Asymptotic properties of the minimum contrast estimators for projections of inhomogeneous space-time shot-noise Cox processes

Jiří Dvořák; Michaela Prokešová

Displaying similar documents to “Asymptotic properties of the minimum contrast estimators for projections of inhomogeneous space-time shot-noise Cox processes”

On the tail index estimation of an autoregressive Pareto process

Marta Ferreira (2013)

Discussiones Mathematicae Probability and Statistics

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In this paper we consider an autoregressive Pareto process which can be used as an alternative to heavy tailed MARMA. We focus on the tail behavior and prove that the tail empirical quantile function can be approximated by a Gaussian process. This result allows to derive a class of consistent and asymptotically normal estimators for the shape parameter. We will see through simulation that the usual estimation procedure based on an i.i.d. setting may fall short of the desired precision. ...

Prediction problems related to a first-order autoregressive process in the presence of outliers

Sugata Sen Roy, Sourav Chakraborty (2006)

Applicationes Mathematicae

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Outliers in a time series often cause problems in fitting a suitable model to the data. Hence predictions based on such models are liable to be erroneous. In this paper we consider a stable first-order autoregressive process and suggest two methods of substituting an outlier by imputed values and then predicting on the basis of it. The asymptotic properties of both the process parameter estimators and the predictors are also studied.

An estimator for parameters of a nonlinear nonnegative multidimensional AR(1) process

Jiří Anděl (1998)

Applications of Mathematics

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Let $𝕖_{t} = {(e_{t 1}, \dots, e_{t p})}^{'}$ be a $p$ -dimensional nonnegative strict white noise with finite second moments. Let $h_{i j} (x)$ be nondecreasing functions from $[0, \infty)$ onto $[0, \infty)$ such that $h_{i j} (x) \leq x$ for $i, j = 1, \dots, p$ . Let $𝕌 = (u_{i j})$ be a $p \times p$ matrix with nonnegative elements having all its roots inside the unit circle. Define a process $𝕏_{t} = {(X_{t 1}, \dots, X_{t p})}^{'}$ by $X_{t j} = u_{j 1} h_{1 j} (X_{t - 1, 1}) + \dots + u_{j p} h_{p j} (X_{t - 1, p}) + e_{t j}$ for $j = 1, \dots, p$ . A method for estimating $𝕌$ from a realization $𝕏_{1}, \dots, 𝕏_{n}$ is proposed. It is proved that the estimators are strongly consistent.

Estimators of the asymptotic variance of stationary point processes - a comparison

Michaela Prokešová (2011)

Kybernetika

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We investigate estimators of the asymptotic variance $σ^{2}$ of a $d$ –dimensional stationary point process $Ψ$ which can be observed in convex and compact sampling window $W_{n} = n W$ . Asymptotic variance of $Ψ$ is defined by the asymptotic relation $V a r (Ψ (W_{n})) \sim σ^{2} | W_{n} |$ (as $n \to \infty$ ) and its existence is guaranteed whenever the corresponding reduced covariance measure $γ_{red}^{(2)} (\cdot)$ has finite total variation. The three estimators discussed in the paper are the kernel estimator, the estimator based on the second order intesity of the point process...

Optimal trend estimation in geometric asset price models

Michael Weba (2005)

Discussiones Mathematicae Probability and Statistics

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In the general geometric asset price model, the asset price P(t) at time t satisfies the relation $P (t) = P ₀ \cdot e^{α \cdot f (t) + σ \cdot F (t)}$ , t ∈ [0,T], where f is a deterministic trend function, the stochastic process F describes the random fluctuations of the market, α is the trend coefficient, and σ denotes the volatility. The paper examines the problem of optimal trend estimation by utilizing the concept of kernel reproducing Hilbert spaces. It characterizes the class of trend functions with the property that the trend...

Estimating of Parameters: Nuar(1) Process

Miroslav M. Ristić, Biljana Č. Popović (2001)

Publications de l'Institut Mathématique

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Estimation of summary characteristics from replicated spatial point processes

Zbyněk Pawlas (2011)

Kybernetika

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Summary characteristics play an important role in the analysis of spatial point processes. We discuss various approaches to estimating summary characteristics from replicated observations of a stationary point process. The estimators are compared with respect to their integrated squared error. Simulations for three basic types of point processes help to indicate the best way of pooling the subwindow estimators. The most appropriate way depends on the particular summary characteristic,...