我想计算三个核密度函数的乘积。为了做到这一点，在找到内核密度后，我应该找到它们的乘积的近似函数，然后计算积分（具有参数上限）。请参阅下面的代码，这给了我一个错误。我认为在计算近似函数或积分部分时应该存在问题。
library(ks)
library(rgl)
zz <- " longitude latitude depth time magnitude
277.728371 139.925845 0.75103658 26.40786514 0.943718276
426.087586 168.903095 0.2957441 0.241456485 0.759137864
331.549444 74.168092 0.55140397 66.51363095 0.776176433
93.078983 78.588053 0.15328453 104.9418546 0.834896464
492.359229 11.082291 0.08173915 111.3391451 0.874798119
86.85704 42.34973 0.23081904 152.8098572 0.878111793
128.038949 73.935782 0.66160123 157.8933315 0.990100773
295.300125 1.935765 0.49789785 159.9134319 0.842815655
294.688309 1.024583 0.44789667 165.7092358 0.886545275
221.246937 151.217171 0.6337224 167.6213491 0.885163617
111.240376 156.04214 0.55752237 171.2039395 0.885273526
25.929383 136.975153 0.0271747 172.6574772 0.812214826
415.726989 158.482975 0.37340509 184.3767148 0.90837174
73.921877 60.031908 0.15224511 189.6429637 0.791403228
8.811256 124.676545 0.26806101 193.7498013 0.813638308"
x <- read.table(text=zz, header = TRUE)
y1 <- x[,1:3]
y2<- x[ ,4]
y3<- x[ ,5]
fhat1 <- kde(x=y1)
fhat2 <- kde(x=y2)
fhat3 <- kde(x=y3)
integrand <- function(p){fhat1(p,y1)* fhat2(p,y2)* fhat3(p,y3)}
Vintegrand <- Vectorize(integrand)
integrate(Vintegrand, lower = 0, upper = t)