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For a concise introduction to the fundamentals of statistics, refer to Stuart, A.; old, J.K. (1994). "Ch. 8 – Probability and statistical inference" in Kendall's Advanced Theory of Statistics, Volume I: Distribution Theory (6th ed.), published by Edward Arnold.
Statistics is a mathematical body of science that pertains to the collection, analysis, interpretation or explanation, and presentation of data, [5] or as a branch of mathematics. [6] Some consider statistics to be a distinct mathematical science rather than a branch of mathematics. While many scientific investigations make use of data ...
Statistics is a field of inquiry that studies the collection, analysis, interpretation, and presentation of data. It is applicable to a wide variety of academic disciplines , from the physical and social sciences to the humanities ; it is also used and misused for making informed decisions in all areas of business and government .
Independence is a fundamental notion in probability theory, as in statistics and the theory of stochastic processes.Two events are independent, statistically independent, or stochastically independent [1] if, informally speaking, the occurrence of one does not affect the probability of occurrence of the other or, equivalently, does not affect the odds.
Mathematical statistics is the application of probability theory, a branch of mathematics, to statistics, as opposed to techniques for collecting statistical data. Specific mathematical techniques which are used for this include mathematical analysis , linear algebra , stochastic analysis , differential equations , and measure theory .
Foundations of statistics involves issues in theoretical statistics, its goals and optimization methods to meet these goals, parametric assumptions or lack thereof considered in nonparametric statistics, model selection for the underlying probability distribution, and interpretation of the meaning of inferences made using statistics, related to the philosophy of probability and the philosophy ...
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.
Nevertheless, the situation in high-dimensional statistics may not be hopeless when the data possess some low-dimensional structure. One common assumption for high-dimensional linear regression is that the vector of regression coefficients is sparse , in the sense that most coordinates of β {\displaystyle \beta } are zero.
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