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...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2022-07-01
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| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/10/13/2321 |
| Summary: | 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. |
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| ISSN: | 2227-7390 |