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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
Consider a decision faced by a cattle breeder. The breeder must decide how many cattle he should sell in the market each year and how many he should retain for breeding purposes. S
Contour plot : A topographical map drawn from data comprising observations on the three variables. One variable is represented on horizontal axis and the second variable is represe
Locally weighted regression is the method of regression analysis in which the polynomials of degree one (linear) or two (quadratic) are used to approximate regression function in
The transformation of the Pearson's product moment correlation coefficient, r, can be given by The statistic z has the normal distribution with mean here ρ is the pop
The approach of controlling the error rate in an exploratory analysis where number of hypotheses are tested, but where the strict control which is provided by multiple comparison p
The graphic representation of the alternatives in a decision making problem which summarizes all the possibilities foreseen by the decision maker. For instance, suppose we are give
Invariant transformations to combine marginal probability functions to form multivariate distributions motivated by the need to enlarge the class of multivariate distributions beyo
Clustered data : The term applied to both the data in which the sampling units are grouped into the clusters sharing some common feature, for instance families or geographical reg
Projection pursuit is a procedure for attaning a low-dimensional (usually two-dimensional) representation of the multivariate data, which will be particularly useful in revealing
Occam's razor is an early statement of the parsimony principle, which was given by William of Occam (1280-1349) namely 'entia non sunt multiplicanda praeter necessitatem'; which m
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