CLT of wavelet estimator in semiparametric model with correlated errors. (English) Zbl 1255.93139
Summary: This paper considers the semiparametric regression model \(y_i=x_i\beta +g(t_i)+V_i\) \((1\leq i\leq n)\), where \((x_i,t_i)\) are known design points, \(\beta\) is an unknown slope parameter, \(g(\cdot)\) is an unknown function, the correlated errors \(V_i = \sum\nolimits_{j = - \infty }^\infty {c_j e_{i-j}} \) with \(\sum\nolimits_{j = - \infty }^\infty {| c_j|} < \infty \), and \(e_i\) are negatively associated random variables. Under appropriate conditions, the authors study the asymptotic normality for wavelet estimators of \(\beta\) and \(g(\cdot)\). A simulation study is undertaken to investigate finite sample behavior of the estimators.
MSC:
| 93E10 | Estimation and detection in stochastic control theory |
| 65T60 | Numerical methods for wavelets |
| 93C55 | Discrete-time control/observation systems |
Keywords:
asymptotic normality; correlated error; negatively associated; semiparametric model; wavelet estimatorReferences:
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