Package 'emplik2'

Computes empirical likelihood ratio and p-value for multiple mean-type hypotheses, based on two independent samples that may contain censored data.

Description

This function is similar to el2.cen.EMs but for several mean type restrictions. This function uses the EM algorithm to calculate a maximized empirical likelihood ratio for a set of $p$ simultaneous hypotheses as follows:

$H_o: E(g(x,y)-mean)=0$

where $E$ indicates expected value; $g(x,y)$ is a vector of user-defined functions: $g_1(x,y), \ldots, g_p(x,y)$; and $mean$ is a vector of $p$ hypothesized values of $E(g(x,y))$. The two 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 asymptotically distributed as chisq(df=p).

Usage

el2.cen.EMm(x, dx, wx=rep(1,length(x)), y, dy, wy=rep(1,length(y)), 
            p, H, xc=1:length(x), yc=1:length(y), mean, maxit=35)

Arguments

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
wx	a vector of data case weight for x
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
wy	a vector of data case weight for y
p	the number of hypotheses
H	a matrix defined as $H = [H_1, H_2, \ldots, H_p]$, where $H_k = [g_k(x_i,y_j)-mu_k], k=1, \ldots, p$
xc	a vector containing the indices of the x datapoints, controls if tied x collapse or not
yc	a vector containing the indices of the y datapoints, ditto
mean	the hypothesized value of $E(g(x,y)$)
maxit	a positive integer used to control the maximum number of iterations of the EM algorithm; default is 35

Details

The value of $mean_k$ should be chosen between the maximum and minimum values of $g_k(x_i,y_j)$; otherwise there may be no distributions for $x$ and $y$ that will satisfy $H_o$. If $mean_k$ is inside this interval, but the convergence is still not satisfactory, then the value of $mean_k$ should be moved closer to the NPMLE for $E(g_k(x,y))$. (The NPMLE itself should always be a feasible value for $mean_k$.)

Value

el2.cen.EMm returns a list of values as follows:

xd1	a vector of unique, uncensored $x$-values in ascending order
yd1	a vector of unique, uncensored $y$-values in ascending order
temp3	a list of values returned by the el2.test.wtm function (which is called by el2.cen.EMm)
mean	the hypothesized value of $E(g(x,y))$
NPMLE	a non-parametric-maximum-likelihood-estimator vector of $E(g(x,y))$
logel00	the log of the unconstrained empirical likelihood
logel	the log of the constrained empirical likelihood
"-2LLR"	-2*(log-likelihood-ratio) for the p simultaneous hypotheses
Pval	the p-value for the p simultaneous hypotheses, equal to 1 - pchisq(-2LLR, df = p)
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

Author(s)

William H. Barton <[email protected]>

References

Barton, W. (2010). Comparison of two samples by a nonparametric likelihood-ratio test. PhD dissertation at University of Kentucky.

Chang, M. and Yang, G. (1987). “Strong Consistency of a Nonparametric Estimator of the Survival Function with Doubly Censored Data.” Ann. Stat.,15, pp. 1536-1547.

Dempster, A., Laird, N., and Rubin, D. (1977). “Maximum Likelihood from Incomplete Data via the EM Algorithm.” J. Roy. Statist. Soc., Series B, 39, pp.1-38.

Gomez, G., Julia, O., and Utzet, F. (1992). “Survival Analysis for Left-Censored Data.” In Klein, J. and Goel, P. (ed.), Survival Analysis: State of the Art. Kluwer Academic Publishers, Boston, pp. 269-288.

Li, G. (1995). “Nonparametric Likelihood Ratio Estimation of Probabilities for Truncated Data.” J. Amer. Statist. Assoc., 90, pp. 997-1003.

Owen, A.B. (2001). Empirical Likelihood. Chapman and Hall/CRC, Boca Raton, pp. 223-227.

Turnbull, B. (1976). “The Empirical Distribution Function with Arbitrarily Grouped, Censored and Truncated Data.” J. Roy. Statist. Soc., Series B, 38, pp. 290-295.

Zhou, M. (2005). “Empirical likelihood ratio with arbitrarily censored/truncated data by EM algorithm.” J. Comput. Graph. Stat., 14, pp. 643-656.

Zhou, M. (2009) emplik package on CRAN website. The function el2.cen.EMm here extends el.cen.EM2 inside emplik package from one-sample to two-samples.

Examples

x<-c(10, 80, 209, 273, 279, 324, 391, 415, 566, 85, 852, 881, 895, 954, 1101, 1133,
1337, 1393, 1408, 1444, 1513, 1585, 1669, 1823, 1941)
dx<-c(1, 1, 1, 1, 1, 1, 1, 1, 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(1,1,1,1,1,1,2,2,1,1,1,1,1,2,1,1,1,1,1,1,0,0,1,1,0,0,1,0,0,0)
nx<-length(x)
ny<-length(y)
xc<-1:nx
yc<-1:ny
wx<-rep(1,nx)
wy<-rep(1,ny)
mu=c(0.5,0.5)
p <- 2
H1<-matrix(NA,nrow=nx,ncol=ny)
H2<-matrix(NA,nrow=nx,ncol=ny)
for (i in 1:nx) {
  for (j in 1:ny) {
   H1[i,j]<-(x[i]>y[j])
   H2[i,j]<-(x[i]>1060) } }
H=matrix(c(H1,H2),nrow=nx,ncol=p*ny)

# Ho1: X is stochastically equal to Y (i.e. P(X>Y)=0.5)
# Ho2: P(X>1060)=0.5 

el2.cen.EMm(x=x, dx=dx, y=y, dy=dy, p=2, H=H, mean=mu)

# Result: Pval is 0.6310234, so we cannot with 95 percent confidence reject the two
# simultaneous hypotheses Ho1 and Ho2

---

Computes empirical likelihood ratio and p-value for a single mean-type hypothesis, based on two independent samples that may contain censored data.

Description

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 default: $g(x,y)=I[x \geq y]$, $mean=0.5$. 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(df=1).

Usage

el2.cen.EMs(x,dx,y,dy,fun=function(x,y){x>=y},mean=0.5,
                                tol.u=1e-6,tol.v=1e-6,maxit=50)

Arguments

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, weight-function $g(x,y)$ used to define the mean 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
tol.u	Error tolerance for iteration control. L1 norm of the u-uOLD is used. Default 1e-6
tol.v	Error tolerance for iteration control. L1 norm of the v-vOLD is used. Default 1e-6
maxit	a positive integer used to set the maximum number of iterations of the EM algorithm; default is 50

Details

The empirical likelihood used here is

$EL(mean) = \max_{\mu_i, \nu_j} \left\{ \prod \mu_i \prod \nu_j ; s.t. \sum_i \sum_j g(x_i, y_j) \mu_i \nu_j = mean; \sum \mu_i =1; \sum \nu_j =1. \right\}$

for uncensored data. If data were censored, approapriate adjustments are used accordingly. See Owen (2001) section 11.4.

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 $mean$. This NPMLE value is in the output.)

Value

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 $\sum_{i=1}^n \sum_{j=1}^m (g(x_i,y_j) - mean) \mu_i \nu_j$, where $\mu_i$ 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.

Author(s)

William H. Barton <[email protected]> ; modified by Mai Zhou.

References

Barton, W. (2010). Comparison of two samples by a nonparametric likelihood-ratio test. PhD dissertation at University of Kentucky.

Chang, M. and Yang, G. (1987). “Strong Consistency of a Nonparametric Estimator of the Survival Function with Doubly Censored Data.” Ann. Stat.,15, pp. 1536-1547.

Dempster, A., Laird, N., and Rubin, D. (1977). “Maximum Likelihood from Incomplete Data via the EM Algorithm.” J. Roy. Statist. Soc., Series B, 39, pp.1-38.

Gomez, G., Julia, O., and Utzet, F. (1992). “Survival Analysis for Left-Censored Data.” In Klein, J. and Goel, P. (ed.), Survival Analysis: State of the Art. Kluwer Academic Publishers, Boston, pp. 269-288.

Li, G. (1995). “Nonparametric Likelihood Ratio Estimation of Probabilities for Truncated Data.” J. Amer. Statist. Assoc., 90, pp. 997-1003.

Owen, A.B. (2001). Empirical Likelihood. Chapman and Hall/CRC, Boca Raton, pp.223-227.

Turnbull, B. (1976). “The Empirical Distribution Function with Arbitrarily Grouped, Censored and Truncated Data.” J. Roy. Statist. Soc., Series B, 38, pp. 290-295.

Zhou, M. (2005). “Empirical likelihood ratio with arbitrarily censored/truncated data by EM algorithm.” J. Comput. Graph. Stat., 14, pp. 643-656.

Zhou, M. (2009) emplik package on CRAN website. The el2.cen.EMs function here extends the el.cen.EM function inside emplik package from one sample to two-samples.

Examples

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 (i.e. P(X>Y)=0.5) 
el2.cen.EMs(x, dx, y, dy, fun=function(x,y){x>=y}, mean=0.5)
# Result: Pval = 0.7090658, so we cannot with 95 percent confidence reject Ho1
# Remark: may be we should be more careful for the (x=y) cases, if any.

# Ho2: mean of X equals mean of Y
el2.cen.EMs(x, dx, y, dy, fun=function(x,y){x-y}, mean=0)
# Result: Pval = 0.9716493, so we cannot with 95 percent confidence reject Ho2

---

Computes maximum-likelihood probability jumps for multiple mean-type hypotheses, based on two independent uncensored samples

Description

This function computes the maximum-likelihood probability jumps for multiple mean-type hypotheses, based on two samples that are independent, uncensored, and weighted. The target function for the maximization is the (Lagrangian) constrained log(empirical likelihood) which can be expressed as,

$\sum_{dx_i=1} wx_i \log{\mu_i} + \sum_{dy_j=1} wy_j \log{\nu_j} - \eta ( 1 -\sum_{dx_i=1} \mu_i ) - \delta ( 1 -\sum_{dy_j=1} \nu_j ) - \lambda ( \mu^T H_1 \nu, \ldots , \mu^T H_p \nu )^T$

where the variables are defined as follows:

$x$ is a vector of uncensored data for the first sample

$y$ is a vector of uncensored data for the second sample

$wx$ is a vector of estimated weights for the first sample

$wy$ is a vector of estimated weights for the second sample

$\mu$ is a vector of estimated probability jumps for the first sample

$\nu$ is a vector of estimated probability jumps for the second sample

$H_k = [ g_k(x_i, y_j) - mean_k ], k=1, \ldots , p$, where $g_k(x,y)$ is a user-chosen function

$H = [H_1, ... , H_p]$ (used as argument in el.cen.EMm function, which calls el2.test.wtm)

$mean$ is a vector of length $p$ of hypothesized means, such that $mean_k$ is the hypothesized value of $E(g_k(x,y))$

$E$ indicates “expected value”

Usage

el2.test.wtm(xd1,yd1,wxd1new, wyd1new, muvec, nuvec, Hu, Hmu, Hnu, p, mean, maxit=35)

Arguments

xd1	a vector of uncensored data for the first sample
yd1	a vector of uncensored data for the second sample
wxd1new	a vector of estimated weights for xd1
wyd1new	a vector of estimated weights for yd1
muvec	a vector of estimated probability jumps for xd1
nuvec	a vector of estimated probability jumps for yd1
Hu	$H_u = [ H_1 - [mean_1], \ldots , H_p - [mean_p] ], dx_i=1, dy_j=1$
Hmu	a matrix, whose calculation is shown in the example below
Hnu	a matrix, whose calculation is shown in the example below
p	the number of hypotheses
mean	a vector of hypothesized values of $E(g_k(u,v)), k=1, \ldots,p$
maxit	a positive integer used to control the maximum number of iterations in the Newton-Raphson algorithm; default is 35

Details

This function is called by el2.cen.EMm. It is listed here because the user may find it useful elsewhere.

The value of $mean_k$ should be chosen between the maximum and minimum values of $g_k(xd1_i,yd1_j)$; otherwise there may be no distributions for $xd1$ and $yd1$ that will satisfy the the mean-type hypothesis. If $mean_k$ is inside this interval, but the convergence is still not satisfactory, then the value of $mean_k$ should be moved closer to the NPMLE for $E(g(xd1,yd1))$. (The NPMLE itself should always be a feasible value for $mean_k$.) The calculations for this function are derived in Owen (2001).

Value

el2.test.wtm returns a list of values as follows:

constmat	a matrix of row vectors, where the $k$th row vector holds successive values of $\mu^T H_k \nu , k=1, \ldots, p$, generated by the Newton-Raphson algorith m
lam	the vector of Lagrangian mulipliers used in the calculations
muvec1	the vector of probability jumps for the first sample that maximize the weighted empirical likelihood
nuvec1	the vector of probability jumps for the second sample that maximize the weighted empirical likelihood
mean	the vector of hypothesized means

Author(s)

William H. Barton <[email protected]>

References

Owen, A.B. (2001). Empirical Likelihood. Chapman and Hall/CRC, Boca Raton, pp.223-227.

Examples

#Ho1: P(X>Y) = 0.5
#Ho2: P(X>1060) = 0.5
#g1(x) = I[x > y]
#g2(y) = I[x > 1060]

mean<-c(0.5,0.5)
p<-2

xd1<-c(10,85,209,273,279,324,391,566,852,881,895,954,1101,1393,1669,1823,1941)
nx1=length(xd1)
yd1<-c(21,38,39,51,77,185,524,610,612,677,798,899,946,1010,1074,1147,1154,1329,1484,1602,1952)
ny1=length(yd1)

wxd1new<-c(2.267983, 1.123600, 1.121683, 1.121683, 1.121683, 1.121683, 1.121683,
 1.000000, 1.000000, 1.000000, 1.000000, 1.000000, 1.000000, 1.261740, 2.912753,
 2.912753, 2.912753)
muvec<-c(0.08835785, 0.04075290, 0.04012084, 0.04012084, 0.04012084, 0.04012084,
 0.04012084, 0.03538020, 0.03389263, 0.03389263, 0.03389263, 0.03322693, 0.04901516,
 0.05902008, 0.13065491, 0.13065491, 0.13065491)

wyd1new<-c(1.431653, 1.431653, 1.431653, 1.431653, 1.431653, 1.438453, 1.079955, 1.080832,
 1.080832, 1.080832, 1.080832, 1.000000, 1.000000, 1.000000, 1.000000, 1.000000, 1.000000,
 1.222883, 1.227865, 1.739636, 5.809616)
nuvec<-c(0.04249966, 0.04249966, 0.04249966, 0.04249966, 0.04249966, 0.04316922, 0.03425722,
 0.03463312, 0.03463312, 0.03463312, 0.03463312, 0.03300598, 0.03300598, 0.03333333,
 0.03333333, 0.03382827, 0.03382827, 0.04136800, 0.04229270, 0.05992020, 0.22762676)


H1u<-matrix(NA,nrow=nx1,ncol=ny1)
H2u<-matrix(NA,nrow=nx1,ncol=ny1)
for (i in 1:nx1) {
   for (j in 1:ny1) {
        H1u[i,j]<-(xd1[i]>yd1[j])
        H2u[i,j]<-(xd1[i]>1060) } }
Hu=matrix(c(H1u,H2u),nrow=nx1,ncol=p*ny1)
for (k in 1:p) {
     M1 <- matrix(mean[k], nrow=nx1, ncol=ny1)
     Hu[,((k-1)*ny1+1):(k*ny1)] <- Hu[,((k-1)*ny1+1):(k*ny1)] - M1}
Hmu <- matrix(NA,nrow=p, ncol=ny1*nx1)
Hnu <- matrix(NA,nrow=p, ncol=ny1*nx1) 
for (i in 1:p) {
   for (k in 1:nx1) {
        Hmu[i, ((k-1)*ny1+1):(k*ny1)] <-  Hu[k,((i-1)*ny1+1):(i*ny1)] } }
for (i in 1:p) {
   for (k in 1:ny1) {
        Hnu[i,((k-1)*nx1+1):(k*nx1)] <- Hu[(1:nx1),(i-1)*ny1+k]} }

el2.test.wtm(xd1,yd1,wxd1new, wyd1new, muvec, nuvec, Hu, Hmu,
  Hnu, p, mean, maxit=10)

#muvec1
# [1] 0.08835789 0.04075290 0.04012083 0.04012083 0.04012083 0.04012083 0.04012083
# [8] 0.03538021 0.03389264 0.03389264 0.03389264 0.03322693 0.04901513 0.05902002
# [15] 0.13065495 0.13065495 0.13065495

#nuvec1
# [1] 0.04249967 0.04249967 0.04249967 0.04249967 0.04249967 0.04316920 0.03425722
# [8] 0.03463310 0.03463310 0.03463310 0.03463310 0.03300597 0.03300597 0.03333333
# [15] 0.03333333 0.03382827 0.03382827 0.04136801 0.04229269 0.05992018 0.22762677

#  $lam
#        [,1]      [,2]
#  [1,] 8.9549 -10.29119

---

Computes maximium-likelihood probability jumps for a single mean-type hypothesis, based on two independent uncensored samples

Description

This function computes the maximum-likelihood probability jumps for a single mean-type hypothesis, based on two samples that are independent, uncensored, and weighted. The target function (Lagrangian) for the maximization is the constrained log(empirical likelihood) which can be expressed as,

$\sum_{dx_i=1} wx_i \log{\mu_i} + \sum_{dy_j=1} wy_j \log{\nu_j} - \eta ( 1 - \sum_{dx_i=1} \mu_i ) - \delta ( 1 -\sum_{dy_j=1} \nu_j ) - \lambda \sum_{dx_i=1} \sum_{dy_j=1} ( g(x_i,y_j)- mean ) \mu_i \nu_j$

where the variables are defined as follows:

$x$ is a vector of data for the first sample

$y$ is a vector of data for the second sample

$wx$ is a vector of estimated weights for the first sample

$wy$ is a vector of estimated weights for the second sample

$\mu$ is a vector of estimated probability jumps for the first sample

$\nu$ is a vector of estimated probability jumps for the second sample

Usage

el2.test.wts(u,v,wu,wv,mu0,nu0,indicmat,mean,lamOld=0)

Arguments

u	a vector of uncensored data for the first sample
v	a vector of uncensored data for the second sample
wu	a vector of estimated weights for u
wv	a vector of estimated weights for v
mu0	a vector of estimated probability jumps for u
nu0	a vector of estimated probability jumps for v
indicmat	a matrix $[g(u_i,v_j)-mean]$ where $g(u, v)$ is a user-chosen function
mean	a hypothesized value of $E(g(u,v))$, where $E$ indicates “expected value.”
lamOld	The previous solution of lambda, used as the starting point to search for new solution of lambda.

Details

This function is called by el2.cen.EMs. It is listed here because the user may find it useful elsewhere.

The value of $mean$ should be chosen between the maximum and minimum values of $(u_i,v_j)$; otherwise there may be no distributions for $u$ and $v$ that will satisfy the the mean-type hypothesis. 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 $E(g(u,v))$. (The NPMLE itself should always be a feasible value for $mean$.) The calculations for this function are derived in Owen (2001).

Value

el2.test.wts returns a list of values as follows:

u	the vector of uncensored data for the first sample
wu	the vector of weights for $u$
jumpu	the vector of probability jumps for $u$ that maximize the weighted empirical likelihood
v	the vector of uncensored data for the second sample
wv	the vector of weights for $v$
jumpv	the vector of probability jumps for $v$ that maximize the weighted empirical likelihood
lam	the value of the Lagrangian multipler found by the calculations

Author(s)

William H. Barton <[email protected]> and modified by Mai Zhou.

References

Owen, A.B. (2001). Empirical Likelihood. Chapman and Hall/CRC, Boca Raton, pp.223-227.

Examples

u<-c(10, 209, 273, 279, 324, 391, 566, 785)
v<-c(21, 38, 39, 51, 77, 185, 240, 289, 524)
wu<-c(2.442931, 1.122365, 1.113239, 1.113239, 1.104113, 1.104113, 1.000000, 1.000000)
wv<-c( 1, 1, 1, 1, 1, 1, 1, 1, 1)
mu0<-c(0.3774461, 0.1042739, 0.09649724, 0.09649724, 0.08872055, 0.08872055, 0.0739222, 0.0739222)
nu0<-c(0.1013718, 0.1013718, 0.1013718, 0.1013718, 0.1013718, 0.1013718, 0.1095413, 0.1287447,
 0.1534831)
mean<-0.5

#let fun=function(x,y){x>=y}
indicmat<-matrix(nrow=8,ncol=9,c(
-0.5,  0.5,  0.5,  0.5,  0.5,  0.5,  0.5,  0.5, 
-0.5,  0.5,  0.5,  0.5,  0.5,  0.5,  0.5,  0.5,
-0.5,  0.5,  0.5,  0.5,  0.5,  0.5,  0.5,  0.5,
-0.5,  0.5,  0.5,  0.5,  0.5,  0.5,  0.5,  0.5,
-0.5,  0.5,  0.5,  0.5,  0.5,  0.5,  0.5,  0.5,
-0.5,  0.5,  0.5,  0.5,  0.5,  0.5,  0.5,  0.5,
-0.5, -0.5,  0.5,  0.5,  0.5,  0.5,  0.5,  0.5,
-0.5, -0.5, -0.5, -0.5,  0.5,  0.5,  0.5,  0.5,
-0.5, -0.5, -0.5, -0.5, -0.5, -0.5,  0.5,  0.5))
el2.test.wts(u,v,wu,wv,mu0,nu0,indicmat,mean)

# jumpu
# [1] 0.3774461, 0.1042739, 0.09649724, 0.09649724, 0.08872055, 0.08872055, 0.0739222, 0.0739222

# jumpv
# [1] 0.1013718, 0.1013718, 0.1013718, 0.1013718, 0.1013718, 0.1013718, 0.1095413, 0.1287447,
# [9] 0.1534831

# lam
# [1] 7.055471

---