Every time I think I know what's going on, suddenly there's another layer of complications.
2017年3月21日星期二
2017年3月6日星期一
The plug-in principle
The plug-in principle is a technique used in probability theory and statistics to approximately compute or to estimate a feature of a probability distribution (e.g., the expected value, the variance, a quantile) that cannot be computed exactly. It is widely used in the theories of Monte Carlo simulation and bootstrapping.
Roughly speaking, the plug-in principle says that a feature of a given distribution can be approximated by the same feature of the empirical distribution of a sample of observations drawn from the given distribution. The feature of the empirical distribution is called a plug-in estimate of the feature of the given distribution. For example, a quantile of a given distribution can be approximated by the analogous quantile of the empirical distribution of a sample of draws from the given distribution.
https://www.statlect.com/asymptotic-theory/plug-in-principle
2017年2月26日星期日
2017年2月14日星期二
2017年2月12日星期日
Basic matrix operations
BASIC FACTS ABOUT MATRICES
[1] A + B = B + A
[2] x(A + B) = xA + xB, where x is any number
[3] (x+y)A = xA + yB
[4] AB does not always equal BA
[5] A(BC) = (AB)C
[6] A(BC) does not always equal (AC)B (for example, consider A = I)
[7] AA-1 = I, the Identity matrix
[8] (AT)T = A
[9] (A + B)T = AT + BT
[10] (xA)T = x AT
[11] (AB)-1 = B-1 A-1
[12] (AB)T = BT AT
[13] (A-1)T = (AT)-1
2017年2月10日星期五
Why is the largest element of symmetric, positive semidefinite matrix on the diagonal
http://math.stackexchange.com/questions/1382940/why-is-the-largest-element-of-symmetric-positive-semidefinite-matrix-on-the-dia/1382954
http://math.stackexchange.com/questions/1286813/largest-entry-in-symmetric-positive-definite-matrix
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