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Rissanen J. — Stochastic complexity in statistical inquiry
Rissanen J. — Stochastic complexity in statistical inquiry

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Название: Stochastic complexity in statistical inquiry

Автор: Rissanen J.

Аннотация:

This book describes how model selection and statistical inference can be founded on the shortest code length for the observed data, called the stochastic complexity. This generalization of the algorithmic complexity not only offers an objective view of statistics, where no prejudiced assumptions of "true" data generating distributions are needed, but it also in one stroke leads to calculable expressions in a range of situations of practical interest and links very closely with mainstream statistical theory. The search for the smallest stochastic complexity extends the classical maximum likelihood technique to a new global one, in which models can be compared regardless of their numbers of parameters. The result is a natural and far reaching extension of the traditional theory of estimation, where the Fisher information is replaced by the stochastic complexity and the Cramer-Rao inequality by an extension of the Shannon-Kullback inequality. Ideas are illustrated with applications from parametric and non-parametric regression, density and spectrum estimation, time series, hypothesis testing, contingency tables, and data compression


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1989

Количество страниц: 177

Добавлена в каталог: 08.12.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
AIC criterion      93 94
Alphabet      21
ARMA, ARMAX      140
Asymptotically optimal      87
Attribute      163
BIC      56
Binary representation      32
Bit      5
Bootsrap      105
Carry-over      31
Channel capacity      85
Cholesky-factorization      142
Code      21 22
Codeword      22
Coding system      49
Compatibility condition      17
complete      22 23
Complexity, algorithmic      47
Complexity, combinatorial      42 43
Complexity, recursive      47
Complexity, relative to coding system      51
Complexity, Shannon      37
Complexity, stochastic      58
compress      24
Confidence, index      114
Confidence, interval      102
Conjugate prior      64
Consistent estimator      137
Contingency table      119 120
Criterion, AIC      93 94
Criterion, BIC      56
Criterion, Cross — Validation      95
Criterion, MDL      56
Criterion, PMDL      69 153
Critical region      107
Data string      21
entropy      26
Error, first kind      108
Error, second kind      108
features      155
Forward validation      68
Generalized ME principle      100
Gram — Schmidt      141
histogram      75
Honest      131
Hypothesis, composite      110
Hypothesis, null      107
Independent      28
Index of confidence      123
Information, divergence      41
Information, mutual      39
Information, source      27
Information, source, independent      28
Information, source, stationary      28
Innovation      142
Kalman predictor      140
Kernel estimator      77
Kraft-inequality      23
Leaf, 22 -item level of significance      107
MA process      144
Maximum likelihood principle      6
MDL-principle      79
ME-principle      96
Message      21
ML-II technique      61
Model      12 15 53
Model, class      53
Model, family      80
Model, hierarchy      85
Non-parametric      16 73 74
One sided moving average      145
Outliers      113
Parameter, hyperparameter      61
Parameter, nuisance      61
Power      108
Predictive, code length      68
Predictive, distribution      60
Predictive, least squares      69 121 132
Prefix, code      22
Prefix, property      22
Prequential      68
Prior knowledge      82 83
Recursively enumerable      46
reference prior      85
standard Bayes      115
Stationary      28
sufficient statistics of data      47
Symbol      21
symmetric PLS      131
test      161
Theory      12
Training sample      164
Truncation      74
Unbiased      126
Universal, prior      35
Universal, r.e. set      46
Universal, test power      112
Universal, test statistic      111
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