Journal ArticleDOI
Maximum likelihood estimation for continuous-time stochastic processes
TLDR
In this paper, the role of martingale limit theory in the theory of maximum likelihood estimation for continuous-time stochastic processes is investigated and analogues of classical statistical concepts and quantities are also suggested.Abstract:
This paper is mainly concerned with the asymptotic theory of maximum likelihood estimation for continuous-time stochastic processes. The role of martingale limit theory in this theory is developed. Some analogues of classical statistical concepts and quantities are also suggested. Various examples that illustrate parts of the theory are worked through, producing new results in some cases. The role of diffusion approximations in estimation is also explored. MAXIMUM LIKELIHOOD ESTIMATION; CONTINUOUS-TIME STOCHASTIC PROCESSES; ASYMPTOTIC THEORY; MARTINGALE LIMIT THEORY; DIFFUSION APPROXIMATIONSread more
Citations
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Journal ArticleDOI
The Lagrange Multiplier Test and its Applications to Model Specification in Econometrics
Trevor Breusch,Adrian Pagan +1 more
TL;DR: The Lagrange multiplier (LM) statistic as mentioned in this paper is based on the maximum likelihood ratio (LR) procedure and is used to test the effect on the first order conditions for a maximum of the likelihood of imposing the hypothesis.
Journal ArticleDOI
Convergence of Probability Measures
TL;DR: Convergence of Probability Measures as mentioned in this paper is a well-known convergence of probability measures. But it does not consider the relationship between probability measures and the probability distribution of probabilities.
Book
The Statistical Analysis of Recurrent Events
TL;DR: Models and Frameworks for Analysis of Recurrent Events based on Counts and Rate Functions and Analysis of Gap Times are presented.
Journal ArticleDOI
An Extension of Cox's Regression Model
TL;DR: In this paper, it is shown how one can construct a model for a jump process depending on an arbitrary intensity measure with the property that if the measure is absolutely continuous it reduces to Cox's regression model for survival data.
Journal ArticleDOI
Single Molecule Detection of Nitric Oxide Enabled by d(AT)15 DNA Adsorbed to Near Infrared Fluorescent Single-Walled Carbon Nanotubes
Jingqing Zhang,Ardemis A. Boghossian,Paul W. Barone,Alina Y. Rwei,Jong-Ho Kim,Dahua Lin,Daniel A. Heller,Andrew J. Hilmer,Nitish Nair,Nigel F. Reuel,Michael S. Strano +10 more
TL;DR: The ability to detect nitric oxide quantitatively at the single-molecule level may find applications in new cellular assays for the study of nitricoxide carcinogenesis and chemical signaling, as well as medical diagnostics for inflammation.
References
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Book
Convergence of Probability Measures
TL;DR: Weak Convergence in Metric Spaces as discussed by the authors is one of the most common modes of convergence in metric spaces, and it can be seen as a form of weak convergence in metric space.
Book
Linear statistical inference and its applications
TL;DR: Algebra of Vectors and Matrices, Probability Theory, Tools and Techniques, and Continuous Probability Models.
Journal ArticleDOI
Convergence of Probability Measures
TL;DR: Convergence of Probability Measures as mentioned in this paper is a well-known convergence of probability measures. But it does not consider the relationship between probability measures and the probability distribution of probabilities.
Journal ArticleDOI
Linear Statistical Inference and its Applications
P. G. Moore,C. Radhakrishna Rao +1 more
TL;DR: The theory of least squares and analysis of variance has been studied in the literature for a long time, see as mentioned in this paper for a review of some of the most relevant works. But the main focus of this paper is on the analysis of variance.