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Articles 31 - 33 of 33
Full-Text Articles in Statistical Theory
Bivariate Current Status Data, Mark J. Van Der Laan, Nicholas P. Jewell
Bivariate Current Status Data, Mark J. Van Der Laan, Nicholas P. Jewell
U.C. Berkeley Division of Biostatistics Working Paper Series
In many applications, it is often of interest to estimate a bivariate distribution of two survival random variables. Complete observation of such random variables is often incomplete. If one only observes whether or not each of the individual survival times exceeds a common observed monitoring time C, then the data structure is referred to as bivariate current status data (Wang and Ding, 2000). For such data, we show that the identifiable part of the joint distribution is represented by three univariate cumulative distribution functions, namely the two marginal cumulative distribution functions, and the bivariate cumulative distribution function evaluated on the …
A New Partitioning Around Medoids Algorithm, Mark J. Van Der Laan, Katherine S. Pollard, Jennifer Bryan
A New Partitioning Around Medoids Algorithm, Mark J. Van Der Laan, Katherine S. Pollard, Jennifer Bryan
U.C. Berkeley Division of Biostatistics Working Paper Series
Kaufman & Rousseeuw (1990) proposed a clustering algorithm Partitioning Around Medoids (PAM) which maps a distance matrix into a specified number of clusters. A particularly nice property is that PAM allows clustering with respect to any specified distance metric. In addition, the medoids are robust representations of the cluster centers, which is particularly important in the common context that many elements do not belong well to any cluster. Based on our experience in clustering gene expression data, we have noticed that PAM does have problems recognizing relatively small clusters in situations where good partitions around medoids clearly exist. In this …
Maximum Likelihood Estimation Of Ordered Multinomial Parameters, Nicholas P. Jewell, John D. Kalbfleisch
Maximum Likelihood Estimation Of Ordered Multinomial Parameters, Nicholas P. Jewell, John D. Kalbfleisch
U.C. Berkeley Division of Biostatistics Working Paper Series
The pool-adjacent violator-algorithm (Ayer, et al., 1955) has long been known to give the maximum likelihood estimator of a series of ordered binomial parameters, based on an independent observation from each distribution (see Barlow et al., 1972). This result has immediate application to estimation of a survival distribution based on current survival status at a set of monitoring times. This paper considers an extended problem of maximum likelihood estimation of a series of ‘ordered’ multinomial parameters. By making use of variants of the pool adjacent violator algorithm, we obtain a simple algorithm to compute the maximum likelihood estimator and demonstrate …