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Maximum likelihood estimation is an estimation procedure involving maximization of the likelihood or the log-likelihood with respect to the parameters. Such type of estimators is particularly important because of their many desirable statistical properties such as consistency, and asymptotic efficiency. As an example considers the number of successes, X, in a sequence of random variables from a Bernoulli distribution with success probability p. The likelihood can be given by differentiating the log-likelihood, L, with respect to p gives the following
A law supposedly applicable to voting behaviour which has a history of several decades. It may be stated thus: Consider a two-party system and suppose that the representatives of t
how to calculate the semi average method when 8 observations are given?
Kalman filter : A recursive procedure which gives an estimate of the signal when only the 'noisy signal' can be observed. The estimate is efficiently constructed by putting the exp
The probability distribution, f (x), of largest extreme can be given as The location parameter, α is the mode and β is the scale parameter. The mean, variance skewn
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
Attitude scaling : The process of analysing the positions of the individuals on scales purporting to measure attitudes, for instance a liberal-conservative scale, ora risk-willingn
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
Collapsing categories : A procedure generally applied to contingency tables in which the two or more row or column categories are combined, in number of cases so as to yield the re
Centile reference charts : Charts which are used inmedicine to observe the clinical measurements on individual patients in the context of the population values. If the population i
Regression to the mean is the procedure first noted by Sir Francis Galton that 'each peculiarity in man is shared by his kinsmen, but on average to the less degree.' Hence the ten
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