stone.select.ww: Tuning parameter selector for Stone (1975)'s location...

In nilanjanalaha/log.location: What the Package Does (One Line, Title Case)

Description

giveth computes the location estimator in a location shift model using Stone (1975)'s estimator. This function depends on tuning parameters dn and tn. We estimate the MSE of the estimators and to choose the best (dn,tn) from a set of options.

Usage

stone.select.ww(x, inth)

Arguments

x	An array of length n; the dataset.
inth	A vector of initial estimators
D	An array of real numbers, contains values of D, parameter needed for tuning dn. See details.
t	An array of real numbers, contains values of t, parameter needed for tuning tn. See details.

Details

To this end, we split the dataset in tan parts. Then we compute estimators \hat θ_i(dn,tn) for each (dn,tn) under consideration from the i-th part of the data, where i=1,...,10. We then estimate the MSE corresponding to each (dn, tn) by computing

\frac{∑_{i=1}^10(\hatθ_i(dn,tn)-\hatθ(dn, tn))^2}{10}.

We choose the (dn, tn) pairs which minimize the estimated MSE.

For asymptotic efficiency of the estimators, a) dn\to∞ and tn\to 0 b)

\frac{(dn)^2}{n^{1-ε}(tn)^6}=O(1)

for some ε>0. We take dn=Dn^{1/2}(tn)^3 and tn=t n^{-1/7}. We generate a set of (dn, tn) by varying D and t in the set (0.5, 1, 1.5, 2, 3, 4,....., 20).

Value

A list is returned:

• param: A matrix with 2 columns, the number of rows is same as the length of inth. Each row gives the optimal (dn, tn) for the corresponding inth value.

• estimte: An array of same length as inth. Gives the estimators of θ using the optimal (dn, tn)'s.

Author(s)

Nilanjana Laha (maintainer), [e-mail].

References

Laha, N. Location estimation fr symmetric and log-concave densities. Submitted.

Stone, C. (1975). Adaptive maximum likelihood estimators of a location parameter, Ann. Statist., 3, 267-284.

See Also

giveth

Examples

x <- rnorm(100); inth <- mean(x);
 giveth(x, inth=inth)
 giveth(x)

nilanjanalaha/log.location documentation built on Dec. 31, 2020, 12:07 a.m.