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mmfreq |
MM Frequency
Estimation |

**DESCRIPTION**- Estimates a sum of sinusoidal signals using M estimators for the scale and the signal. The M estimators are chosen for 95% efficiency under normal errors.
**USAGE**`mmfreq(y,x=NULL,freq,coef=NULL,constant=F,scale=NULL,trace=F)`**REQUIRED ARGUMENTS**`y`numeric vector of observations. `freq`numeric vector of starting values for the frequencies. **OPTIONAL ARGUMENTS**`x`numeric vector of time points. Defaults to `0:(length(y)-1)``coef`numeric vector of starting values for the coefficients. By default these are estimated using the built-in S-Plus function ltsreg. `constant`logical constant. If true, include a constant or intercept in the model. `scale`numeric constant giving scale of the residuals. By default this is estimated using mscale for the starting parameter values. `trace`logical constant. If true, frequencies and criterion are printed at each iteration. **VALUE**`freq`numeric vector of estimated frequencies. `coef`numeric vector of estimated coefficients. `fitted`numeric vector of same length as y of fitted values. `residuals`numeric vector of same length as y of residuals. `scale`numeric constant giving the estimated or input scale. `criterion`numeric constant giving the estimated criterion functoin. **DETAILS**- Uses Hampel's redescending psi function. The estimators simultaneously have high
breakdown and 95% efficiency under normal errors if consistent high breakdown starting
values can be found.
If constant = T then the assumed model is

y = a[1] + a[2]*cos(x*f[1]) + ... + a[p+1]*cos(x*f[p]) + a[p+2]*sin(x*f[1]) + ... + a[2*p+1]*sin(x*f[p])

where coef = a, freq = f and p = length(f). If constant = F then the model is

y = a[1]*cos(x*f[1]) + ... + a[p]*cos(x*f[p]) + a[p+1]*sin(x*f[1]) + ... + a[2*p]*sin(x*f[p])

The values for*f*define the freq vector while the values for*a*define the coef vector.

**REFERENCES**- Yohai, V. J. (1987). High breakdown point and high efficiency robust estimates for
regression.
*Ann. Statist*.**15**, 642-656.Stromberg, A. J. (1993). Computation of high breakdown nonlinear regression parameters.

*J. Amer. Statist. Assoc*.**88**, 237-244. - Smyth, G. K., and Hawkins, D. M. (2000). Robust frequency estimation using elemental
sets.
*Journal of Computational and Graphical Statistics***9**, 196-214. (Abstract - Zipped PostScript) **SEE ALSO**- mmnl, mscale, rho.hampel, psi.hampel, robfreq
**EXAMPLES**- The function robfreq uses mmfreq.

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Gordon Smyth.
Copyright © 1996-2016. *Last modified:
10 February 2004*