Published 2025-01-01
“…Let <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>{</mo><msub><mi>X</mi><mi>i</mi></msub><mo>,</mo><mi>i</mi><mo>≥</mo><mn>1</mn><mo>}</mo></mrow></semantics></math></inline-formula> be i.i.d. random variables and consider
symmetric and degenerate kernel functions in the form <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>h</mi><mrow><mo>(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>)</mo></mrow><mo>=</mo><msubsup><mo>∑</mo><mrow><mi>l</mi><mo>=</mo><mn>1</mn></mrow><mo>∞</mo></msubsup><msub><mi>λ</mi><mi>l</mi></msub><msub><mi>g</mi><mi>l</mi></msub><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><msub><mi>g</mi><mi>l</mi></msub><mrow><mo>(</mo><mi>y</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula>, where <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>λ</mi><mi>l</mi></msub><mo>></mo><mn>0</mn></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>E</mi><msub><mi>g</mi><mi>l</mi></msub><mrow><mo>(</mo><msub><mi>X</mi><mn>1</mn></msub><mo>)</mo></mrow><mo>=</mo><mn>0</mn></mrow></semantics></math></inline-formula>, and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>g</mi><mi>l</mi></msub><mrow><mo>(</mo><msub><mi>X</mi><mn>1</mn></msub><mo>)</mo></mrow></mrow></semantics></math></inline-formula> is in the domain of attraction of a normal law for all <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>l</mi><mo>≥</mo><mn>1</mn></mrow></semantics></math></inline-formula>. …”
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