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Structural and Statistical Problems for a Class of Stochastic Processes

The First Samuel Stanley Wilks Lecture at Princeton University, March 7, 1970

Harald Cramér

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Princeton University Press img Link Publisher

Naturwissenschaften, Medizin, Informatik, Technik / Mathematik

Beschreibung

Professor Cramer, author of the pivotal Mathematical Methods of Statistics (1946), examines problems in the theory of stochastic processes that can be considered as generalizations of problems in the classical theory of statistical inference. He discusses first the representation formula and then treats its application to the multiplicity problem, classes of processes with multiplicity N= 1, normal or Gaussian processes. He concludes with a discussion of problems of estimation for a normal process. A distinguished mathematician, Harald Cramer has been President of the University of Stockholm and Chancellor of the Swedish Universities. He is a member of many professional societies, including the Royal Swedish Academy of Science and the American Academy of Arts and Sciences.

Originally published in 1971.

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Likelihood-ratio test, Partial derivative, Dirac delta function, Statistical inference, Finite-dimensional distribution, Stationary process, Uniqueness, Cyclic subspace, Mathematical statistics, Derivative, Parameter, Probability distribution, Diagonal, Constant function, Eigenfunction, Root mean square, Statistic, Representation theorem, Projection (linear algebra), Volterra integral equation, Certainty, Disjoint sets, Hilbert space, Statistical Science, Wiener process, Reproducing kernel Hilbert space, Existential quantification, Alternative hypothesis, Statistics, Joint probability distribution, Neyman–Pearson lemma, Integral equation, Statistician, Linear combination, Absolute continuity, Zero element, Addition, Equivalence class, Normal distribution, Inference, Markov process, Theorem, Covariance function, Statistical hypothesis testing, Almost surely, Prediction, Random variable, Iteration, Probability, Stochastic calculus, Quadratic variation, Calculation, Linear least squares (mathematics), Radon–Nikodym theorem, Partially ordered set, Probability measure, Special case, Correlation coefficient, Stochastic process, Least squares, Real number, Theory, Equation, Ulf Grenander, Summation, Natural number, Variance, Year, Probability space, Eigenvalues and eigenvectors