p.mle: The partial MLE estimator of Laha (2020).

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

Description

Suppose n univariate observations are sampled from a density f(x-m) where m is the location parameter and f is an unknown symmetric density. This function computes a one step estimator to estimte m. This estimator uses the log-concave MLE estimator from the package logcondens.mode to estimate f, and is root-n consistent for m provided f is log-concave.

Usage

p.mle(x, init, q = 0, alpha = 0.05)

Arguments

x	An array of length n; represents the data.
init	Optional. An initial estimator of m. The default value is the sample median.
q	A fraction between 0 and 1/2. Corresponds to the truncation parameter. The default is 0, which indicates no truncation.
alpha	The confidence level for the confidence bands. An (1-alpha) percent confidence interval is constructed. Alpha should lie in the interval (0, 0.50). The default value is 0.05.

Details

q: If q is positive, the function (1-2*q) percent observations from both tails while computing the one step estimator. The scores are estimated using the full data. See Laha et al. for more details.

init: The default is mean. If init is the median, some jitter (0.0001) is added.

Value

A list of length two.

• estimate: A matrix of two columns, and the rownumber equals the length of q. The firs column is q, and the second column is estimates corresponding to q.

• CI: A matrix of three columns, the first column is q, the second column is the left point and the third column is the right point of the confidence intervals corresponding to q.

Author(s)

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

References

Laha N. (2020). Location estimation for symmetric and log-concave densities. submitted.

Examples

x <- rlogis(100); p.mle(x, q=c(0, 0.001, 0.01))

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