Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Estimation of functional derivatives   Situations of a functional predictor paired with a scalar response are
increasingly encountered in data analysis. Predictors are often appropriately
modeled as square integrable smooth random functions. Imposing minimal
assumptions on the nature of the functional relationship, we aim to estimate
the directional derivatives and gradients of the response with respect to the
predictor functions. In statistical applications and data analysis, functional
derivatives provide a quantitative measure of the often intricate relationship
between changes in predictor trajectories and those in scalar responses. This
approach provides a natural extension of classical gradient fields in vector
space and provides directions of steepest descent. We suggest a kernel-based
method for the nonparametric estimation of functional derivatives that utilizes
the decomposition of the random predictor functions into their eigenfunctions.
These eigenfunctions define a canonical set of directions into which the
gradient field is expanded. The proposed method is shown to lead to
asymptotically consistent estimates of functional derivatives and is
illustrated in an application to growth curves.

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The categories of this paper are: mtrl-th
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The categories of this paper are: patt-sol
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The categories of this paper are: funct-an
5
The categories of this paper are: gr-qc
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The categories of this paper are: alg-geom
13
The categories of this paper are: quant-ph
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The categories of this paper are: eess
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The categories of this paper are: hep-ex
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The categories of this paper are: q-fin
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The categories of this paper are: plasm-ph
4
The categories of this paper are: cond-mat
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The categories of this paper are: nucl-ex
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The categories of this paper are: econ
12
The categories of this paper are: nucl-th
14
The categories of this paper are: math-ph
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The categories of this paper are: cmp-lg