Incomplete Split-Plot Designs Supplemented by a Single Control

The article deals with the constructing methods for experiments carried out in an incomplete split-plot design supplemented by an additional treatment, called a single control. The control treatment has been treated usually as one specific factor level while not necessarily. The control cannot be connected with treatment combinations in an experiment. This distinguishes this article from others in the area considered. The proposed supplementation of whole incomplete split-plot designs leads to the designs with generally accepted methodological requirements, especially randomization. Moreover, we propose a few methods for constructing considered types of the designs with desirable statistical properties such as general balance and efficiency balance of the design with respect to treatment contrasts.     

On Jointly Estimating Parameters and Missing Data by Maximizing the Complete-Data Likelihood

One approach to handling incomplete data occasionally encountered in the literature is to treat the missing data as parameters and to maximize the complete-data likelihood over the missing data and parameters. This article points out that although this approach can be useful in particular problems, it is not a generally reliable approach to the analysis of incomplete data. In particular, it does not share the optimal properties of maximum likelihood estimation, except under the trivial asymptotics in which the proportion of missing data goes to zero as the sample size increases.     

E-optimal block designs under heteroscedastic model

This paper mainly studies the E-optimality of block designs under a general heteroscedastic setting. The C-matrix of a block design under a heteroscedastic setting is obtained by using generalized least squares. Some bounds for the smallest positive eigenvalue of C-matrix are obtained in some general classes of connected designs. Use of these bounds is then made to obtain certain E-optimal block designs in various classes of connected block designs.     

Improved conditions for the robustness of binary block designs against the loss of whole blocks

Several authors have investigated conditions for a binary block design, D, to be maximally robust such that every eventual design obtained from D by eliminating r_[υ]−1 blocks is connected, where r_[υ] is the smallest treatment replication. Four new results for the maximal robustness of D with superior properties are given. An extension of these results to widen the assessment of robustness of the planned design is also presented.     

METHOD OF ESTIMATION FOR SAMPLING FROM INCOMPLETE FRAMES

The planning of any sample survey or census requires the existence of a sampling frame comprising a list of all the sampling units. But unfortunately there is hardly a situation in practice where the frame is available in the form the sampler desires to use. Most commonly some units of the target population are not listed in the frame, and the frame may contain units which do not belong to the target population. In this investigation a suitable method of estimation is proposed when sampling is done from such imperfect frames and a geographical ordering of the units can be established.     

On density and regression estimation with incomplete data

We consider the problem of estimation of a density function in the presence of incomplete data and study the Hellinger distance between our proposed estimators and the true density function. Here, the presence of incomplete data is handled by utilizing a Horvitz–Thompson-type inverse weighting approach, where the weights are the estimates of the unknown selection probabilities. We also address the problem of estimation of a regression function with incomplete data.     

Some inequalities in incomplete beta functions by using statistical techniques

In this paper an inequality concerning incomplete beta functions is stated and proved. From this inequality several other inequalities are derived. The main inequality can be given by using the properties of incomplete beta functions but an interesting derivation by using statistical techniques is given.     

On the Computation of Gauss Hypergeometric Functions

The pioneering study undertaken by Liang et al. in 2008 (Journal of the American Statistical Association, 103, 410–423) and the hundreds of papers citing that work make use of certain hypergeometric functions. Liang et al. and many others claim that the computation of the hypergeometric functions is difficult. Here, we show that the hypergeometric functions can in fact be reduced to simpler functions that can often be computed using a pocket calculator.     

Distribution-free subset selection for incompletely ranked data

In market research and some other areas, it is common that a sample of n judges (consumers, evaluators, etc.) are asked to independently rank a series of k objects or candidates. It is usually difficult to obtain the judges' full cooperation to completely rank all k objects. A practical way to overcome this difficulty is to give each judge the freedom to choose the number of top candidates he is willing to rank. A frequently encountered question in this type of survey is how to select the best object or candidate from the incompletely ranked data. This paper proposes a subset selection procedure which constructs a random subset of all the k objects involved in the survey such that the best object is included in the subset with a prespecified confidence. It is shown that the proposed subset selection procedure is distribution-free over a very broad class of underlying distributions. An example from a market research study is used to illustrate the proposed procedure.     

Synthesizing categorical datasets to enhance inference

A common data analysis setting consists of a collection of datasets of varying sizes that are all relevant to a particular scientific question, but which include different subsets of the relevant variables, presumably with some overlap. Here, we demonstrate that synthesizing cross-classified categorical datasets drawn from an incompletely cross-classified common population, where many of the sets are incomplete (i.e., one or more of the classification variables is unobserved), but at least one is completely observed is expected to reduce uncertainty about the cell probabilities in the associated multi-way contingency table as well as for derived quantities such as relative risks and odds ratios. The use of the word “expected” here is the key point. When synthesizing complete datasets from a common population, we are assured to reduce uncertainty. However, when we work with a log-linear model to explain the complete table, because this model cannot be fitted to any of the incomplete datasets, improvement is not assured. We provide technical clarification of this point as well as a series of simulation examples, motivated by an adverse birth outcomes investigation, to illustrate what can be expected under such synthesis.     

Semiparametric predictive mean matching

Predictive mean matching is an imputation method that combines parametric and nonparametric techniques. It imputes missing values by means of the Nearest Neighbor Donor with distance based on the expected values of the missing variables conditional on the observed covariates, instead of computing the distance directly on the values of the covariates. In ordinary predictive mean matching the expected values are computed through a linear regression model. In this paper a generalization of the original predictive mean matching is studied. Here the expected values used for computing the distance are estimated through an approach based on Gaussian mixture models. This approach includes as a special case the original predictive mean matching but allows one to deal also with nonlinear relationships among the variables. In order to assess its performance, an empirical evaluation based on simulations is carried out.     

Estimating Transition Probabilities for Ignorable Intermittent Missing Data in a Discrete-Time Markov Chain

This article considers a discrete-time Markov chain for modeling transition probabilities when multiple successive observations are missing at random between two observed outcomes using three methods: a na\"?ve analog of complete-case analysis using the observed one-step transitions alone, a non data-augmentation method (NL) by solving nonlinear equations, and a data-augmentation method, the Expectation-Maximization (EM) algorithm. The explicit form of the conditional log-likelihood given the observed information as required by the E step is provided, and the iterative formula in the M step is expressed in a closed form. An empirical study was performed to examine the accuracy and precision of the estimates obtained in the three methods under ignorable missing mechanisms of missing completely at random and missing at random. A dataset from the mental health arena was used for illustration. It was found that both data-augmentation and nonaugmentation methods provide accurate and precise point estimation, and that the na\"?ve method resulted in estimates of the transition probabilities with similar bias but larger MSE. The NL method and the EM algorithm in general provide similar results whereas the latter provides conditional expected row margins leading to smaller standard errors.     

Specifying a Gaussian Markov Random Field by a Sparse Cholesky Triangle

ABSTRACT

This note discusses the approach of specifying a Gaussian Markov random field (GMRF) by the Cholesky triangle of the precision matrix. A such representation can be made extremely sparse using numerical techniques for incomplete sparse Cholesky factorization, and provide very computational efficient representation for simulating from the GMRF. However, we provide theoretical and empirical justification showing that the sparse Cholesky triangle representation is fragile when conditioning a GMRF on a subset of the variables or observed data, meaning that the computational cost increases.     

On the statistical computation of the sample multiple correlation moefficient

Based on the recursive formulas of Lee (1988) and Singh and Relyea (1992) for computing the noncentral F distribution, a numerical algorithm for evaluating the distributional values of the sample squared multiple correlation coefficient is proposed. The distributional function of this statistic is usually represented as an infinite weighted sum of the iterative form of incomplete beta integral. So an effective algorithm for the incomplete beta integral is crucial to the numerical evaluation of various distribution values. Let a and b denote two shape parameters shown in the incomplete beta integral and hence formed in the sampling distribution functionn be the sample size, and p be the number of random variates. Then both 2a = p - 1 and 2b = n - p are positive integers in sampling situations so that the proposed numerical procedures in this paper are greatly simplified by recursively formulating the incomplete beta integral. By doing this, it can jointly compute the distributional values of probability dens function (pdf) and cumulative distribution function (cdf) for which the distributional value of quantile can be more efficiently obtained by Newton's method. In addition, computer codes in C are developed for demonstration and performance evaluation. For the less precision required, the implemented method can achieve the exact value with respect to the jnite significant digit desired. In general, the numerical results are apparently better than those by various approximations and interpolations of Gurland and Asiribo (1991),Gurland and Milton (1970), and Lee (1971, 1972). When b = (1/2)(n -p) is an integer in particular, the finite series formulation of Gurland (1968) is used to evaluate the pdf/cdf values without truncation errors, which are served as the pivotal one. By setting the implemented codes with double precisions, the infinite series form of derived method can achieve the pivotal values for almost all cases under study. Related comparisons and illustrations are also presented     

Likelihood-free stochastic approximation EM for inference in complex models

A maximum likelihood methodology for the parameters of models with an intractable likelihood is introduced. We produce a likelihood-free version of the stochastic approximation expectation-maximization (SAEM) algorithm to maximize the likelihood function of model parameters. While SAEM is best suited for models having a tractable “complete likelihood” function, its application to moderately complex models is a difficult or even impossible task. We show how to construct a likelihood-free version of SAEM by using the “synthetic likelihood” paradigm. Our method is completely plug-and-play, requires almost no tuning and can be applied to both static and dynamic models.     

A protective estimator for longitudinal binary data subject to non-ignorable non-monotone missingness

Summary.  In longitudinal studies missing data are the rule not the exception. We consider the analysis of longitudinal binary data with non-monotone missingness that is thought to be non-ignorable. In this setting a full likelihood approach is complicated algebraically and can be computationally prohibitive when there are many measurement occasions. We propose a 'protective' estimator that assumes that the probability that a response is missing at any occasion depends, in a completely unspecified way, on the value of that variable alone. Relying on this 'protectiveness' assumption, we describe a pseudolikelihood estimator of the regression parameters under non-ignorable missingness, without having to model the missing data mechanism directly. The method proposed is applied to CD4 cell count data from two longitudinal clinical trials of patients infected with the human immunodeficiency virus.     

Bayesian estimation of the complete sample size from an incomplete poisson sample

For the Poisson a posterior distribution for the complete sample size, N, is derived from an incomplete sample when any specified subset of the classes are missing.Means as well as other posterior characteristics of N are obtained for two examples with various classes removed. For the special case of a truncated ‘missing zero class’ Poisson sample a simulation experiment is performed for the small ‘N=25’ sample situation applying both Bayesian and maximum likelihood methods of estimation.     

Maximum likelihood estimation using the empirical fisher information matrix

In this paper the use of the empirical Fisher information matrix as an estimator of the information matrix is considered in the context of response models and incomplete data problems. The introduction of an additional stochastic component into such models is shown to greatly increase the range of situations in which the estimator can be employed. In particular the conditions for its use in incomplete data problems are shown to be the same as those needed to justify the use of the EM algorithm.