Optimising prediction error among completely monotone covariance sequences
نویسندگان
چکیده
منابع مشابه
Optimising Prediction Error among Completely Monotone Covariance Sequences
In [9] the aggregation of simple dynamic equations, in particular AR(1) models, was introduced as a means for generating processes displaying long memory. Since this paper, the idea of aggregating has become a popular approach for constructing time series with a flexible covariance structure (see, for instance [1, 12, 2, 19, 15, 17]). Aggregation has also become a useful way to represent certai...
متن کاملCompletely Monotone Sequences and Universally Prestarlike Functions
We introduce universally convex, starlike and prestarlike functions in the slit domain C \ [1,∞), and show that there exists a very close link to completely monotone sequences and Pick functions.
متن کاملThe Estimation of Prediction Error: Covariance Penalties and Cross-Validation
Having constructed a data-based estimation rule, perhaps a logistic regression or a classification tree, the statistician would like to know its performance as a predictor of future cases. There are two main theories concerning prediction error: (1) penalty methods such as Cp, Akaike’s information criterion, and Stein’s unbiased risk estimate that depend on the covariance between data points an...
متن کاملConvergence and Error Bounds for Universal Prediction of Nonbinary Sequences
Solomonoff’s uncomputable universal prediction scheme ξ allows to predict the next symbol xk of a sequence x1...xk−1 for any Turing computable, but otherwise unknown, probabilistic environment μ. This scheme will be generalized to arbitrary environmental classes, which, among others, allows the construction of computable universal prediction schemes ξ. Convergence of ξ to μ in a conditional mea...
متن کاملSet Sequences and Monotone Class
In this paper we first defined the partial-union sequence, the partial-intersection sequence, and the partial-difference-union sequence of given sequence of subsets, and then proved the additive theorem of infinite sequences and sub-additive theorem of finite sequences for probability. Further, we defined the monotone class of families of subsets, and discussed the relations between the monoton...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Electronic Communications in Probability
سال: 2008
ISSN: 1083-589X
DOI: 10.1214/ecp.v13-1355