This thesis is concerned with nonlinear regression when some observations are censored, and the asymptotic distribution of likelihood ratio in INID (Independent Not Identically Distributed) case. An algorithm based on EM procedure which finds the maximum likelihood estimator is proposed. This algorithm treats the conditional expectations of censored data under the condition of censoring as complete data and minimizes the sum of squares of errors and finds the least squares estimator. This estimator then assumed to be true parameter and the conditional expectations of censored data are revised. This process is repeated until convergence.
Hoadley's conditions of consistency and those of asymptotic normality are checked. These reduce to f (x,θ) having continuous second derivative with respect to θ and $lim_{\mid{\theta}\mid \to \infty}\mid{f(x, \theta)}\mid=\infty$ for each x.
The limiting distribution of the likelihood ratio (λ) in INID case is derived using the second order Taylor expansion of log likelihood function. The -2 log λ converges in law to distribution under suitable conditions. Using this result the limiting distribution of likelihood ratio in nonlinear regression when some observations are censored is derived.
