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PCA is a linear transformation that transforms the data to a new coordinate system such that the greatest variance by any projection of the data comes to lie on the first coordinate (called the first principal component), the second greatest variance on the second coordinate, and so on. The PCA can be used for dimensionality reduction in a dataset while retaining those characteristics of the dataset that contribute most to its variance, by keeping lower-order principal components and ignoring higher-order ones. Such low-order components often contain the "most important" aspects of the data. But this is not necessarily the case, depending on the application. Let p and tn denote respectively the original and reduced number of variables. The original variables are denoted X. In the simplest case our measure of accuracy of reconstruction is the sum ofp squared multiple correlations between X-variables and the predictions of X made froin the factors. In the more general case we can weight each squared multiple correlation by the variance of the corresponding X-variable.
Since we can set those variances ourselves by multiplying scores on each variable,by any constant we choose, this amounts to the ability to assign any weights we choose to the different variables.
This question explores the effect of estimation error on apparent arbitrage opportunities in a controlled simulation setting. We simulate returns for N = 10 assets over T = 30 year
In an examination 600 candidates appeared, boys outnumbered girls by 16% of all candidates. number of passed candidates exceeded the number of failed candidates by 310. Boys failin
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The Neatee Eatee Hamburger Joint specializes in soyabean burgers. Customers arrive according to the following inter - arrival times between 11.00 am and 2.00 pm: Interval-arriva
a) What is meant by secular trend? Discuss any two methods of isolating trend values in a time series.
What is an example of a real life situation when I would use each of these test
Replacement times for CD players are normally distributed with a mean of 7.1 years and standard deviation of 1.4years. Find the probability that a randomly selected CD player will
Main stages of Statistical Inquiry The following are the various stages of a statistical inquiry (1) Planning the Inquiry: First of all we have to assess the problem und
types of sampling method
The median, as the name suggests, is the middle value of a series arranged in any of the orders of magnitude i.e. ascending or descending order. As distinct from the arithmetic
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