# Simple Plug in badnwidth selector Provides the asymptotic MISE optimal plug-in bandwidth for the local linear hazard rate estimator `LocLinEst`, defined in (4), [Bagkavos (2011)](https://link.springer.com/article/10.1007/s10463-010-0277-6). This is the binned data version of the `PlugInBand` AMISE optimal bandwidth rule. ```r LLHRPlugInBand(BinCenters, h, kfun, Delta, xin, xout, IntKfun, ci, cens) ``` ## Arguments - `BinCenters`: A vector of data points, the centers of the bins resulting from the discretization of the data. - `h`: Bandwidth for the estimate of the distribution function. - `kfun`: A kernel function. - `Delta`: A scalar. The length of the bins. - `xin`: A vector of data points - `xout`: The point at which the estimates should be calculated. - `IntKfun`: The integrated kernel function. - `ci`: Crude hazard rate estimates. - `cens`: Censoring Indicators. ## Details The bandwidth selector requires binned data, i.e. data in the form $(x_i, y_i)$ where $x_i$ are the bin centers and $y_i$ are empirircal hazard rate estimates at each $x_i$. This is achieved via the `DiscretizeData` function. As it can be seen from (4) in [Bagkavos (2011)](https://link.springer.com/article/10.1007/s10463-010-0277-6), the bandwidth selector also requires an estimate of the functional $$ \int \left \{ \lambda^{(2)}(x) \right \}^2 \,dx $$ which is readily implemented in `PlugInBand`. It also requires an estimate of the constant $$ \int \frac{\lambda(x)}{1-F(x)} \,dx $$ For this reason additionally the plug in bandwidth rule is also used, as it is implemented in the `bw.nrd` distribution function default bandwidth rule of [Swanepoel and Van Graan (2005)](https://onlinelibrary.wiley.com/doi/abs/10.1111/j.1467-9469.2005.00472.x). The constants $R(K)$ and $\mu_2^2(K)$ are deterministic and specific to the kernel used in the implementation hence can be claculated precisely. ## Returns A scalar with the value of the suggested bandwidth. ## References [Bagkavos (2011), Annals of the Institute of Statistical Mathematics, 63(5), 1019-1046.](https://link.springer.com/article/10.1007/s10463-010-0277-6) ## See Also `PlugInBand` ## Examples ```r x<-seq(0, 5,length=100) #design points where the estimate will be calculated SampleSize<-100 #amount of data to be generated ti<- rweibull(SampleSize, .6, 1) # draw a random sample ui<-rexp(SampleSize, .2) # censoring sample cat("\n AMOUNT OF CENSORING: ", length(which(ti>ui))/length(ti)*100, "\n") x1<-pmin(ti,ui) # observed data cen<-rep.int(1, SampleSize) # initialize censoring indicators cen[which(ti>ui)]<-0 # 0's correspond to censored indicators a.use<-DiscretizeData(ti, x) # discretize the data BinCenters<-a.use$BinCenters # get the data centers ci<-a.use$ci # get empircal hazard rate estimates Delta=a.use$Delta # Binning range h2<-bw.nrd(ti) # Bandwidth to use in constant est. of the plug in rule h.use<-h2 # the first element is the band to use huse1<- LLHRPlugInBand(BinCenters,h.use,Epanechnikov,Delta,ti,x,IntEpanechnikov,ci,cen) huse1 ```

LLHRPlugInBand function