Download A chain rule formula in BV and application to lower by De Cicco V., Fusco N., Verde A. PDF

By De Cicco V., Fusco N., Verde A.

Show description

Read or Download A chain rule formula in BV and application to lower semicontinuity PDF

Similar nonfiction_1 books

Extra resources for A chain rule formula in BV and application to lower semicontinuity

Sample text

M n(n − 1) i< j ˆ are exact formulae, It is important to observe that M and M unlike the approximations M =N N − n1 N −1n N (Y i − R X i ) 2 1 ˆ = N N ( N − n) M n(n − 1) (Y i − Rˆ X i ) 2 i∈s where R = Y/X, Rˆ = y/x and 1 1 y= Yi, x = Xi n i∈s n i∈s due to COCHRA N (1977). For the approximations n is required to be large and N much larger than n. cls 20 dk2429˙ch02 January 27, 2005 11:19 Chaudhuri and Stenger hard to calculate even if X i is known for every i = 1, . . , N . ˆ ˆ it is enough to know only X i for i ∈ s, but to use M To use M one must know X i for i ∈ / s as well.

A resulting q is called a controlled design and a corresponding scheme of selection is called a controlled sampling scheme. Quite a sizeable literature has grown around this problem of finding appropriate controlled designs. The methods of implementing such a scheme utilize theories of incomplete block designs and predominantly involve ingeneous devices of reducing the size of support of possible samples demanding trials and errors. But RA O and NIGA M (1990) have recently presented a simple solution by posing it as a linear programming problem and applying the well-known simplex algorithm to demonstrate their ability to work out suitable controlled schemes.

4 Therefore, with p SRSWR of size n, = Y (1 − Y ) ≤ V p ( N y) = N 2 ≤ σ yy n N2 4n . From Ep y = Y we derive that the random interval N y±3 N2 3 1 = N y± √ 4n 2 n covers the unknown N Y with a probability of at least 8/9. It may be noted that Y is regarded as fixed (nonstochastic) and s is a random variable with a probability distribution p(s) that the investigator adopts at pleasure. It is through p alone that for a fixed Y the interval t ± 3σ p (t) is a random interval. In practice an upper bound of σ p (t) may be available, as in the above example, or σ p (t) is estimated from survey data d plus auxiliary information by, for example, σˆ p (t) inducing necessary changes in the above confidence statements.

Download PDF sample

Rated 4.17 of 5 – based on 41 votes