Udo Bankhofer

Hot deck methods for imputing missing data: the effects of limiting donor usage

Missing data methods, within the data mining context, are limited in computational complexity due to large data amounts. Amongst the computationally simple yet effective imputation methods are the hot deck procedures. Hot deck methods impute missing values within a data matrix by using available values from the same matrix. The object, from which these available values are taken for imputation within another, is called the donor. The replication of values leads to the problem, that a single donor might be selected to accommodate multiple recipients. The inherent risk posed by this is that too many, or even all, missing values may be imputed with the values from a single donor. To mitigate this risk, some hot deck variants limit the amount of times any one donor may be selected for donating its values. This inevitably leads to the question under which conditions such a limitation is sensible. This study aims to answer this question though an extensive simulation. The results show rather clear differences between imputations by hot deck methods in which the donor limit was varied. In addition to these differences, influencing factors are identified that determine whether or not a donor limit is sensible.

On Limiting Donor Usage for Imputation of Missing Data via Hot Deck Methods

Hot deck methods impute missing values within a data matrix by using available values from the same matrix. The object from which these available values are taken for imputation is called the donor. Selection of a suitable donor for the receiving object can be done within imputation classes. The risk inherent to this strategy is that any donor might be selected for multiple value recipients. In extreme cases one donor can be selected for too many or even all values. To mitigate this donor over usage risk, some hot deck procedures limit the amount of times one donor may be selected for value donation. This study answers if limiting donor usage is a superior strategy when considering imputation variance and bias in parameter estimates.

Decision Trees for the Imputation of Categorical Data

Resolving the problem of missing data via imputation can theoretically be done by any prediction model. In the field of machine learning, a well known type of prediction model is a decision tree. However, the literature on how suitable a decision tree is for imputation is still scant to date. Therefore, the aim of this paper is to analyze the imputation quality of decision trees. Furthermore, we present a way to conduct a stochastic imputation using decision trees. We ran a simulation study to compare the deterministic and stochastic imputation approach using decision trees among each other and with other imputation methods. For this study, real datasets and various missing data settings are used. In addition, three different quality criteria are considered. The results of the study indicate that the choice of imputation method should be based on the intended analysis.

Aufgaben zur Wahrscheinlichkeitsrechnung

Professor Muller halt am Donnerstag, dem 27. Mai 2010, wie gewohnt die Statistikvorlesung. Es ist ein besonderer Tag fur ihn, denn er hat seinen 60. Geburtstag. Im Horsaal sind n Studierende anwesend.

Aufgaben zur beschreibenden Statistik

In einem Unternehmen fallen fur die Versendung von funf ausgewahlten Erzeugnissen unterschiedliche Verpackungskosten pro Stuck an.

Lösungen zu den Klausuren

In der nachfolgenden Losung zur Klausur sind in den einzelnen Losungsteilen auch die jeweils erreichbaren Punkte angegeben.

Aufgaben zur Datenanalyse

In der folgenden Datenmatrix wurden fur funf Champagner die Merkmale Suse, Alkoholgehalt (in Vol. %) und Preis (in Euro) erhoben.

Lösungen zur Wahrscheinlichkeitsrechnung

G1 sei das zufallige Ereignis, dass mindestens einer der anwesenden Horer am 27. Mai Geburtstag hat. G0 sei das dazu komplementare Ereignis, dass an diesem Tag keiner Geburtstag hat.

Aufgaben zur schließenden Statistik

Es sei X1 ,X2 ,X3 ,X4 eine mathematische Stichprobe zu einem Merkmal X mit Erwartungswert μ und Varianz σ 2 .

Aufgaben zum Data Mining

Die folgende Tabelle enthalt die Daten von 15 Bestellungen, die von verschiedenen Gasten eines Cafes aufgegeben wurden. Dabei bezeichnet ein Wert von 1, dass der Artikel in der entsprechenden Bestellung enthalten war, wahrend ein Wert von 0 angibt, dass dieser Artikel in der Bestellung nicht enthalten war.