| Summary: | In this paper, we investigate the CUSUM-type estimator of mean change-point models based on <i>m</i>-asymptotically almost negatively associated (<i>m</i>-AANA) sequences. The family of <i>m</i>-AANA sequences contains AANA, NA, <i>m</i>-NA, and independent sequences as special cases. Under some weak conditions, some convergence rates are obtained such as <inline-formula><math display="inline"><semantics><mrow><msub><mi>O</mi><mi>P</mi></msub><mrow><mo>(</mo><msup><mi>n</mi><mrow><mn>1</mn><mo>/</mo><mi>p</mi><mo>−</mo><mn>1</mn></mrow></msup><mo>)</mo></mrow></mrow></semantics></math></inline-formula>, <inline-formula><math display="inline"><semantics><mrow><msub><mi>O</mi><mi>P</mi></msub><mrow><mo>(</mo><msup><mi>n</mi><mrow><mn>1</mn><mo>/</mo><mi>p</mi><mo>−</mo><mn>1</mn></mrow></msup><msup><mo form="prefix">log</mo><mrow><mn>1</mn><mo>/</mo><mi>p</mi></mrow></msup><mi>n</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula> and <inline-formula><math display="inline"><semantics><mrow><msub><mi>O</mi><mi>P</mi></msub><mrow><mo>(</mo><msup><mi>n</mi><mrow><mi>α</mi><mo>−</mo><mn>1</mn></mrow></msup><mo>)</mo></mrow></mrow></semantics></math></inline-formula>, where <inline-formula><math display="inline"><semantics><mrow><mn>0</mn><mo>≤</mo><mi>α</mi><mo><</mo><mn>1</mn></mrow></semantics></math></inline-formula> and <inline-formula><math display="inline"><semantics><mrow><mn>1</mn><mo><</mo><mi>p</mi><mo>≤</mo><mn>2</mn></mrow></semantics></math></inline-formula>. Our rates are better than the ones obtained by Kokoszka and Leipus (Stat. Probab. Lett., 1998, 40, 385–393). In order to illustrate our results, we do perform simulations based on <i>m</i>-AANA sequences. As important applications, we use the CUSUM-type estimator to do the change-point analysis based on three real data such as Quebec temperature, Nile flow, and stock returns for Tesla. Some potential applications to change-point models in finance and economics are also discussed in this paper.
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