Missing at Random (MAR) in Nonparametric Regression - A Simulation Experiment

This paper considers an additive model y = f(x) + e 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 of the fact that the complete case analysis is not expected to be suitable. A simulation study is reported and methods are compared based on superiority measures as the sample mean squared error, sample variance and estimated sample bias. In detail, complete case analysis, zero order regression plus random noise, single imputation and nearest neighbor imputation are discussed

The Additive Model with Missing Values in the Independent Variable - Theory and Simulation

After a short introduction of the model, the missing mechanism and the method of inference some imputation procedures are introduced with special focus on the simulation experiment. Within this experiment, the simple additive model y = f(x) + e is assumed to have missing values in the independent variable according to MCAR. Besides the well-known complete case analysis, mean imputation plus random noise, a single imputation and two ways of nearest neighbor imputation are used. These methods are compared within a simulation experiment based on the average mean square error, variances and biases of \hat{f}(x) at the knots

Estimating A Polynomial Regression With Measurement Errors In The Structural And In The Functional Case - A Comparison

Two methods of estimating the parameters of a polynomial regression with measurement errors in the regressor variable are compared to each other with respect to their relative efficiency and robustness. One of the two estimators (SLS) is valid for the structural variant of the model and uses the assumption that the true regressor variable is normally distributed, while the other one (ALS and also its small sample modification MALS) does not need any assumption on the regressor distribution. SLS turns out to react rather strongly on violations of the normality assumption as far as its bias is concerned but is quite robust with respect to its MSE. It is more efficient than ALS or MALS whenever the normality assumption holds true

Identifying Missing Data Mechanisms in (2 x 2)-Contingency Tables

Consider the sample of two binary variables X and Y with some missing structure within X or Y. The knowledge about the corresponding values of the observed covariate allows to play through all possible `originally' complete data sets. After defining the notation, including some theoretical work, a test for non--MCAR within the complete case table is presented. Simulating all possible tables enables some testing on non--MAR. A simulation experiment is used to illustrate this context

The Classical Linear Regression Model with one Incomplete Binary Variable

We present three different methods based on the conditional mean imputation when binary explanatory variables are incomplete. Apart from the single imputation and multiple imputation especially the so-called pi imputation is presented as a new procedure. Seven procedures are compared in a simulation experiment when missing data are confined to one independent binary variable: complete case analysis, zero order regression, categorical zero order regression, pi imputation, single imputation, multiple imputation, modified first order regression. After a brief theoretical description of the simulation experiment, MSE-ratio, variance and bias are used to illustrate differences within and between the approaches

Statistische Methoden bei unvollständigen Daten

Dieser Artikel gibt einen überblick über die Problematik fehlender Daten im Rahmen der statistischen Datenanalyse. Im Prinzip sollte er auch Lesern mit geringem mathematischen und statistischen Wissen dienlich sein und sie mathematisch nicht überfordern.Gegebenenfalls kann über allzu theoretische Komponenten hinweggelesen werden