Results 1  10
of
128
ANOVA decomposition
, 2010
"... This paper studies the ANOVA decomposition of a dvariate function f defined on the whole of R d, where f is the maximum of a smooth function and zero (or f could be the absolute value of a smooth function). Our study is motivated by option pricing problems. We show that under suitable conditions al ..."
Abstract
 Add to MetaCart
This paper studies the ANOVA decomposition of a dvariate function f defined on the whole of R d, where f is the maximum of a smooth function and zero (or f could be the absolute value of a smooth function). Our study is motivated by option pricing problems. We show that under suitable conditions
The smoothing effect of the ANOVA decomposition
, 2008
"... We show that the lowerorder terms in the ANOVA decomposition of a function f(x): = max(φ(x), 0) for x ∈ [0, 1] d, with φ a smooth function, may be smoother than f itself. Specifically, f belongs only to W1 d,∞, i.e., f has one essentially bounded derivative with respect to any component of x, where ..."
Abstract

Cited by 10 (2 self)
 Add to MetaCart
We show that the lowerorder terms in the ANOVA decomposition of a function f(x): = max(φ(x), 0) for x ∈ [0, 1] d, with φ a smooth function, may be smoother than f itself. Specifically, f belongs only to W1 d,∞, i.e., f has one essentially bounded derivative with respect to any component of x
The Smoothing Effect of the ANOVA Decomposition
"... We show that the lowerorder terms in the ANOVA decomposition of a function f(x): = max(φ(x), 0) for x ∈ [0, 1] d, with φ a smooth function, may be smoother than f itself. Specifically, f in general belongs only to W1 d,∞, i.e., f has one essentially bounded derivative with respect to any component ..."
Abstract
 Add to MetaCart
We show that the lowerorder terms in the ANOVA decomposition of a function f(x): = max(φ(x), 0) for x ∈ [0, 1] d, with φ a smooth function, may be smoother than f itself. Specifically, f in general belongs only to W1 d,∞, i.e., f has one essentially bounded derivative with respect to any component
Hierarchical array priors for ANOVA decompositions
, 2012
"... ANOVA decompositions are a standard method for describing and estimating heterogeneity among the means of a response variable across levels of multiple categorical factors. In such a decomposition, the complete set of main effects and interaction terms can be viewed as a collection of vectors, matri ..."
Abstract

Cited by 4 (1 self)
 Add to MetaCart
ANOVA decompositions are a standard method for describing and estimating heterogeneity among the means of a response variable across levels of multiple categorical factors. In such a decomposition, the complete set of main effects and interaction terms can be viewed as a collection of vectors
Support Vector Regression with ANOVA Decomposition Kernels
, 1997
"... Support Vector Machines using ANOVA Decomposition Kernels (SVAD) [Vapng] are a way of imposing a structure on multidimensional kernels which are generated as the tensor product of onedimensional kernels. This gives more accurate control over the capacity of the learning machine (VCdimension) . SVA ..."
Abstract

Cited by 39 (1 self)
 Add to MetaCart
Support Vector Machines using ANOVA Decomposition Kernels (SVAD) [Vapng] are a way of imposing a structure on multidimensional kernels which are generated as the tensor product of onedimensional kernels. This gives more accurate control over the capacity of the learning machine (VCdimension
Anchor points matter in ANOVA decomposition
 Rønquist (Eds.), Spectral and High Order Methods for Partial Differential Equations
, 2011
"... Abstract We focus on the analysis of variance (ANOVA) method for high dimensional approximations employing the Dirac measure. This anchoredANOVA representation converges exponentially fast for certain classes of functions but the error depends strongly on the anchor points. We employ the concept o ..."
Abstract

Cited by 2 (1 self)
 Add to MetaCart
Abstract We focus on the analysis of variance (ANOVA) method for high dimensional approximations employing the Dirac measure. This anchoredANOVA representation converges exponentially fast for certain classes of functions but the error depends strongly on the anchor points. We employ the concept
Estimating mean dimensionality of ANOVA decompositions
 Journal of the American Statistical Association
"... The analysis of variance is now often applied to functions defined on the unit cube, where it serves as a tool for the exploratory analysis of functions. The mean dimension of a function, defined as a natural weighted combination of its ANOVA mean squares, provides one measure of how hard or easy t ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
The analysis of variance is now often applied to functions defined on the unit cube, where it serves as a tool for the exploratory analysis of functions. The mean dimension of a function, defined as a natural weighted combination of its ANOVA mean squares, provides one measure of how hard or easy
Element I: ANOVA Decomposition Multivariate Decomposition
, 2015
"... f (x)dx Applications: e.g., in finance d = 360 = 12 × 30. Some integration problems are easier than others, e.g., f (x) = d∑ i=1 fi(xi). ..."
Abstract
 Add to MetaCart
f (x)dx Applications: e.g., in finance d = 360 = 12 × 30. Some integration problems are easier than others, e.g., f (x) = d∑ i=1 fi(xi).
HOEFFDINGANOVA DECOMPOSITIONS FOR SYMMETRIC STATISTICS OF EXCHANGEABLE OBSERVATIONS
, 2004
"... Consider a (possibly infinite) exchangeable sequence X = {Xn:1 ≤ n < N}, where N ∈ N ∪ {∞}, with values in a Borel space (A, A), and note Xn = (X1,...,Xn). We say that X is Hoeffding decomposable if, for each n, every square integrable, centered and symmetric statistic based on Xn can be written ..."
Abstract

Cited by 8 (7 self)
 Add to MetaCart
Consider a (possibly infinite) exchangeable sequence X = {Xn:1 ≤ n < N}, where N ∈ N ∪ {∞}, with values in a Borel space (A, A), and note Xn = (X1,...,Xn). We say that X is Hoeffding decomposable if, for each n, every square integrable, centered and symmetric statistic based on Xn can be written as an orthogonal sum of n Ustatistics with degenerated and symmetric kernels of increasing order. The only two examples of Hoeffding decomposable sequences studied in the literature are i.i.d. random variables and extractions without replacement from a finite population. In the first part of the paper we establish a necessary and sufficient condition for an exchangeable sequence to be Hoeffding decomposable, that is, called weak independence. We show that not every exchangeable sequence is weakly independent, and, therefore, that not every exchangeable sequence is Hoeffding decomposable. In the second part we apply our results to a class of exchangeable and weakly independent random vectors X (α,c) n = (X (α,c)
Results 1  10
of
128