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- W2116147125 abstract "Abstract The paper studies the linear regression model <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:msub> <mml:mi>y</mml:mi> <mml:mi>t</mml:mi> </mml:msub> <mml:mo>=</mml:mo> <mml:msubsup> <mml:mi>x</mml:mi> <mml:mi>t</mml:mi> <mml:mi>T</mml:mi> </mml:msubsup> <mml:mi>β</mml:mi> <mml:mo>+</mml:mo> <mml:msub> <mml:mi>ε</mml:mi> <mml:mi>t</mml:mi> </mml:msub> <mml:mo>,</mml:mo> <mml:mspace /> <mml:mi>t</mml:mi> <mml:mo>=</mml:mo> <mml:mn>1</mml:mn> <mml:mo>,</mml:mo> <mml:mn>2</mml:mn> <mml:mo>,</mml:mo> <mml:mo>…</mml:mo> <mml:mo>,</mml:mo> <mml:mi>n</mml:mi> <mml:mo>,</mml:mo> </mml:math> where <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mi>d</mml:mi> <mml:msub> <mml:mi>ε</mml:mi> <mml:mi>t</mml:mi> </mml:msub> <mml:mo>=</mml:mo> <mml:mi>λ</mml:mi> <mml:mo>(</mml:mo> <mml:mi>μ</mml:mi> <mml:mo>−</mml:mo> <mml:msub> <mml:mi>ε</mml:mi> <mml:mi>t</mml:mi> </mml:msub> <mml:mo>)</mml:mo> <mml:mspace /> <mml:mi>d</mml:mi> <mml:mi>t</mml:mi> <mml:mo>+</mml:mo> <mml:mi>σ</mml:mi> <mml:mspace /> <mml:mi>d</mml:mi> <mml:msub> <mml:mi>B</mml:mi> <mml:mi>t</mml:mi> </mml:msub> <mml:mo>,</mml:mo> </mml:math> with parameters <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mi>λ</mml:mi> <mml:mo>,</mml:mo> <mml:mi>σ</mml:mi> <mml:mo>∈</mml:mo> <mml:msup> <mml:mi>R</mml:mi> <mml:mo>+</mml:mo> </mml:msup> </mml:math> , <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mi>μ</mml:mi> <mml:mo>∈</mml:mo> <mml:mi>R</mml:mi> </mml:math> and <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mo>{</mml:mo> <mml:msub> <mml:mi>B</mml:mi> <mml:mi>t</mml:mi> </mml:msub> <mml:mo>,</mml:mo> <mml:mi>t</mml:mi> <mml:mo>≥</mml:mo> <mml:mn>0</mml:mn> <mml:mo>}</mml:mo> </mml:math> the standard Brownian motion. Firstly, the maximum likelihood (ML) estimators of β , λ and <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:msup> <mml:mi>σ</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:math> are given. Secondly, under general conditions, the asymptotic properties of the ML estimators are investigated. And then, limiting distributions for likelihood ratio test statistics of the hypothesis are also given. Lastly, the validity of the method are illuminated by two real examples. MSC: 62J05, 62M10, 60J60." @default.
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- W2116147125 date "2014-08-19" @default.
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- W2116147125 title "Maximum likelihood estimators in linear regression models with Ornstein-Uhlenbeck process" @default.
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