Quantile-Wavelet Nonparametric Estimates for Time-Varying Coefficient Models
The paper considers quantile-wavelet estimation for time-varying coefficients by embedding a wavelet kernel into quantile regression. Our methodology is quite general in the sense that we do not require the unknown time-varying coefficients to be smooth curves of a common degree or the errors to be...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-07-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/13/2321 |
| _version_ | 1827625974049538048 |
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| author | Xingcai Zhou Guang Yang Yu Xiang |
| author_facet | Xingcai Zhou Guang Yang Yu Xiang |
| author_sort | Xingcai Zhou |
| collection | DOAJ |
| description | The paper considers quantile-wavelet estimation for time-varying coefficients by embedding a wavelet kernel into quantile regression. Our methodology is quite general in the sense that we do not require the unknown time-varying coefficients to be smooth curves of a common degree or the errors to be independently distributed. Quantile-wavelet estimation is robust to outliers or heavy-tailed data. The model is a dynamic time-varying model of nonlinear time series. A strong Bahadur order <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>O</mi><mfenced separators="" open="{" close="}"><msup><mfenced separators="" open="(" close=")"><mfrac><msup><mn>2</mn><mi>m</mi></msup><mi>n</mi></mfrac></mfenced><mrow><mn>3</mn><mo>/</mo><mn>4</mn></mrow></msup><msup><mrow><mo>(</mo><mo form="prefix">log</mo><mi>n</mi><mo>)</mo></mrow><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msup></mfenced></mrow></semantics></math></inline-formula> for the estimation is obtained under mild conditions. As applications, the rate of uniform strong convergence and the asymptotic normality are derived. |
| first_indexed | 2024-03-09T12:46:10Z |
| format | Article |
| id | doaj.art-c795be6d570c40df80822605f048fe23 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T12:46:10Z |
| publishDate | 2022-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-c795be6d570c40df80822605f048fe232023-11-30T22:12:09ZengMDPI AGMathematics2227-73902022-07-011013232110.3390/math10132321Quantile-Wavelet Nonparametric Estimates for Time-Varying Coefficient ModelsXingcai Zhou0Guang Yang1Yu Xiang2School of Statistics and Data Science, Nanjing Audit University, Nanjing 211085, ChinaSchool of Statistics and Data Science, Nanjing Audit University, Nanjing 211085, ChinaSchool of Statistics and Data Science, Nanjing Audit University, Nanjing 211085, ChinaThe paper considers quantile-wavelet estimation for time-varying coefficients by embedding a wavelet kernel into quantile regression. Our methodology is quite general in the sense that we do not require the unknown time-varying coefficients to be smooth curves of a common degree or the errors to be independently distributed. Quantile-wavelet estimation is robust to outliers or heavy-tailed data. The model is a dynamic time-varying model of nonlinear time series. A strong Bahadur order <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>O</mi><mfenced separators="" open="{" close="}"><msup><mfenced separators="" open="(" close=")"><mfrac><msup><mn>2</mn><mi>m</mi></msup><mi>n</mi></mfrac></mfenced><mrow><mn>3</mn><mo>/</mo><mn>4</mn></mrow></msup><msup><mrow><mo>(</mo><mo form="prefix">log</mo><mi>n</mi><mo>)</mo></mrow><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msup></mfenced></mrow></semantics></math></inline-formula> for the estimation is obtained under mild conditions. As applications, the rate of uniform strong convergence and the asymptotic normality are derived.https://www.mdpi.com/2227-7390/10/13/2321quantile-waveletnonparametric estimationtime-varying coefficientBahadur representationstrong mixing |
| spellingShingle | Xingcai Zhou Guang Yang Yu Xiang Quantile-Wavelet Nonparametric Estimates for Time-Varying Coefficient Models Mathematics quantile-wavelet nonparametric estimation time-varying coefficient Bahadur representation strong mixing |
| title | Quantile-Wavelet Nonparametric Estimates for Time-Varying Coefficient Models |
| title_full | Quantile-Wavelet Nonparametric Estimates for Time-Varying Coefficient Models |
| title_fullStr | Quantile-Wavelet Nonparametric Estimates for Time-Varying Coefficient Models |
| title_full_unstemmed | Quantile-Wavelet Nonparametric Estimates for Time-Varying Coefficient Models |
| title_short | Quantile-Wavelet Nonparametric Estimates for Time-Varying Coefficient Models |
| title_sort | quantile wavelet nonparametric estimates for time varying coefficient models |
| topic | quantile-wavelet nonparametric estimation time-varying coefficient Bahadur representation strong mixing |
| url | https://www.mdpi.com/2227-7390/10/13/2321 |
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