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- W2044484001 abstract "Given a sequence<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=$X_1 ,X_2 , ldots ,X_n $><mml:msub><mml:mi>X</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mi>X</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:mo>,</mml:mo><mml:mo>…</mml:mo><mml:mo>,</mml:mo><mml:msub><mml:mi>X</mml:mi><mml:mi>n</mml:mi></mml:msub></mml:math>of<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=$m$><mml:mi>m</mml:mi></mml:math>-dependent random variables with moments of order<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=$3 + alpha left( {0 $Ssigma ^{ - 1} left( {S = X_1 + X_2 + ldots + X_n ,sigma ^2 = ES^2 } right)$ alpha leqq 1} right)$><mml:mn>3</mml:mn><mml:mo>+</mml:mo><mml:mi>α</mml:mi><mml:mrow><mml:mo> (</mml:mo><mml:mrow><mml:mn>0</mml:mn><mml:mo><</mml:mo><mml:mi>α</mml:mi><mml:mo>≦</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:math>, we give an Edgeworth expansion of the distribution of<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=$Ssigma ^{ - 1} left( {S = X_1 + X_2 + ldots + X_n ,sigma ^2 = ES^2 } right)$><mml:mi>S</mml:mi><mml:msup><mml:mi>σ</mml:mi><mml:mrow><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>S</mml:mi><mml:mo>=</mml:mo><mml:msub><mml:mi>X</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>X</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:mo>…</mml:mo><mml:mo>+</mml:mo><mml:msub><mml:mi>X</mml:mi><mml:mi>n</mml:mi></mml:msub><mml:mo>,</mml:mo><mml:msup><mml:mi> σ</mml:mi><mml:mn>2</mml:mn></mml:msup><mml:mo>=</mml:mo><mml:mi>E</mml:mi><mml:msup><mml:mi>S</mml:mi><mml:mn>2</mml:mn></mml:msup></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:math>under the assumption that<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=$Eleft[ {exp left( {{mathrm{it }}Ssigma ^1 } right)} right]$><mml:mi>E</mml:mi><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:mo>exp</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mtext>it</mml:mtext><mml:mi>S</mml:mi><mml:msup><mml:mi>σ</mml:mi><mml:mn>1</mml:mn></mml:msup></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>]</mml:mo></mml:mrow></mml:math>is small away from the origin. The result is of the best possible order." @default.
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- W2044484001 date "1985-01-01" @default.
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- W2044484001 title "An edgeworth expansion for a sum of<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=$M$><mml:mi>M</mml:mi></mml:math>-Dependent random variables" @default.
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- W2044484001 doi "https://doi.org/10.1155/s0161171285000618" @default.
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