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Title:

Semi-parametric Inference for Regression Models Based on Marked Point Processes

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Introduction and Basic Definitions The monography by Andersen et al. (1993) presents a kind of canonical approach to the statistical analysis of point process models. It deals with multivariate point processes where each random event carries information on the occurrence time and the type of event, the latter being from a finite set E of alterna...

Introduction and Basic Definitions The monography by Andersen et al. (1993) presents a kind of canonical approach to the statistical analysis of point process models. It deals with multivariate point processes where each random event carries information on the occurrence time and the type of event, the latter being from a finite set E of alternatives. The theoretical fundament to multivariate point processes was laid - among others - by Jacod (1975), Bremaud (1981) and Dellacherie & Meyer (1982). There are applications, however, where an uncountable set E (e.g., E the set of real numbers) of alternatives - now called marks - is more appropriate, see Scheike (1994a,b), Murphy (1995) and Pruscha (1997). A mathematical foundation of marked point processes (MPP's) is given by Last and Brandt (1995), but this work does not contain all tools necessary for statistical analysis. The first goal of the present paper is to fill this gap. We Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2009-04-13

Source:

ftp://ftp.stat.uni-muenchen.de/pub/sfb386/paper78.ps.Z

ftp://ftp.stat.uni-muenchen.de/pub/sfb386/paper78.ps.Z Minimize

Document Type:

text

Language:

en

Subjects:

Marked point process ; intensity kernel ; locally square integrable) martingale ; local characteristic ; partial likelihood ; M-estimator

Marked point process ; intensity kernel ; locally square integrable) martingale ; local characteristic ; partial likelihood ; M-estimator Minimize

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330 Economics *(computed)*

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Metadata may be used without restrictions as long as the oai identifier remains attached to it.

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Title:

Asymptotic Behaviour of Estimation Equations With Functional Nuisance Or Working Parameter

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INTRODUCTION The starting point of our investigations is an estimation equation of the form U n (`; ff) = 0. It contains a finite dimensional parameter ` being of primary interest and a functional parameter ff. The latter may play the role of a nuisance parameter (in the classical sense) or that of a working parameter (coming into statistical us...

INTRODUCTION The starting point of our investigations is an estimation equation of the form U n (`; ff) = 0. It contains a finite dimensional parameter ` being of primary interest and a functional parameter ff. The latter may play the role of a nuisance parameter (in the classical sense) or that of a working parameter (coming into statistical use with Liang and Zeger, 1986). A nonparametric estimator ff n Theresienstr.39, D-80333 Munich, Germany 1 is assumed to be given showing a certain kind of limit behaviour, the special type of the estimator being of no regard. For estimators ` n of ` which solve (asymptotically) the estimation equation we will prove consistency and asymptotic normality. A special feature of the present paper is a consequent functionally orientated approach. The Taylor method---well established for Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2009-04-14

Source:

ftp://ftp.stat.uni-muenchen.de/pub/sfb386/paper79.ps.Z

ftp://ftp.stat.uni-muenchen.de/pub/sfb386/paper79.ps.Z Minimize

Document Type:

text

Language:

en

Subjects:

Some key words ; Asymptotic normality ; Consistent estimation equation estimator ; Hadamard differentiation ; Nuisance parameter ; Semiparametric estimation equation ; Semiparametric linear regression ; Working parameter

Some key words ; Asymptotic normality ; Consistent estimation equation estimator ; Hadamard differentiation ; Nuisance parameter ; Semiparametric estimation equation ; Semiparametric linear regression ; Working parameter Minimize

DDC:

310 Collections of general statistics *(computed)*

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Metadata may be used without restrictions as long as the oai identifier remains attached to it.

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Title:

Semi-parametric Inference for Regression Models Based on Marked Point Processes

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SUMMARY. We study marked point processes (MPP's) with an arbitrary mark space. First we develop some statistically relevant topics in the theory of MPP's admitting an intensity kernel t(dz), namely martingale results, central limit theorems for both the number n of objects under observation and the time t tending to in nity, the decomposition in...

SUMMARY. We study marked point processes (MPP's) with an arbitrary mark space. First we develop some statistically relevant topics in the theory of MPP's admitting an intensity kernel t(dz), namely martingale results, central limit theorems for both the number n of objects under observation and the time t tending to in nity, the decomposition into a local characteristic ( t � t(dz)) and a likelihood approach. Then we present semi-parametric statistical inference in a class of Aalen (1975)-type multiplicative regression models for MPP's as n!1, using partial likelihood methods. Furthermore, considering the case t!1,we study purely parametric M-estimators. Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2008-08-14

Source:

http://epub.ub.uni-muenchen.de/1472/1/paper_78.pdf

http://epub.ub.uni-muenchen.de/1472/1/paper_78.pdf Minimize

Document Type:

text

Language:

en

Subjects:

Marked point process ; intensity kernel ; locally square integrable) martingale ; local characteristic ; partial likelihood ; M-estimator

Marked point process ; intensity kernel ; locally square integrable) martingale ; local characteristic ; partial likelihood ; M-estimator Minimize

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Metadata may be used without restrictions as long as the oai identifier remains attached to it.

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Book reviews

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N. Obata ; E. Collani ; S. Csörgö ; H. Pruscha ; D. Burkholder ; W. Weil ; R. Schaßberger ; C. Deniau ; P. Meyer

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article

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Probability and Statistics. Theory and Applications - G. Blom.

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Pruscha, H.;: Metrika. 38 1991

Pruscha, H.;: Metrika. 38 1991 Minimize

Document Type:

Text

Subjects:

510.Mathematics

510.Mathematics Minimize

Rights:

Open Access ; Mathematics

Open Access ; Mathematics Minimize

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Book Reviews.

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Topics in Statistical Methodology - S. Biswas.

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Pruscha, H.;: Metrika. 41 1994

Pruscha, H.;: Metrika. 41 1994 Minimize

Document Type:

Text

Subjects:

510.Mathematics

510.Mathematics Minimize

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Open Access ; Mathematics

Open Access ; Mathematics Minimize

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Book Reviews.

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Title:

Residual and forecast methods in time series models with covariates

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We are dealing with time series which are measured on an arbitrary scale, e.g. on a categorical or ordinal scale, and which are recorded together with time varying covariates. The conditional expectations are modelled as a regression model, its parameters are estimated via likelihood- or quasi-likelihood-approach. Our main concern are diagnostic...

We are dealing with time series which are measured on an arbitrary scale, e.g. on a categorical or ordinal scale, and which are recorded together with time varying covariates. The conditional expectations are modelled as a regression model, its parameters are estimated via likelihood- or quasi-likelihood-approach. Our main concern are diagnostic methods and forecasting procedures for such time series models. Diagnostics are based on (partial) residual measures as well as on (partial) residual variables; l-step predictors are gained by an approximation formula for conditional expectations. The various methods proposed are illustrated by two different data sets. Minimize

Year of Publication:

1996-01-01

Document Type:

doc-type:workingPaper ; Paper ; NonPeerReviewed

Subjects:

Sonderforschungsbereich 386 ; Sonderforschungsbereich 386 ; ddc:510

Sonderforschungsbereich 386 ; Sonderforschungsbereich 386 ; ddc:510 Minimize

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http://epub.ub.uni-muenchen.de/1434/1/paper_33.pdf ; Pruscha, H. (1996): Residual and forecast methods in time series models with covariates. Sonderforschungsbereich 386, Discussion Paper 33

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Title:

Semiparametric Estimation in Regression Models for Point Processes based on One Realization

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We are dealing with regression models for point processes having a multiplicative intensity process of the form alpha(t) * b_t . The deterministic function alpha describes the long-term trend of the process. The stochastic process b accounts for the short-term random variations and depends on a finite-dimensional parameter. The semiparametric es...

We are dealing with regression models for point processes having a multiplicative intensity process of the form alpha(t) * b_t . The deterministic function alpha describes the long-term trend of the process. The stochastic process b accounts for the short-term random variations and depends on a finite-dimensional parameter. The semiparametric estimation procedure is based on one single observation over a long time interval. We will use penalized estimation functions to estimate the trend alpha, while the likelihood approach to point processes is employed for the parametric part of the problem. Our methods are applied to earthquake data as well as to records on 24-hours ECG. Minimize

Year of Publication:

1997-01-01

Document Type:

doc-type:workingPaper ; Paper ; NonPeerReviewed

Subjects:

Sonderforschungsbereich 386 ; Sonderforschungsbereich 386 ; ddc:510

Sonderforschungsbereich 386 ; Sonderforschungsbereich 386 ; ddc:510 Minimize

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http://epub.ub.uni-muenchen.de/1460/1/paper_66.pdf ; Pruscha, H. (1997): Semiparametric Estimation in Regression Models for Point Processes based on One Realization. Sonderforschungsbereich 386, Discussion Paper 66

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Title:

Semiparametric Point Process and Time Series Models for Series of Events

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We are dealing with series of events occurring at random times tau_n and carrying further quantitive information xi_n . Examples are sequences of extrasystoles in ECGrecords. We will present two approaches for analyzing such (typically long) sequences (tau_n, xi_n ), n = 1, 2, . . (i) A point process model is based on an intensity of the form a...

We are dealing with series of events occurring at random times tau_n and carrying further quantitive information xi_n . Examples are sequences of extrasystoles in ECGrecords. We will present two approaches for analyzing such (typically long) sequences (tau_n, xi_n ), n = 1, 2, . . (i) A point process model is based on an intensity of the form alpha(t) * b_t(theta), t >= 0, with b_t a stochastic intensity of the selfexciting type. (ii) A time series approach is based on a transitional GLM. The conditional expectation of the waiting time sigma_{n+1} = tau_{n+1} - tau_n is set to be v(tau_n) * h(eta_n(theta)), with h a response function and eta_n a regression term. The deterministic functions alpha and v, respectively, describe the long-term trend of the process. Minimize

Year of Publication:

1998-01-01

Document Type:

doc-type:workingPaper ; Paper ; NonPeerReviewed

Subjects:

Sonderforschungsbereich 386 ; Sonderforschungsbereich 386 ; ddc:510

Sonderforschungsbereich 386 ; Sonderforschungsbereich 386 ; ddc:510 Minimize

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http://epub.ub.uni-muenchen.de/1503/1/paper_114.pdf ; Pruscha, H. (1998): Semiparametric Point Process and Time Series Models for Series of Events. Sonderforschungsbereich 386, Discussion Paper 114

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