Nonparametric Maximum Likelihood Estimation pada Data Tersensor Bivariat Melalui Teori Graf; Nonparametric Maximum Likelihood Estimation on Bivariate Censored Data through Graph Theory

Fatekurohman, M, Lina Aryati

2015 | Tesis | FMIPA

In the health or medicine, the incubation period is the time from the infection of agent exposure until the signs and symptoms of the disease appear or from the entry of germs/viruses into the human body until early symptoms of disease appear. The incubation period of HIV to AIDS is defined as the time between HIV infection and AIDS. According to Maathuis (2003), the lower limit of the incubation period of HIV to AIDS is 6 years and the upper limit is 13 years. If X represents the time interval of infection i.e (xLeft,xRight] and Y represents the time interval of onset i.e (yLower,yupper], then as well as estimating the joint distribution function of the time of HIV infection and AIDS onset time. We use non-parametric method because no specific assumptions that must be met, the free distribution it has no close form shape, and the results with the numerical approach. NPMLE calculation in the case of bivariate interval censored data is composed of two parts, the first is determined the intersection area of rectangles and the second is find the maximum likelihood. The results obtained in this study is the intersection graph algorithm complexity O(n2) and the complexity of obtaining estimator with rooted tree algorithm O(n3). If the value of first derivative of the maximum likelihood function is less than or equal to the rank of clique matrix A and the second derivative (Hessian matrix) is negative definite then the likelihood function is a strictly concave function. The estimator pˆ is unique. The main advantages of finding the rooted tree algorithm is the simplification of NPMLE computation. Estimator obtained is self consistency estimator and every NPLME is self consistency estimator.

Kata Kunci : NPMLE; bivariate censored data; rooted tree; incubation period; self consistency estimator.