A NOTE ON CHROMATOGRAPHIC PARAMETER ESTIMATION

A Note on Adaptive Estimation

Adaptive Estimation An adaptive estimator is an efficient estimator for a model that is only partially specified. For example, consider estimating a parameter that describes a sample of observations drawn from a distribution F . One natural question is: Is it possible that an estimator of the parameter constructed without knowledge of F could be as efficient (asymptotically) as any well-behaved...

A Note on Entropy Estimation

We compare an entropy estimator H(z) recently discussed by Zhang (2012) with two estimators, H(1) and H(2), introduced by Grassberger (2003) and Schürmann (2004). We prove the identity H(z) ≡ H(1), which has not been taken into account by Zhang (2012). Then we prove that the systematic error (bias) of H(1) is less than or equal to the bias of the ordinary likelihood (or plug-in) estimator of en...

Short Note Parameter optimization for multiscale PEF estimation

Note on the Unbiased Estimation of a Function of the Parameter of the Geometric Distribution

Kolmogorov studied the problem of whether a function of the parameter p of the Bernoulli distribution Bernoulli[p] has an unbiased estimator based on a sample X1, X2, . . . , Xn of size n and proved that exactly the polynomial functions of degree at most n can be estimated. For the geometric distribution Geometric[p], we prove that exactly the functions that are analytic at p = 1 have unbiased ...

A note on sampling and parameter estimation in linear stochastic systems

Numerical differentiation formulas that yield consistent least squares parameter estimates from sampled observations of linear, time invariant higher order systems have been introduced previously by Duncan et al. The formulas given by Duncan et al. have the same limiting system of equations as in the continuous time case. The formula presented in this note can be characterized as preserving asy...