### Abstract

In this paper we consider a multiple dyadic stationary process with the Walsh spectral density matrix fθ(λ), where θ is an unknown parameter vector. We define a quasi-maximum likelihood estimator {Mathematical expression} of θ, and give the asymptotic distribution of {Mathematical expression} under appropriate conditions. Then we propose an information criterion which determines the order of the model, and show that this criterion gives a consistent order estimate. As for a finite order dyadic autoregressive model, we propose a simpler order determination criterion, and discuss its asymptotic properties in detail. This criterion gives a strong consistent order estimate. In Section 5 we discuss testing whether an unknown parameter θ satisfies a linear restriction. Then we give the asymptotic distribution of the likelihood ratio criterion under the null hypothesis.

Original language | English |
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Pages (from-to) | 205-225 |

Number of pages | 21 |

Journal | Annals of the Institute of Statistical Mathematics |

Volume | 41 |

Issue number | 2 |

DOIs | |

Publication status | Published - 1989 Jun 1 |

### Keywords

- Dyadic stationary process
- Walsh spectral density
- information criterion
- likelihood ratio criterion
- quasi-maximum likelihood estimator

### ASJC Scopus subject areas

- Statistics and Probability

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## Cite this

*Annals of the Institute of Statistical Mathematics*,

*41*(2), 205-225. https://doi.org/10.1007/BF00049392