R help - Jan 2005 - cubic spline smoother with heterogeneous variance.

Hello.  I want to estimate the predicted values and standard errors of
Y=f(t) and its first derivative at each unique value of t using the
smooth.spline function.  However, the data (plant growth as a function
of time) show substantial heterogeneity of variance since the variance
of plant mass increases over time.  What is the consequence of such
heterogeneity of variance in terms of bias in the estimate of the
predicted value of Y and its first derivative?  I could Ln-transform the
data to achieve homogeneity of variance, but this would give me the mean
of Ln(Y) at each time (i.e. the mode of Y when back-transformed) and the
derivative of Ln(Y) with time (i.e. d(Ln(Y))/dt = dY/YDt), not dY/dt.

Can anyone suggest the best strategy for solving this problem?

 

Bill Shipley

Subject Matter Editor, Ecology

North American Editor, Annals of Botany

Département de biologie, Université de Sherbrooke,

Sherbrooke (Québec) J1K 2R1 CANADA

Bill.Shipley@USherbrooke.ca

 <http://callisto.si.usherb.ca:8080/bshipley/>
http://callisto.si.usherb.ca:8080/bshipley/

 


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AFAIK the impact of heteroscedasticity on smoothers in general is that
automatic smoothing parameter selection (e.g., via cv or gcv) could be
suboptimal.  One possibility is to supply weights to smooth.spline().  The
problem is how to estimate the weights?  One possibility is to smooth the
squared residuals of an undersmoothed estimate; i.e., use a smoothing
parameter that you know to be surely too small, and smooth the  squared
residuals from that.

[Note though, that at least for local polynomial/kernel smoothers, weighting
by estimates of local variance might not be the best thing to do.  See the
paper by M. C. Jones (1993) in the Australian Journal of Statistics, pp.
89-92.]

Andy
> From: Bill Shipley
> 
> Hello.  I want to estimate the predicted values and standard errors of
> Y=f(t) and its first derivative at each unique value of t using the
> smooth.spline function.  However, the data (plant growth as a function
> of time) show substantial heterogeneity of variance since the variance
> of plant mass increases over time.  What is the consequence of such
> heterogeneity of variance in terms of bias in the estimate of the
> predicted value of Y and its first derivative?  I could 
> Ln-transform the
> data to achieve homogeneity of variance, but this would give 
> me the mean
> of Ln(Y) at each time (i.e. the mode of Y when 
> back-transformed) and the
> derivative of Ln(Y) with time (i.e. d(Ln(Y))/dt = dY/YDt), not dY/dt.
> 
> Can anyone suggest the best strategy for solving this problem?
> 
>  
> 
> Bill Shipley
> 
> Subject Matter Editor, Ecology
> 
> North American Editor, Annals of Botany
> 
> D?partement de biologie, Universit? de Sherbrooke,
> 
> Sherbrooke (Qu?bec) J1K 2R1 CANADA
> 
> Bill.Shipley at USherbrooke.ca
> 
 <http://callisto.si.usherb.ca:8080/bshipley/>
http://callisto.si.usherb.ca:8080/bshipley/

 


	[[alternative HTML version deleted]]

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