190,378 research outputs found
ESTIMATION AND TESTING AN ADDITIVE PARTIALLY LINEAR MODEL IN A SYSTEM OF ENGEL CURVES
The form of the Engel curve has long been a subject of discussion in appliedeconometrics and until now there has no been definitive conclusion about its form. In this paperan additive partially linear model is used to estimate semiparametrically the effect of totalexpenditure in the context of the Engel curves. Additionally, we consider the non-parametricinclusion of some regressors which traditionally have a non linear effect such as age andschooling. To that end we compare an additive partially linear model with the fullynonparametric one using recent popular test statistics. We also provide the p-values computedby bootstrap and subsampling schemes for the proposed test statistics. Empirical analysis basedon data drawn from the Spanish Expenditure Survey 1990-91 shows that modelling the effectsof expenditure, age and schooling on budget share deserves a treatment better than that adoptedin simple semiparametric analysis.Engel curve, expenditure, nonparametric estimation, marginal integration
On spectral analysis in varieties containing the solutions of inhomogeneous linear functional equations
The aim of the paper is to investigate the solutions of special inhomogeneous
linear functional equations by using spectral analysis in a translation
invariant closed linear subspace of additive/multiadditive functions containing
the restrictions of the solutions to finitely generated fields. The application
of spectral analysis in some related varieties is a new and important trend in
the theory of functional equations; especially they have successful
applications in case of homogeneous linear functional equations. The foundation
of the theory can be found in M. Laczkovich and G. Kiss \cite{KL}, see also G.
Kiss and A. Varga \cite{KV}. We are going to adopt the main theoretical tools
to solve some inhomogeneous problems due to T. Szostok \cite{KKSZ08}, see also
\cite{KKSZ} and \cite{KKSZW}. They are motivated by quadrature rules of
approximate integration
Efficient estimation of generalized additive nonparametric regression models.
We define new procedures for estimating generalized additive nonparametric regression models that are more efficient than the Linton and Härdle (1996, Biometrika 83, 529–540) integration-based method and achieve certain oracle bounds. We consider criterion functions based on the Linear exponential family, which includes many important special cases. We also consider the extension to multiple parameter models like the gamma distribution and to models for conditional heteroskedasticity.
The stochastic wave equation in high dimensions: Malliavin differentiability and absolute continuity
We consider the class of non-linear stochastic partial differential equations
studied in \cite{conusdalang}. Equivalent formulations using integration with
respect to a cylindrical Brownian motion and also the Skorohod integral are
established. It is proved that the random field solution to these equations at
any fixed point (t,x)\in[0,T]\times \Rd is differentiable in the Malliavin
sense. For this, an extension of the integration theory in \cite{conusdalang}
to Hilbert space valued integrands is developed, and commutation formulae of
the Malliavin derivative and stochastic and pathwise integrals are proved. In
the particular case of equations with additive noise, we establish the
existence of density for the law of the solution at (t,x)\in]0,T]\times\Rd.
The results apply to the stochastic wave equation in spatial dimension .Comment: 34 page
On spectral synthesis in varieties containing the solutions of inhomogeneous linear functional equations
As a continuation of our previous work \cite{KV2} the aim of the recent paper
is to investigate the solutions of special inhomogeneous linear functional
equations by using spectral synthesis in translation invariant closed linear
subspaces of additive/multiadditive functions containing the restrictions of
the solutions to finitely generated fields. The idea is based on the
fundamental work of M. Laczkovich and G. Kiss \cite{KL}. Using spectral
analysis in some related varieties we can prove the existence of special
solutions (automorphisms) of the functional equation but the spectral synthesis
allows us to describe the entire space of solutions on a large class of
finitely generated fields. It is spanned by the so-called exponential monomials
which can be given in terms of automorphisms of \cc and differential
operators. We apply the general theory to some inhomogeneous problems motivated
by quadrature rules of approximate integration \cite{KKSZ08}, see also
\cite{KKSZ} and \cite{KKSZW}
Logistic Regression Based on Statistical Learning Model with Linearized Kernel for Classification
In this paper, we propose a logistic regression classification method based on the integration of a statistical learning model with linearized kernel pre-processing. The single Gaussian kernel and fusion of Gaussian and cosine kernels are adopted for linearized kernel pre-processing respectively. The adopted statistical learning models are the generalized linear model and the generalized additive model. Using a generalized linear model, the elastic net regularization is adopted to explore the grouping effect of the linearized kernel feature space. Using a generalized additive model, an overlap group-lasso penalty is used to fit the sparse generalized additive functions within the linearized kernel feature space. Experiment results on the Extended Yale-B face database and AR face database demonstrate the effectiveness of the proposed method. The improved solution is also efficiently obtained using our method on the classification of spectra data
Identification of Stochastic Wiener Systems using Indirect Inference
We study identification of stochastic Wiener dynamic systems using so-called
indirect inference. The main idea is to first fit an auxiliary model to the
observed data and then in a second step, often by simulation, fit a more
structured model to the estimated auxiliary model. This two-step procedure can
be used when the direct maximum-likelihood estimate is difficult or intractable
to compute. One such example is the identification of stochastic Wiener
systems, i.e.,~linear dynamic systems with process noise where the output is
measured using a non-linear sensor with additive measurement noise. It is in
principle possible to evaluate the log-likelihood cost function using numerical
integration, but the corresponding optimization problem can be quite intricate.
This motivates studying consistent, but sub-optimal, identification methods for
stochastic Wiener systems. We will consider indirect inference using the best
linear approximation as an auxiliary model. We show that the key to obtain a
reliable estimate is to use uncertainty weighting when fitting the stochastic
Wiener model to the auxiliary model estimate. The main technical contribution
of this paper is the corresponding asymptotic variance analysis. A numerical
evaluation is presented based on a first-order finite impulse response system
with a cubic non-linearity, for which certain illustrative analytic properties
are derived.Comment: The 17th IFAC Symposium on System Identification, SYSID 2015,
Beijing, China, October 19-21, 201
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