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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 particular 'neighbourhoods' of the space of explanatory variables. It is many times useful for smoothing scatter diagrams to allow any structure to be seen more clearly and for identifying the possible non-linear relationships between the response and the explanatory variables. A robust estimation procedure (which is usually known as loess) is taken in use to guard against deviant points distorting the smoothed points. Essentially the procedure involves an adaptation of the iteratively reweighted least squares. The example shown in the figure illustrates the situation in which the locally weighted regression differs considerably from the linear failure of y on x as fitted by least squares estimation.
Markers of disease progression : Quantities which form a general monotonic series throughout the course of the disease and assist with its modelling. In uasual such quantities are
A theorem which shows that any counting process may be uniquely decomposed as the sum of a martingale and a predictable, right-continous process called the compensator, assuming ce
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Procedures for estimating the probability distributions without supposing any particular functional form. Constructing the histogram is perhaps the easiest example of such type of
Catastrophe theory : A theory of how little is the continuous changes in the independent variables which can have unexpected, discontinuous effects on the dependent variables. Exam
Profile plots is a technique of representing the multivariate data graphically. Each of the observation is represented by a diagram comprising of a sequence of equispaced vertical
Weighted least squares is the method of estimation in which the estimates arise from minimizing the weighted sum of squares of the differences between response variable and its pr
Mean squarederror is the expected value of square of the difference between an estimator and the true value of the parameter. If the estimator is unbiased then the mean of the squ
Conjoint analysis : The method used basically in market research which is similar in many respects to the various dimensional scaling. The method attempts to assign values to the l
Pascal's triangle is an arrangement of numbers described by Pascal in his Traité du Triangle Arithmétique published in the year 1665 as 'The number in each cell is equal to in the
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