6,247 research outputs found
Multiariate Wavelet-based sahpe preserving estimation for dependant observation
We present a new approach on shape preserving estimation of probability distribution and density functions using wavelet methodology for multivariate dependent data. Our estimators preserve shape constraints such as monotonicity, positivity and integration to one, and allow for low spatial regularity of the underlying functions. As important application, we discuss conditional quantile estimation for financial time series data. We show that our methodology can be easily implemented with B-splines, and performs well in a finite sample situation, through Monte Carlo simulations.Conditional quantile; time series; shape preserving wavelet estimation; B-splines; multivariate process
A perturbation analysis of some Markov chains models with time-varying parameters
We study some regularity properties in locally stationary Markov models which
are fundamental for controlling the bias of nonparametric kernel estimators. In
particular, we provide an alternative to the standard notion of derivative
process developed in the literature and that can be used for studying a wide
class of Markov processes. To this end, for some families of V-geometrically
ergodic Markov kernels indexed by a real parameter u, we give conditions under
which the invariant probability distribution is differentiable with respect to
u, in the sense of signed measures. Our results also complete the existing
literature for the perturbation analysis of Markov chains, in particular when
exponential moments are not finite. Our conditions are checked on several
original examples of locally stationary processes such as integer-valued
autoregressive processes, categorical time series or threshold autoregressive
processes
Multiplicative functionals on ensembles of non-intersecting paths
The purpose of this article is to develop a theory behind the occurrence of
"path-integral" kernels in the study of extended determinantal point processes
and non-intersecting line ensembles. Our first result shows how determinants
involving such kernels arise naturally in studying ratios of partition
functions and expectations of multiplicative functionals for ensembles of
non-intersecting paths on weighted graphs. Our second result shows how Fredholm
determinants with extended kernels (as arise in the study of extended
determinantal point processes such as the Airy_2 process) are equal to Fredholm
determinants with path-integral kernels. We also show how the second result
applies to a number of examples including the stationary (GUE) Dyson Brownian
motion, the Airy_2 process, the Pearcey process, the Airy_1 and Airy_{2->1}
processes, and Markov processes on partitions related to the z-measures.Comment: 32 pages, 1 figur
A framework for structured linearizations of matrix polynomials in various bases
We present a framework for the construction of linearizations for scalar and
matrix polynomials based on dual bases which, in the case of orthogonal
polynomials, can be described by the associated recurrence relations. The
framework provides an extension of the classical linearization theory for
polynomials expressed in non-monomial bases and allows to represent polynomials
expressed in product families, that is as a linear combination of elements of
the form , where and
can either be polynomial bases or polynomial families
which satisfy some mild assumptions. We show that this general construction can
be used for many different purposes. Among them, we show how to linearize sums
of polynomials and rational functions expressed in different bases. As an
example, this allows to look for intersections of functions interpolated on
different nodes without converting them to the same basis. We then provide some
constructions for structured linearizations for -even and
-palindromic matrix polynomials. The extensions of these constructions
to -odd and -antipalindromic of odd degree is discussed and
follows immediately from the previous results
Semi-nonparametric IV estimation of shape-invariant Engel curves
This paper studies a shape-invariant Engel curve system with endogenous total expenditure, in which the shape-invariant specification involves a common shift parameter for each demographic group in a pooled system of nonparametric Engel curves. We focus on the identification and estimation of both the nonparametric shapes of the Engel curves and the parametric specification of the demographic scaling parameters. The identification condition relates to the bounded completeness and the estimation procedure applies the sieve minimum distance estimation of conditional moment restrictions, allowing for endogeneity. We establish a new root mean squared convergence rate for the nonparametric instrumental variable regression when the endogenous regressor could have unbounded support. Root-n asymptotic normality and semiparametric efficiency of the parametric components are also given under a set of "low-level" sufficient conditions. Our empirical application using the U.K. Family Expenditure Survey shows the importance of adjusting for endogeneity in terms of both the nonparametric curvatures and the demographic parameters of systems of Engel curves
Harmonic density interpolation methods for high-order evaluation of Laplace layer potentials in 2D and 3D
We present an effective harmonic density interpolation method for the
numerical evaluation of singular and nearly singular Laplace boundary integral
operators and layer potentials in two and three spatial dimensions. The method
relies on the use of Green's third identity and local Taylor-like
interpolations of density functions in terms of harmonic polynomials. The
proposed technique effectively regularizes the singularities present in
boundary integral operators and layer potentials, and recasts the latter in
terms of integrands that are bounded or even more regular, depending on the
order of the density interpolation. The resulting boundary integrals can then
be easily, accurately, and inexpensively evaluated by means of standard
quadrature rules. A variety of numerical examples demonstrate the effectiveness
of the technique when used in conjunction with the classical trapezoidal rule
(to integrate over smooth curves) in two-dimensions, and with a Chebyshev-type
quadrature rule (to integrate over surfaces given as unions of non-overlapping
quadrilateral patches) in three-dimensions
- …