This paper considers estimation of the rate HIV diagnosis in a population of HIV positive individuals. A number of previous papers have studied the situation where time of first positive HIV test is available for AIDS cases, and possibly for individuals who have not yet developed AIDS. In this context, AIDS diagnoses are linked to prior HIV diagnoses. The present paper focuses on the case where AIDS incidence data, and data on new HIV diagnoses, are unlinked. Although there is less information available when there is no linking AIDS diagnosis and HIV tests, it is shown that a useful assessment can be made of the pattern of HIV testing over time. The methodology makes use of back-projection estimates of HIV incidence and involves fitting a model for HIV diagnosis to the observed pattern of new positive HIV tests. Smooth non-parametric estimates are obtained by minimizing a penalized residual sum of squares. In analysis of data on HIV diagnoses among the homosexual/bisexual population in the state of Victoria, Australia, we find strong evidence of a significant decrease in testing rates during the latter part of the 1980s. Subsequent testing rate estimates are subject to greater uncertainty, but are of a comparable magnitude to estimates based on linked data in other countries.