Statistics and Computing. New York, NY: Springer. xiii, 290 p. DM 129.00; öS 942.00; sFr 117.50; £49.50; $ 64.95 (1999).
Suppose a dataset consists of pairs of observations , where is a (nonrandom) predictor variable (real or vector valued) and is a (random) response variable related to the predictor variable. The problem is to predict for a fixed value which may not belong to the set . It is obvious that a kind of interpolation (or perhaps extrapolation) between the points is needed, and that those of the points which are nearer to should play a greater role. If a model of the form with a deterministic function and random error is assumed, the problem is known as that of local regression.
Ch. 2 of the book gives details. For a model of the form “ has a probability density function ” with given form of and , a local maximum likelihood estimate for the parameter may be conctructed. The Local Likelihood Model is discussed in Ch. 4. Similarly one can formulate the problem of local density estimation (Ch. 5), local Survival and Failure Time Analysis (Ch. 6), and so on.
The book gives us a complete and uptodate review of the state of the art. Practical applications and computer software (LOCFIT) are presented in detail.