Permuting incomplete paired data: a novel exact and asymptotic correct randomization test

Various statistical tests have been developed for testing the equality of means in matched pairs with missing values. However, most existing methods are commonly based on certain distributional assumptions such as normality, 0-symmetry or homoscedasticity of the data. The aim of this paper is to develop a statistical test that is robust against deviations from such assumptions and also leads to valid inference in case of heteroscedasticity or skewed distributions. This is achieved by applying a clever randomization approach to handle missing data. The resulting test procedure is not only shown to be asymptotically correct but is also finitely exact if the distribution of the data is invariant with respect to the considered randomization group. Its small sample performance is further studied in an extensive simulation study and compared to existing methods. Finally, an illustrative data example is analysed.     

Convergence rate of wavelet density estimator with data missing randomly when covariables are present

In this article, we study global L₂ error of non linear wavelet estimator of density in the Besov space B^s_pq for missing data model when covariables are present and prove that the estimator can achieve the optimal rate of convergence, which is similar to the result studied by Donoho et al. (1996) Donoho, D.L., Johnstone, I.M., Kerkyacharian, G., Picard, D. (1996). Density estimation by wavelet thresholding. Ann. Stat. 24:508–539.[Crossref], [Web of Science ®] , [Google Scholar] in complete independent data case with term-by-term thresholding of the empirical wavelet coefficients. Finite-sample behavior of the proposed estimator is explored via simulations.     

Ignorability conditions for frequentist non parametric analysis of conditional distributions with incomplete data

Rubin (1976 Rubin, D.B. (1976). Inference and missing data. Biometrika 63(3):581–592.[Crossref], [Web of Science ®] , [Google Scholar]) derived general conditions under which inferences that ignore missing data are valid. These conditions are sufficient but not generally necessary, and therefore may be relaxed in some special cases. We consider here the case of frequentist estimation of a conditional cdf subject to missing outcomes. We partition a set of data into outcome, conditioning, and latent variables, all of which potentially affect the probability of a missing response. We describe sufficient conditions under which a complete-case estimate of the conditional cdf of the outcome given the conditioning variable is unbiased. We use simulations on a renal transplant data set (Dienemann et al.) to illustrate the implications of these results.     

Empirical likelihood confidence bands for distribution functions with missing responses

Distribution function estimation plays a significant role of foundation in statistics since the population distribution is always involved in statistical inference and is usually unknown. In this paper, we consider the estimation of the distribution function of a response variable Y with missing responses in the regression problems. It is proved that the augmented inverse probability weighted estimator converges weakly to a zero mean Gaussian process. A augmented inverse probability weighted empirical log-likelihood function is also defined. It is shown that the empirical log-likelihood converges weakly to the square of a Gaussian process with mean zero and variance one. We apply these results to the construction of Gaussian process approximation based confidence bands and empirical likelihood based confidence bands of the distribution function of Y. A simulation is conducted to evaluate the confidence bands.     

A formula for a missing plot in a general incomplete block design,when recovery of interblock information is used

In this paper, Yate's missing plot technique is used to derive the formula for substitution in a missing plot in a general incomplete block design, where blocks are assumed to be independent normal. The use of penalized normal equations, using BLUPS, makes this task simpler.     

A pattern-mixture odds ratio model for incomplete categorical data

Most models for incomplete data are formulated within the selection model framework. Pattern-mixture models are increasingly seen as a viable alternative, both from an interpretational as well as from a computational point of view (Little 1993, Hogan and Laird 1997, Ekholm and Skinner 1998). Whereas most applications are either for continuous normally distributed data or for simplified categorical settings such as contingency tables, we show how a multivariate odds ratio model (Molenberghs and Lesaffre 1994, 1998) can be used to fit pattern-mixture models to repeated binary outcomes with continuous covariates. Apart from point estimation, useful methods for interval estimation are presented and data from a clinical study are analyzed to illustrate the methods.     

k-POD: A Method for k-Means Clustering of Missing Data

The k-means algorithm is often used in clustering applications but its usage requires a complete data matrix. Missing data, however, are common in many applications. Mainstream approaches to clustering missing data reduce the missing data problem to a complete data formulation through either deletion or imputation but these solutions may incur significant costs. Our k-POD method presents a simple extension of k-means clustering for missing data that works even when the missingness mechanism is unknown, when external information is unavailable, and when there is significant missingness in the data.

[Received November 2014. Revised August 2015.]     

Robust estimation of AR coefficients under simultaneously influencing outliers and missing values

A family of robust estimators for coefficients of Gaussian AR(p) time series under simultaneously influencing distortions of two types: outliers and missing values, is proposed. The estimators are based on special properties of the Cauchy probability distribution; consistency and the asymptotic normality of these estimators are proven. An approximate solution of the problem of minimization of the asymptotic variance within the proposed family of estimators is found. Performance of the proposed estimators is illustrated for simulated time series and for real data sets.     

晚唐小说与政治——从《杜阳杂编》等看"甘露之变"后的唐文宗

“从古未有”的“甘露之变”,不可能在当时的文学作品中没有反映。文章以唐小说集《杜阳杂编》、《松窗杂录》、《阙史》为例,考论其对“甘露之变”后文宗受制于宦官的处境和心态,以至郁郁而殁的描述,具有证史、补史的意义。     

Missing at random (MAR) in nonparametric regression - A simulation experiment

The additive model is considered when some observations on x are missing at random but corresponding observations on y are available. Especially for this model, missing at random is an interesting case because the complete case analysis is expected to be no more suitable. A simulation experiment is reported and the different methods are compared based on their superiority with respect to the sample mean squared error. Some focus is also given on the sample variance and the estimated bias. In detail, the complete case analysis, a kind of stochastic mean imputation, a single imputation and the nearest neighbor imputation are discussed.