Survey sampling

∙ \bullet ∙What is survey sampling?(c.f.census survey)(c.f.:参考，查看，来源于拉丁语)

∙ \bullet ∙understanding the whole by a f r a c t i o n ‾ \underline{fraction} fraction​(i.e.a s a m p l e ‾ \underline{sample} sample​)

Population:

Q:What is the population to survey?(In some cases,it can be difficult to identify or determine)

N:population size

a sample of size n:a subgroup of n members(n<N)

Q:Which n members should be included in the sample?(i.e.how to produce a r e p r e s e n t a t i v e ‾ \underline{representative} representative​ sample)

quantity of interest:

x i , i = 1 , 2 , 3 ⋯ N x_i,i=1,2,3\cdots N xi​,i=1,2,3⋯N(each labeled by an integer)

x i x_i xi​can be n u m e r i c a l ‾ \underline{numerical} numerical​ or c a t e g o r i a l ‾ \underline{categorial} categorial​

Multivariate ( x i 1 , x i 2 ⋯ x i k ) , i = 1 , 2 , 3 … N (x_{i1},x_{i2}\cdots x_{ik}),i=1,2,3 \dots N (xi1​,xi2​⋯xik​),i=1,2,3…N

D e f i n i t i o n : ‾ \underline{Definition : } Definition:​(survey sampling)

A technique to obtain i n f o r m a t i o n ‾ \underline{information} information​ about a l a r g e ‾ \underline{large} large​ population by examining only