stone.select: Tuning parameter selector for Stone (1975)'s location...
In nilanjanalaha/log.location: What the Package Does (One Line, Title Case)

Description Usage Arguments Details Value Author(s) References See Also Examples

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.

1	stone.select(x, inth, D, t, B)

`x`	An array of length n; the dataset.
`inth`	A number; the initial estimator. The default is the median.
`D`	Optional, an array of real numbers, contains values of D, parameter needed for tuning dn. See details.
`t`	Optional, an array of real numbers, contains values of t, parameter needed for tuning tn. See details.
`B`	Optional, the number of bootstrap samples. The default is 100.

To this end, we generate B Bootstrap samples and for each pair of (dn, tn), we estimate the MSE by computing

\frac{∑_{i=1}^B(\hatθ_i(dn,tn)-inth)^2}{B}

where θ_i(dn,tn) is the estimator based on the i-th bootstrap sample.

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 to be the minimum of \min(D n^{1/2}(tn)^3 and max(|x|)+2 (sd(x)*tn). Since dn is the truncation parameter and Stone (1975) uses kernel smoothening, we use the bound max(|x|)+2 (sd(x)tn). and we take tn to be the minimum between one and t n^{-1/7}/100. We generate a set of (dn, tn) by varying D and t acrros a grid. The default choice of the grid for t is c(0.01, seq(0.10, 0.80, by=0.05)) and that for D is (0.5, 1, 1.5, 2, 3, 4,....., 20).

A list is returned:

param: A 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: Gives the estimators of θ using the optimal (dn, tn)'s.
default_estimate:A

Nilanjana Laha (maintainer), nlaha@hsph.harvard.edu.

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.

giveth