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Articles 31 - 34 of 34
Full-Text Articles in Categorical Data Analysis
Choice Of Monitoring Mechanism For Optimal Nonparametric Functional Estimation For Binary Data, Nicholas P. Jewell, Mark J. Van Der Laan, Stephen Shiboski
Choice Of Monitoring Mechanism For Optimal Nonparametric Functional Estimation For Binary Data, Nicholas P. Jewell, Mark J. Van Der Laan, Stephen Shiboski
U.C. Berkeley Division of Biostatistics Working Paper Series
Optimal designs of dose levels in order to estimate parameters from a model for binary response data have a long and rich history. These designs are based on parametric models. Here we consider fully nonparametric models with interest focused on estimation of smooth functionals using plug-in estimators based on the nonparametric maximum likelihood estimator. An important application of the results is the derivation of the optimal choice of the monitoring time distribution function for current status observation of a survival distribution. The optimal choice depends in a simple way on the dose response function and the form of the functional. …
Semiparametric Binary Regression Under Monotonicity Constraints, Moulinath Banerjee, Pinaki Biswas, Debashis Ghosh
Semiparametric Binary Regression Under Monotonicity Constraints, Moulinath Banerjee, Pinaki Biswas, Debashis Ghosh
The University of Michigan Department of Biostatistics Working Paper Series
Summary: We study a binary regression model where the response variable $\Delta$ is the indicator of an event of interest (for example, the incidence of cancer) and the set of covariates can be partitioned as $(X,Z)$ where $Z$ (real valued) is the covariate of primary interest and $X$ (vector valued) denotes a set of control variables. For any fixed $X$, the conditional probability of the event of interest is assumed to be a monotonic function of $Z$. The effect of the control variables is captured by a regression parameter $\beta$. We show that the baseline conditional probability function (corresponding to …
Maximum Likelihood Estimation Of Ordered Multinomial Parameters , Nicholas P. Jewell, Jack Kalbfleisch
Maximum Likelihood Estimation Of Ordered Multinomial Parameters , Nicholas P. Jewell, Jack Kalbfleisch
The University of Michigan Department 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 pi = (p1i, p2i, . . . , pmi) for 1 < = I < = k, where ordered means that pj1 < = pj2 < = .. . < = pjk for each j with 1 < = j < = m-1. The data consist of k independent observations X1, . . . ,Xk where Xi has a multinomial distribution with probability parameter pi and known index ni > = 1. By making use of variants of the pool adjacent violator algorithm, …
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 …