248,465 research outputs found
Most Likely Transformations
We propose and study properties of maximum likelihood estimators in the class
of conditional transformation models. Based on a suitable explicit
parameterisation of the unconditional or conditional transformation function,
we establish a cascade of increasingly complex transformation models that can
be estimated, compared and analysed in the maximum likelihood framework. Models
for the unconditional or conditional distribution function of any univariate
response variable can be set-up and estimated in the same theoretical and
computational framework simply by choosing an appropriate transformation
function and parameterisation thereof. The ability to evaluate the distribution
function directly allows us to estimate models based on the exact likelihood,
especially in the presence of random censoring or truncation. For discrete and
continuous responses, we establish the asymptotic normality of the proposed
estimators. A reference software implementation of maximum likelihood-based
estimation for conditional transformation models allowing the same flexibility
as the theory developed here was employed to illustrate the wide range of
possible applications.Comment: Accepted for publication by the Scandinavian Journal of Statistics
2017-06-1
Smoothing under Diffeomorphic Constraints with Homeomorphic Splines
In this paper we introduce a new class of diffeomorphic smoothers based on general spline smoothing techniques and on the use of some tools that have been recently developed in the context of image warping to compute smooth diffeomorphisms. This diffeomorphic spline is defined as the solution of an ordinary differential equation governed by an appropriate time-dependent vector field. This solution has a closed form expression which can be computed using classical unconstrained spline smoothing techniques. This method does not require the use of quadratic or linear programming under inequality constraints and has therefore a low computational cost. In a one dimensional setting incorporating diffeomorphic constraints is equivalent to impose monotonicity. Thus, as an illustration, it is shown that such a monotone spline can be used to monotonize any unconstrained estimator of a regression function, and that this monotone smoother inherits the convergence properties of the unconstrained estimator. Some numerical experiments are proposed to illustrate its finite sample performances, and to compare them with another monotone estimator. We also provide a two-dimensional application on the computation of diffeomorphisms for landmark and image matching
Yield--Optimized Superoscillations
Superoscillating signals are band--limited signals that oscillate in some
region faster their largest Fourier component. While such signals have many
scientific and technological applications, their actual use is hampered by the
fact that an overwhelming proportion of the energy goes into that part of the
signal, which is not superoscillating. In the present article we consider the
problem of optimization of such signals. The optimization that we describe here
is that of the superoscillation yield, the ratio of the energy in the
superoscillations to the total energy of the signal, given the range and
frequency of the superoscillations. The constrained optimization leads to a
generalized eigenvalue problem, which is solved numerically. It is noteworthy
that it is possible to increase further the superoscillation yield at the cost
of slightly deforming the oscillatory part of the signal, while keeping the
average frequency. We show, how this can be done gradually, which enables a
trade-off between the distortion and the yield. We show how to apply this
approach to non-trivial domains, and explain how to generalize this to higher
dimensions.Comment: 8 pages, 5 figure
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