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A unified approach to all problems of prediction, estimation, and hypothesis testing. It is based on concept of the decision function, which tells the performer of experiment how to conduct the statistical aspects of an experiment and which action to take for each possible outcome. Choosing the decision function needs a loss function to be defined which assigns numerical values to making bad or good decisions. Explicitly a general loss function is denoted by L d; expressing how bad it would be to make decision d if the parameter value were. A quadratic loss function, it could be defined as and a bilinear loss function as
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
The biggest and smallest variate values among the sample of observations. Significant in various regions, for instance flood levels of the river, speed of wind and snowfall.
The scatter plot of SRES1 versus totexp demonstrates that there is non-linear relationship that exists as most of the points are below and above zero. The scatter plot show that th
Minimum volume ellipsoid is a term for ellipsoid of the minimum volume which covers some specified proportion of the set of multivariate data. It is commonly used to construct rob
Ask quesoil company is considering whether or not to bid for an offshore drilling contract. If they bid, the value would be $600m with a 65% chance of gaining the contract. The com
Chebyshev's inequality: A statement about the proportion of the observations which fall within some number of the standard deviations of the mean for any of the probability distri
Computer-intensive methods : The statistical methods which require almost identical computations on the data repeated number of times. The term computer intensive is, certainly, a
Principal components regression analysis is a process often taken in use to overcome the problem of multicollinearity in the regression, when simply deleting a number of the expla
Bimodal distribution : The probability distribution, or we can simply say the frequency distribution, with two modes. Figure 15 shows the example of each of them
Misspecification is the term is applied to describe the assumed statistical models which are incorrect for one of the several of reasons, for instance, using the wrong probability
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