# mu_sigmasqhat: Estimates the mu and sigma squared parameters from a... In genscore: Generalized Score Matching Estimators

## Description

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

## Usage

 `1` ```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/σ^2,μ/σ^2]=(sum(h(Xi)*[Xi,-1][Xi,-1]'))^(-1) (sum([h(Xi)+h'(Xi)Xi, -h'(Xi)])).

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

sum(h(Xi)Xi-σ^2*h'(Xi))/sum(h(Xi)).

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

sum(h(Xi)(Xi-μ)^2)/(sum(h(Xi)+h'(Xi)(Xi-μ))).

## Value

A vector that contains the `mu` and the `sigmasq` estimates.

genscore documentation built on April 28, 2020, 1:06 a.m.