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Articles 1 - 9 of 9
Full-Text Articles in Statistics and Probability
Robust Likelihood-Based Analysis Of Multivariate Data With Missing Values, Rod Little, An Hyonggin
Robust Likelihood-Based Analysis Of Multivariate Data With Missing Values, Rod Little, An Hyonggin
The University of Michigan Department of Biostatistics Working Paper Series
The model-based approach to inference from multivariate data with missing values is reviewed. Regression prediction is most useful when the covariates are predictive of the missing values and the probability of being missing, and in these circumstances predictions are particularly sensitive to model misspecification. The use of penalized splines of the propensity score is proposed to yield robust model-based inference under the missing at random (MAR) assumption, assuming monotone missing data. Simulation comparisons with other methods suggest that the method works well in a wide range of populations, with little loss of efficiency relative to parametric models when the latter …
Weighting Adjustments For Unit Nonresponse With Multiple Outcome Variables, Sonya L. Vartivarian, Rod Little
Weighting Adjustments For Unit Nonresponse With Multiple Outcome Variables, Sonya L. Vartivarian, Rod Little
The University of Michigan Department of Biostatistics Working Paper Series
Weighting is a common form of unit nonresponse adjustment in sample surveys where entire questionnaires are missing due to noncontact or refusal to participate. Weights are inversely proportional to the probability of selection and response. A common approach computes the response weight adjustment cells based on covariate information. When the number of cells thus created is too large, a coarsening method such as response propensity stratification can be applied to reduce the number of adjustment cells. Simulations in Vartivarian and Little (2002) indicate improved efficiency and robustness of weighting adjustments based on the joint classification of the sample by two …
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, …
Equivalent Kernels Of Smoothing Splines In Nonparametric Regression For Clustered/Longitudinal Data, Xihong Lin, Naisyin Wang, Alan H. Welsh, Raymond J. Carroll
Equivalent Kernels Of Smoothing Splines In Nonparametric Regression For Clustered/Longitudinal Data, Xihong Lin, Naisyin Wang, Alan H. Welsh, Raymond J. Carroll
The University of Michigan Department of Biostatistics Working Paper Series
We compare spline and kernel methods for clustered/longitudinal data. For independent data, it is well known that kernel methods and spline methods are essentially asymptotically equivalent (Silverman, 1984). However, the recent work of Welsh, et al. (2002) shows that the same is not true for clustered/longitudinal data. First, conventional kernel methods fail to account for the within- cluster correlation, while spline methods are able to account for this correlation. Second, kernel methods and spline methods were found to have different local behavior, with conventional kernels being local and splines being non-local. To resolve these differences, we show that a smoothing …
Efficient Semiparametric Marginal Estimation For Longitudinal/Clustered Data, Naisyin Wang, Raymond J. Carroll, Xihong Lin
Efficient Semiparametric Marginal Estimation For Longitudinal/Clustered Data, Naisyin Wang, Raymond J. Carroll, Xihong Lin
The University of Michigan Department of Biostatistics Working Paper Series
We consider marginal generalized semiparametric partially linear models for clustered data. Lin and Carroll (2001a) derived the semiparametric efficinet score funtion for this problem in the mulitvariate Gaussian case, but they were unable to contruct a semiparametric efficient estimator that actually achieved the semiparametric information bound. We propose such an estimator here and generalize the work to marginal generalized partially liner models. Asymptotic relative efficincies of the estimation or throughout are investigated. The finite sample performance of these estimators is evaluated through simulations and illustrated using a longtiudinal CD4 count data set. Both theoretical and numerical results indicate that properly …
Inference For The Population Total From Probability-Proportional-To-Size Samples Based On Predictions From A Penalized Spline Nonparametric Model, Hui Zheng, Rod Little
Inference For The Population Total From Probability-Proportional-To-Size Samples Based On Predictions From A Penalized Spline Nonparametric Model, Hui Zheng, Rod Little
The University of Michigan Department of Biostatistics Working Paper Series
Inference about the finite population total from probability-proportional-to-size (PPS) samples is considered. In previous work (Zheng and Little, 2003), penalized spline (p-spline) nonparametric model-based estimators were shown to generally outperform the Horvitz-Thompson (HT) and generalized regression (GR) estimators in terms of the root mean squared error. In this article we develop model-based, jackknife and balanced repeated replicate variance estimation methods for the p-spline based estimators. Asymptotic properties of the jackknife method are discussed. Simulations show that p-spline point estimators and their jackknife standard errors lead to inferences that are superior to HT or GR based inferences. This suggests that nonparametric …
Maximization By Parts In Likelihood Inference, Peter Xuekun Song, Yanqin Fan, Jack Kalbfleisch
Maximization By Parts In Likelihood Inference, Peter Xuekun Song, Yanqin Fan, Jack Kalbfleisch
The University of Michigan Department of Biostatistics Working Paper Series
This paper presents and examines a new algorithm for solving a score equation for the maximum likelyhood estimate in certain problems of practical interest. The method circumvents the need to compute second order derivaties of the full likelihood function. It exploits the structure of certain models that yield a natural decomposition of a very complicated likelihood function. In this decomposition, the first part is a log likelihood from a simply analyzed model and the second part is used to update estimates from the first. Convergence properties of this fixed point algorithm are examined and asymptotics are derived for estimators obtained …
Semiparametric Regression Models With Missing Data: The Mathematics In The Work Of Robins Et Al., Menggang Yu, Bin Nan
Semiparametric Regression Models With Missing Data: The Mathematics In The Work Of Robins Et Al., Menggang Yu, Bin Nan
The University of Michigan Department of Biostatistics Working Paper Series
This review is an attempt to understand the landmark papers of Robins, Rotnitzky, and Zhao (1994) and Robins and Rotnitzky (1992). We revisit their main results and corresponding proofs using the theory outlined in the monograph by Bickel, Klaassen, Ritov, and Wellner (1993). We also discuss an illustrative example to show the details of applying these theoretical results.
Penalized Spline Nonparametric Mixed Models For Inference About A Finite Population Mean From Two-Stage Samples, Hui Zheng, Rod Little
Penalized Spline Nonparametric Mixed Models For Inference About A Finite Population Mean From Two-Stage Samples, Hui Zheng, Rod Little
The University of Michigan Department of Biostatistics Working Paper Series
Samplers often distrust model-based approaches to survey inference due to concerns about model misspecification when applied to large samples from complex populations. We suggest that the model-based paradigm can work very successfully in survey settings, provided models are chosen that take into account the sample design and avoid strong parametric assumptions. The Horvitz-Thompson (HT) estimator is a simple design-unbiased estimator of the finite population total in probability sampling designs. From a modeling perspective, the HT estimator performs well when the ratios of the outcome values and the inclusion probabilities are exchangeable. When this assumption is not met, the HT estimator …