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Compact and accurate linear and nonlinear autoregressive moving average model parameter estimation using laguerre functions.

A linear and nonlinear autoregressive moving average (ARMA) identification algorithm is developed for modeling time series data. The algorithm uses Laguerre expansion of kernals (LEK) to estimate Volterra-Wiener kernals. However, instead of estimating linear and nonlinear system dynamics via moving average models, as is the case for the Volterra-Wiener analysis, we propose an ARMA model-based approach. The proposed algorithm is essentially the same as LEK, but this algorithm is extended to include past values of the output as well. Thus, all of the advantages associated with using the Laguerre function remain with our algorithm; but, by extending the algorithm to the linear and nonlinear ARMA model, a significant reduction in the number of Laguerre functions can be made, compared with the Volterra-Wiener approach. This translates into a more compact system representation and makes the physiological interpretation of higher order kernels easier. Furthermore, simulation results show better performance of the proposed approach in estimating the system dynamics than LEK in certain cases, and it remains effective in the presence of significant additive measurement noise.

Algorithms↗
PubMed2005

The distribution of genetic parameter estimates and confidence intervals from small disconnected diallels.

The distributions of genetic variance components and their ratios (heritability and type-B genetic correlation) from 105 pairs of six-parent disconnected half-diallels of a breeding population of loblolly pine (Pinus taeda L.) were examined. A series of simulations based on these estimates were carried out to study the coverage accuracy of confidence intervals based on the usual t-method and several other alternative methods. Genetic variance estimates fluctuated greatly from one experiment to another. Both general combining ability variance (sigma(2) (g)) and specific combining ability variance (sigma(2) (s)) had a large positive skewness. For sigma(2) (g) and sigma(2) (s), a skewness-adjusted t-method proposed by Boos and Hughes-Oliver (Am Stat 54:121-128, 2000) provided better upper endpoint confidence intervals than t-intervals, whereas they were similar for the lower endpoint. Bootstrap BCa-intervals (Efron and Tibshirani, An introduction to the bootstrap. Chapman & Hall, London 436 p, 1993) and Hall's transformation methods (Zhou and Gao, Am Stat 54:100-104, 2000) had poor coverages. Coverage accuracy of Fieller's interval endpoint(J R Stat Soc Ser B 16:175-185, 1954) and t-interval endpoint were similar for both h(2) and r(B) for sample sizes n</=10, but for n=30 the Fieller's method is much better.

Analysis of Variance↗