mu_sigmasqhat {genscore}

Estimates the mu and sigma squared parameters from a univariate truncated normal sample.

Description

Estimates the mu and sigma squared parameters from a univariate truncated normal sample.

Usage

mu_sigmasqhat(x, mode, param1, param2, mu = NULL, sigmasq = NULL)

Arguments

x

A vector, the data.

mode

A string, the class of the h function.

param1

A number, the first parameter to the h function.

param2

A number, the second parameter (may be optional depending on mode) to the h function.

mu

A number, may be NULL. If NULL, an estimate will be given; otherwise, the value will be treated as the known true mu parameter and is used to calculate an estimate for sigmasq, if sigmasq is NULL.

sigmasq

A number, may be NULL. If NULL, an estimate will be given; otherwise, the value will be treated as the known true sigmasq parameter and is used to calculate an estimate for mu, if mu is NULL.

Details

If both mu and sigmasq are provided, they are returned immediately. If neither is provided, the estimates are given as

[1/\sigma^2,\mu/\sigma^2]=\left\{\sum_{i=1}^nh(X_i)[X_i,-1][X_i,-1]^{\top}\right\}^{-1}\left\{\sum_{i=1}^n\left[h(X_i)+h'(X_i)X_i,-h'(X_i)\right]\right\}.

If only sigmasq is provided, the estimate for mu is given as

\sum_{i=1}^n[h(X_i)X_i-\sigma^2 h'(X_i)]/\sum_{i=1}^nh(X_i).

If only mu is given, the estimate for sigmasq is given as

\sum_{i=1}^n h(X_i)(X_i-\mu)^2/\sum_{i=1}^n[h(X_i)+h'(X_i)(X_i-\mu)].

Value

A vector that contains the mu and the sigmasq estimates.