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In statistics, M-estimators are a broad class of extremum estimators for which the objective function is a sample average. [1] Both non-linear least squares and maximum likelihood estimation are special cases of M-estimators. The definition of M-estimators was motivated by robust statistics, which contributed new types of M-estimators.
In statistics, ancillarity is a property of a statistic computed on a sample dataset in relation to a parametric model of the dataset. An ancillary statistic has the same distribution regardless of the value of the parameters and thus provides no information about them.
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The theory of statistics provides a basis for the whole range of techniques, in both study design and data analysis, that are used within applications of statistics. [1] [2] The theory covers approaches to statistical-decision problems and to statistical inference, and the actions and deductions that satisfy the basic principles stated for these different approaches.
Probability theory or probability calculus is the branch of mathematics concerned with probability.Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expressing it through a set of axioms.
In probability theory, a probability density function (PDF), density function, or density of an absolutely continuous random variable, is a function whose value at any given sample (or point) in the sample space (the set of possible values taken by the random variable) can be interpreted as providing a relative likelihood that the value of the ...
Mathematical Statistics, by H. L. Rietz (out of print) Projective Geometry, by J. W. Young (out of print) A History of Mathematics in America before 1900, by D. E. Smith and Jekuthiel Ginsburg (out of print) Fourier Series and Orthogonal Polynomials, by Dunham Jackson - ISBN 978-1258812799 (out of print)
The probability distribution of the sum of two or more independent random variables is the convolution of their individual distributions. The term is motivated by the fact that the probability mass function or probability density function of a sum of independent random variables is the convolution of their corresponding probability mass functions or probability density functions respectively.