# bi.npmle: Bivariate NPMLE In ssa: Simultaneous Signal Analysis

## Description

General nonparametric maximum likelihood estimation for a bivariate mixing distribution, implemented using EM. Assumes that the observed data are tuples (X_{1i},X_{2i}) with marginal likelihood

\int f_1(X_{1i};u_1)f_2(X_{2i};u_2)dG(u_1,u_2),

where G is the mixing distribution to be estimated. Suppose there are p observed tuples and G is to be estimated on a grid of d1 x d2 points.

## Usage

 1 bi.npmle(D1, D2, maxit = 200, tol = 1e-04, verbose = FALSE) 

## Arguments

 D1 p x d1 matrix of conditional density values, where the ijth entry is f_1(X_{1i};u_{1j}). D2 p x d2 matrix of conditional density values, where the ijth entry is f_2(X_{2i};u_{2j}). maxit maximum number of EM iterations tol error tolerance verbose TRUE to print the error attained by each EM iteration

## Value

 g d1 x d2 matrix of probability masses at each grid point

## Examples

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 ## generate parameters from mixing distribution p <- 1000; set.seed(1); theta1 <- rnorm(p); theta2 <- -theta1+rnorm(p); ## generate observed variables X1 <- rnorm(p,theta1,1); X2 <- rnorm(p,theta2,1); ## set grid points d1 <- 25; d2 <- 30; Theta1 <- seq(min(X1),max(X1),length=d1); Theta2 <- seq(min(X2),max(X2),length=d2); ## calculate D matrices D1 <- outer(X1,Theta1,function(x,y){ dnorm(x,y,1); }); D2 <- outer(X2,Theta2,function(x,y){ dnorm(x,y,1); }); ## fit npmle g <- bi.npmle(D1,D2); contour(Theta1,Theta2,g); points(theta1,theta2); 

ssa documentation built on May 1, 2019, 10:27 p.m.