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Functional data analysis of nonlinear modes of variation
Functional data analysis nonlinear modes of variation analysis of variance Fréchet mean Fréchet variance variation in manifolds
2009/9/16
A set of curves or images of similar shape is an increasingly common functional data set collected in the sciences. Principal Component Analysis (PCA) is the most widely used technique to decompose va...
Estimation in a class of nonlinear heteroscedastic time series models
Conditional least-squares estimation Conditional likelihood estimation Heteroscedastic models Kernel density estimation LATEX2ε
2009/9/16
Parameter estimation in a class of heteroscedastic time series models is investigated. The existence of conditional least-squares and conditional likelihood estimators is proved. Their consistency and...
Nonlinear SDEs driven by Lévy processes and related PDEs
Particlesystems Propagationofchaos Nonlinear stochastic differential equations driven by Levy processes
2009/6/12
In this paper we study general nonlinear stochastic differential equations,where the usual Brownian motion is replaced by a Levy process.Moreover,we do not suppose that the coefficient multiplying the...
Oscillation and Non-oscillation in Solutions of Nonlinear Stochastic Delay Differential Equations
Stochastic delay dierential equation oscillation non-Coscillatio
2009/4/28
This paper studies the oscillation and nonoscillation of solutions of a nonlinear stochastic delay differential equation, where the noise perturbation depends on the current state, and the drift depen...
A Resummed Branching Process Representation for a Class of Nonlinear ODEs
Branching processes Nonlinear dierential equations Resummation
2009/4/24
We study some probabilistic representations, based on branching processes, of a simple nonlinear differential equation, i.e. $u'=lambda u(au^R-1)$. The first approach is basically the same used by Le ...
Birnbaum-Saunders nonlinear regression models
Bias correction Birnbaum–Saunders distribution maximumlikelihood estimation nonlinear regression
2010/3/17
We introduce, for the first time, a new class of Birnbaum–Saunders nonlinear
regression models potentially useful in lifetime data analysis. The class generalizes
the regression model described by R...
A Resummed Branching Process Representation for a Class of Nonlinear ODEs
representations Branching Process Nonlinear ODEs
2009/4/7
We study some probabilistic representations, based on branching processes, of a simple nonlinear differential equation, i.e. $u'=lambda u(au^R-1)$. The first approach is basically the same used by Le ...
Discrete time nonlinear filters with informative observations are stable
Discrete time nonlinear filters informative observation
2009/3/23
The nonlinear filter associated with the discrete time signal-observation model $(X_k,Y_k)$ is known to forget its initial condition as $ktoinfty$ regardless of the observation structure when the sign...
Bayesian Inference for Nonlinear and Non-Gaussian Stochastic Volatility Model with Leverage Effect
Bayesian model selection B-splines fat tail leverage effect Markov chain Monte Carlo
2009/3/6
Stochastic volatility (SV) models provide useful tools to describe the evolution of asset returns, which exhibit time-varying volatility. This paper extends a basic SV model to capture a leverage effe...
Support points of locally optimal designs for nonlinear models with two parameters
Design of experiments optimality binary response count data Poisson model Michaelis–Menten model generalized linear model
2010/3/18
We propose a new approach for identifying the support points
of a locally optimal design when the model is a nonlinear model.
In contrast to the commonly used geometric approach, we use an
approach...
LARGE DEVIATIONS AND BERRY–ESSEEN IN-EQUALITIES FOR ESTIMATORS IN NONLINEAR NONHOMOGENEOUS DIFFUSIONS
nonhomogeneous diffusion processes Itˆ o stochastic differential equation drift parameter maximum likelihood estimator Bayes estimators large deviations probability Berry–Esseen type inequality
2009/2/25
Bounds on the large deviations probability of the maximum likelihood estimator and
regular Bayes estimators, and Berry–Esseen type bound for the suitably normalized
maximum likelihood estimator of a...
Parameter estimation for computationally intensive nonlinear regression with an application to climate modeling
Equilibrium climate sensitivity observed and modeled climate space–time modeling statistical surrogate temperature data
2010/3/17
Nonlinear regression is a useful statistical tool, relating observed
data and a nonlinear function of unknown parameters. When the
parameter-dependent nonlinear function is computationally intensive...
The M-estimator in a multi-phase random nonlinear model
multiple change-points M-estimator random parametric regression asymptotic properties
2010/4/29
This paper considers M-estimation of a nonlinear regression model with multiple changepoints
occuring at unknown times. The multi-phase random design regression model, discontinuous
in each change-p...
It is generally accepted that many time series of practical interest exhibit
strong dependence, i.e., long memory. For such series, the sample autocorrelations
decay slowly and log-log periodogram p...
Nonlinear Models Using Dirichlet Process Mixtures
Nonlinear Models Dirichlet Process Mixtures
2010/4/27
We introduce a new nonlinear model for classification, in which we model the joint
distribution of response variable, y, and covariates, x, non-parametrically using Dirichlet process mixtures. We kee...