; for time series, the parameter may be related to the dependence between observations as well as marginal distributions of observation. Notice that parameter is a population concept. The goal of Statistics generally is to render some judgement about a parameter (or population FX ) based on a single draw from this population. This is called inference. We will see three types of inference: estimation, con ̋dence set construction and testing. In performing each task we will sometimes make mistakes, and the quality of the procedure will be related to minimizing the size and/or probability of mistakes. We refer to any function of a random sample as a statistic. Thus, Y = g(X ) = g(X1, ..., Xn) is a statistic. By construction, it is random variable. When calculated for our speci ̋c data set y = g(x) = g(x1, ..., xn) it produces a single realization of this random variable. The distribution of a statistic is called the sampling distribution. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | https://ocw.mit.edu/courses/economics/14-381-statistical-method-in-economics-fall-2018/lecture-notes/MIT14_381F18_lec3.pdf |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
