From theory to practice - page 1457
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Why? What prevents it in the case of incremental dependence?
The sampling distribution function approximates the true distribution function by virtue of Glivenko-Cantelli's theorem, which requires that the sample is a realization of a sequence of independent, equally distributed random variables. Roughly speaking, in the case of strong dependence, the sample may clump together at one point, which would greatly distort the resulting empirical (sampled) distribution function in comparison to the true one.
The sample distribution function approximates the true distribution function by virtue of Glivenko-Cantelli's theorem, which requires that the sample is a realization of a sequence of independent, equally distributed random variables. Roughly speaking, if there is a strong dependence, the sample may clump together at one point, which would greatly distort the resulting empirical (sampling) distribution function compared to the true one.
read.......
I don't think this theorem holds in forex.
Because, as the sample size increases with the number of elements tending to infinity, the real distribution (in red) will deviate from the theoretical distribution (in black), just with probability equal to 1
while the theorem states that it will coincide
heaven and earth kind of....
As for forex, it means that one can successfully pipsip-sat in a flat market and lose losses in a trend.
https://studfiles.net/preview/4287703/page:3/
read.......
i don't think this theorem holds in forex
because as the sample size increases with the number of elements tending towards infinity, the real distribution (in red) will deviate from the theoretical distribution (in black), just with probability equal to 1
while the theorem states that it will coincide
heaven and earth kind of....
And in terms of forex it means that we'll successfully pipsing in the flat and losing money in the trend.
https://studfiles.net/preview/4287703/page:3/
It is not the theorem that is not implemented, but the conditions for its exact application on large time intervals:
1) Gains are dependent (for example, neighboring increments in the flat)
2) They are not equally distributed (non-stationarity)
It can be used as an approximation, on small time intervals without trend change. Something similar was stated by Gorchakov. And the problem about decay is about the same.
The sample distribution function approximates the true distribution function by virtue of Glivenko-Cantelli's theorem, which requires that the sample is a realization of a sequence of independent, equally distributed random variables. Roughly speaking, if there is a strong dependence, the sample can be crowded together at one point, which would greatly distort the resulting empirical (sample) distribution function in comparison to the true one.
It is not very clear why some mathematicians are required to be millionaires and others are not)
But what about conditional distributions? After all, this is a dependence.
Conditional distributions are based on joint distributions. Only in the case of independence (by definition) is the joint distribution function equal to the product of univariate distribution functions. In the case of dependence it is much more complicated - copulae were brought up here recently - this is of that order of magnitude. So the G.-C. theorem (which seems to be generalized to the multivariate case) applies to approximate construction of a two-dimensional distribution from which one can try to construct conditional one-dimensional distributions.
Millionaires are required of those mathematicians who claim to describe financial series)
As far as I know, Shiryaev's theory began to be developed for radiolocation needs, but it is unlikely that anyone required him to be personally on duty at the radar)
It is not the theorem that is not fulfilled, but the conditions for its exact application over large time intervals:
1) The gradients are dependent (e.g. neighbouring gradients in a flat)
2) The gradients are not equally distributed (non-stationarity)
It can be used as an approximation, on small time intervals without trend change. Something similar was stated by Gorchakov. And the discontinuity problem is about the same thing.
no
let's read it snugly.
Let X 1 , ... , X n , ... - infinite sample
Stability of what? There is, for example, stability of the solution of a Lyapunov diffuser or, for example, statistical stability of the frequency of an event (in the sense of convergence to its probability).
no
read snumatically
Let X 1 , ... , X n , ... be an infinite sample
In reality, a statistician always deals with finite samples, so it is always just an approximation to the fulfillment of this theorem. But as the sample size grows, this approximation improves, and this is called the consistency of the estimate.
The article in the Russian wiki about the Glivenko-Cantelli theorem is nonsense, read the English version or some normal textbook.