el2.cen.EMs {emplik2} | R Documentation |
This function uses the EM algorithm to calculate a maximized empirical likelihood ratio for the hypothesis
H_o: E(g(x,y)-mean)=0
where E indicates expected value; g(x,y) is a user-defined function of x and y; and mean is the hypothesized value of E(g(x,y)). The samples x and y are assumed independent. They may be uncensored, right-censored, left-censored, or left-and-right (``doubly'') censored. A p-value for H_o is also calculated, based on the assumption that -2*log(empirical likelihood ratio) is approximately distributed as chisq(1).
el2.cen.EMs(x,dx,y,dy,fun=function(x,y){x>=y}, mean=0.5, maxit=25)
x |
a vector of the data for the first sample |
dx |
a vector of the censoring indicators for x : 0=right-censored, 1=uncensored, 2=left-censored |
y |
a vector of the data for the second sample |
dy |
a vector of the censoring indicators for y : 0=right-censored, 1=uncensored, 2=left-censored |
fun |
a user-defined, continuous-weight-function g(x,y) used in the hypothesis H_o.
The default is fun=function(x,y){x>=y} . |
mean |
the hypothesized value of E(g(x,y)); default is 0.5 |
maxit |
a positive integer used to set the number of iterations of the EM algorithm; default is 25 |
The value of mean should be chosen between the maximum and minimum values of g(x_i,y_j); otherwise there may be no distributions for x and y that will satisfy H_o. If mean is inside this interval, but the convergence is still not satisfactory, then the value of mean should be moved closer to the NPMLE for E(g(x,y)). (The NPMLE itself should always be a feasible value for mean.)
el2.cen.EMs
returns a list of values as follows:
xd1 |
a vector of the unique, uncensored x-values in ascending order |
yd1 |
a vector of the unique, uncensored y-values in ascending order |
temp3 |
a list of values returned by the el2.test.wts function (which is called by el2.cen.EMs ) |
mean |
the hypothesized value of E(g(x,y)) |
funNPMLE |
the non-parametric-maximum-likelihood-estimator of E(g(x,y)) |
logel00 |
the log of the unconstrained empirical likelihood |
logel |
the log of the constrained empirical likelihood |
"-2LLR" |
-2*(logel-logel00) |
Pval |
the estimated p-value for H_o, computed as 1 - pchisq(-2LLR, df = 1) |
logvec |
the vector of successive values of logel computed by the EM algorithm (should
converge toward a fixed value) |
sum_muvec |
sum of the probability jumps for the uncensored x-values, should be 1 |
sum_nuvec |
sum of the probability jumps for the uncensored y-values, should be 1 |
constraint |
the realized value of sum_{i=1}^n sum_{j=1}^m (g(x_i,y_j) - mean) μ_i nu_j,
where μ_i and nu_j are the probability jumps at x_i and y_j, respectively,
that maximize the empirical likelihood ratio. The value of constraint should be close to 0. |
William H. Barton <bbarton@lexmark.com>
Barton, W. (2009). PhD dissertation at University of Kentucky, estimated completion Dec. 2009.
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Zhou, M. (2009) emplik
package on CRAN website. Dr. Zhou is my PhD advisor
at the University of Kentucky. My el2.cen.EMs
function extends Dr. Zhou's el.cen.EM
function from one-sample to two-samples.
x<-c(10,80,209,273,279,324,391,415,566,785,852,881,895,954,1101, 1133,1337,1393,1408,1444,1513,1585,1669,1823,1941) dx<-c(1,2,1,1,1,1,1,2,1,1,1,1,1,1,1,0,0,1,0,0,0,0,1,1,0) y<-c(21,38,39,51,77,185,240,289,524,610,612,677,798,881,899,946, 1010,1074,1147,1154,1199,1269,1329,1484,1493,1559,1602,1684,1900,1952) dy<-c(1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0,0,0) # Ho1: X is stochastically equal to Y el2.cen.EMs(x, dx, y, dy, fun=function(x,y){x>=y}, mean=0.5, maxit=25) # Result: Pval = 0.7090658, so we cannot with 95 percent confidence reject Ho1 # Ho2: mean of X equals mean of Y el2.cen.EMs(x, dx, y, dy, fun=function(x,y){x-y}, mean=0.5, maxit=25) # Result: Pval = 0.9695593, so we cannot with 95 percent confidence reject Ho2