Diagnostic Testing of Finite Moment Conditions for the Consistency and Root-N Asymptotic Normality of the GMM and M Estimators*

This paper questions whether it is possible to derive consistency and asymptotic normality of the Gaussian quasi-maximum likelihood estimator (QMLE) for possibly the simplest multivariate GARCH model, namely, the multivariate ARCH(1) model of the Baba, Engle, Kraft, and Kroner form, under weak moment conditions similar to the univariate case. In contrast to the univariate specification, we show that the expectation of the log-likelihood function is unbounded, away from the true parameter value, if (and only if) the observable has unbounded second moment. Despite this nonstandard feature, consistency of the Gaussian QMLE is still warranted. The same moment condition proves to be necessary and sufficient for the stationarity of the score when evaluated at the true parameter value. This explains why high moment conditions, typically bounded sixth moment and above, have been used hitherto in the literature to establish the asymptotic normality of the QMLE in the multivariate framework.

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Weak moment conditions for time coordinates in first-passage percolation models

Journal of Applied Probability ◽

10.2307/3213206 ◽

1980 ◽

Vol 17 (4) ◽

pp. 968-978 ◽

Cited By ~ 5

Author(s):

John C. Wierman

Keyword(s):

Time Constant ◽

First Passage Times ◽

First Passage Percolation ◽

First Passage ◽

Moment Conditions ◽

Positive Order ◽

Finite Moment ◽

Time Coordinate ◽

Point To Point ◽

Passage Times

A generalization of first-passage percolation theory proves that the fundamental convergence theorems hold provided only that the time coordinate distribution has a finite moment of a positive order. The existence of a time constant is proved by considering first-passage times between intervals of sites, rather than the usual point-to-point and point-to-line first-passage times. The basic limit theorems for the related stochastic processes follow easily by previous techniques. The time constant is evaluated as 0 when the atom at 0 of the time-coordinate distribution exceeds½.

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Weak moment conditions for time coordinates in first-passage percolation models

Journal of Applied Probability ◽

10.1017/s0021900200097254 ◽

1980 ◽

Vol 17 (04) ◽

pp. 968-978 ◽

Cited By ~ 2

Author(s):

John C. Wierman

Keyword(s):

Time Constant ◽

First Passage Times ◽

First Passage Percolation ◽

First Passage ◽

Moment Conditions ◽

Positive Order ◽

Finite Moment ◽

Time Coordinate ◽

Point To Point ◽

Passage Times

A generalization of first-passage percolation theory proves that the fundamental convergence theorems hold provided only that the time coordinate distribution has a finite moment of a positive order. The existence of a time constant is proved by considering first-passage times between intervals of sites, rather than the usual point-to-point and point-to-line first-passage times. The basic limit theorems for the related stochastic processes follow easily by previous techniques. The time constant is evaluated as 0 when the atom at 0 of the time-coordinate distribution exceeds½.

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Multiplicative ergodicity of Laplace transforms for additive functional of Markov chains

ESAIM Probability and Statistics ◽

10.1051/ps/2019003 ◽

2019 ◽

Vol 23 ◽

pp. 607-637 ◽

Cited By ~ 1

Author(s):

Loïc Hervé ◽

Sana Louhichi ◽

Françoise Pène

Keyword(s):

Markov Chain ◽

Markov Chains ◽

Quantitative Study ◽

General Framework ◽

Additive Functional ◽

Exponential Moment ◽

Moment Conditions ◽

Finite Moment ◽

Operator Type ◽

Laplace Type

This article is motivated by the quantitative study of the exponential growth of Markov-driven bifurcating processes [see Hervé et al., ESAIM: PS 23 (2019) 584–606]. In this respect, a key property is the multiplicative ergodicity, which deals with the asymptotic behaviour of some Laplace-type transform of nonnegative additive functional of a Markov chain. We establish a spectral version of this multiplicative ergodicity property in a general framework. Our approach is based on the use of the operator perturbation method. We apply our general results to two examples of Markov chains, including linear autoregressive models. In these two examples the operator-type assumptions reduce to some expected finite moment conditions on the functional (no exponential moment conditions are assumed in this work).

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A new proof of finite moment conditions for GI/G/1 busy periods

Queueing Systems ◽

10.1007/bf01158551 ◽

1989 ◽

Vol 4 (2) ◽

pp. 171-178 ◽

Cited By ~ 11

Author(s):

Saeed Ghahramani ◽

Ronald W. Wolff

Keyword(s):

Moment Conditions ◽

Finite Moment

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Gastroesophageal Reflux Disease: A Gastroenterologist's Perspective

Perspectives on Voice and Voice Disorders ◽

10.1044/vvd21.3.89 ◽

2011 ◽

Vol 21 (3) ◽

pp. 89-99

Author(s):

Michael F. Vaezi

Keyword(s):

Gastroesophageal Reflux Disease ◽

Gastroesophageal Reflux ◽

Reflux Disease ◽

Best Practice ◽

Clinical Care ◽

Diagnostic Testing ◽

Diagnostic Tools ◽

Swallowing Function ◽

Atypical Symptoms

Gastroesophageal reflux disease (GERD) is a commonly diagnosed condition often associated with the typical symptoms of heartburn and regurgitation, although it may present with atypical symptoms such as chest pain, hoarseness, chronic cough, and asthma. In most cases, the patient's reduced quality of life drives clinical care and diagnostic testing. Because of its widespread impact on voice and swallowing function as well as its social implications, it is important that speech-language pathologists (SLPs) understand the nature of GERD and its consequences. The purpose of this article is to summarize the nature of GERD and GERD-related complications such as GERD-related peptic stricture, Barrett's esophagus and adenocarcinoma, and laryngeal manifestations of GERD from a gastroenterologist's perspective. It is critical that SLPs who work with a multidisciplinary team understand terminology, diagnostic tools, and treatment to ensure best practice.

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