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Generalized principal components analysis: The non-linear version of the principal components analysis in which the goal is to determine the non-linear coordinate system which is most in agreement with the data configuration. For instance, for the bivariate data, y1,y2, if the quadratic coordinate system is sought, a variable z is defined as given below: with the coefficients being set up so that the variance of z is a maximum amongst all such quadratic functions of y1 and y2.
Non linear mapping (NLM ) is a technique for obtaining a low-dimensional representation of the set of multivariate data, which operates by minimizing a function of the differences
Correlation matrix : A square, symmetric matrix with the rows and columns corresponding to the variables, in which the non diagonal elements are correlations between the pairs of t
Cauchy integral : The integral of the function, f (x), from a to b are de?ned in terms of the sum In the statistics this leads to the below shown inequality for the expecte
1) Let N1(t) and N2(t) be independent Poisson processes with rates, ?1 and ?2, respectively. Let N (t) = N1(t) + N2(t). a) What is the distribution of the time till the next epoch
Model is the description of the supposed structure of a set of observations which can range from a fairly imprecise verbal account to, more commonly, a formalized mathematical exp
The graph for Partial Autocorrelation Function for RES1 shows that there is no autocorrelation even though there are alternating spikes because they fall inside the 5% significance
a. Explain the meaning of the word non-orthogonal. b. What condition(s) must exist for non-orthogonality to occur? Be specific.
Buffon's needle problem : A problem proposed and solved by the scientist Comte de Buffon in 1777 which includes determining the probability, p, which a needle of length l will inte
The method or technique for producing the sequence of parameter estimates that, under the mild regularity conditions, converges to maximum likelihood estimator. Of particular signi
An oil company thinks that there is a 60% chance that there is oil in the land they own. Before drilling they run a soil test. When there is oil in the ground, the soil test comes
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