missing data is a chronic disease in applications of data envelopment analysis. Very often, important input or output variables are not completely specified and/or the decision-making units do not report all the required statistics. Therefore, the missing values in the inputs and outputs cannot be studied using the original data envelopment analysis models. This paper introduces methods for finding missing data when the existing data is certain. In this article, after explaining the essential concepts of missing values, we describe some methods of missing value imputation that reduce the complexity of data analysis. There are several methods for imputing missing data, including various methods of simple imputation and multiple imputation. This paper is the first systematic attempt to utilize data containing missing values using statistical approaches in the DEA. In particular, we examine what happens if we keep empty entries in the data set and assign a certain numeric value to them. To show how the proposed methods work, they will be used to evaluate a set of secondary public schools in Greece in some of which there are missing input or output values.

In this paper, we are presenting the basic concepts of missing data in a very simple but practical approach.missing data are ubiquitous throughout the social, behavioral, and medical sciences. In Statistics, missing data occur when no data value is stored for the variable in the current observation. missing data reduce the representativeness of the sample and can therefore distort inferences about the population.missing data are a common occurrence and can have a significant effect on the conclusions that can be drawn from the data. All the methods of parameters estimation are based on the completion of data set assumption and only in this case the result will be a non- biased one, and with the increase of missing proportion, the rate of biased results increase too.For decades, researchers have relied on a variety of old techniques that attempt to “fix” the data by discarding incomplete cases or by filling in the missing values. Unfortunately, most of these techniques require a relatively strict assumption about the cause of missing data and are prone to substantial bias.

Multivariate time series data are found in a variety of fields such as bioinformatics, biology, genetics, astronomy, geography and finance. Many time series datasets contain missing data. Multivariate time series missing data imputation is a challenging topic and needs to be carefully considered before learning or predicting time series. Frequent researches have been done on the use of different techniques for time series missing data imputation, which usually include simple analytic methods and modeling in specific applications or univariate time series. In this paper, a hybrid approach to obtain missing data is proposed. An improved version of inverse distance weighting (IDW) interpolation is used to missing data imputation. The IDW interpolation method has two major limitations: 1) finding closest points to missing data 2) Choosing the optimal effect power for missing data neighbors. Clustering has been used to remove the first constraint and find closest points to the missing data. With the help of clustering, the search radius and the number of input points that are supposed to be used in interpolation calculations are limited and controlled, and it is possible to determine which points are used to determine the value of a missing data. Therefore, most similar data to the missing data are found. In this paper, the k-maens clustering method is used to find similar data. This method has been more accurate than other clustering methods in multivariate time series. Evolutionary algorithms are used to find the optimal effect power of each data point to remove the second constraint. Considering that each sample within each cluster has a different effect on the estimation of missing data, cuckoo search is used to find the effect on missing data. The cuckoo search algorithm is applied to the data of each cluster, and each data sample that has more similarity with the missing data has more influence, and each data sample that has less similarity has less influence and has less influence in determining the amount of missing data. Among evolutionary algorithms, evolutionary cuckoo search algorithm is used due to high convergence speed, much less probability of being trapped in local optimal points, and ability to quickly solve high dimensional optimization problems in multivariate time series problems. To evaluate the performance of the proposed method, RMS, MAE, , MSE and MAPE criteria are used. Experimental results are investigated on four UCI datasets with different percentages of missingness and in general, the proposed algorithm performs better than the other three comparative methods with an average RMSE error of 0. 05, MAE error of 0. 04, MSE error of 0. 003, and MAPE error of 5. The correlation between the actual data and the estimated value in the proposed method is about 99%.

In the classical data envelopment analysis (DEA) models, inputs and outputs are assumed as known variables, and these models cannot deal with unknown amounts of variables directly. In recent years, there are few researches on handling missing data. This paper suggests a new interval based approach to apply missing data, which is the modified version of Kousmanen (2009) approach. First, the proposed approach suggests using an acceptable range for missing inputs and outputs, which is determined by the decision maker (DM). Then, applying the least favourable bounds of missing data along with using the proposed range is suggested in estimating the production frontier. A data set is used to illustrate the approach.

missing data is a very common problem in all research fields. Case deletion is a simple way to handle incomplete data sets which could mislead to biased statistical results. A more reliable approach to handle missing values is imputation which allows covariate-dependent missing mechanism, as well. This paper aims to prepare guidance for researchers facing missing data problems by comparing various imputation methods including machine learning techniques, to achieve better results in supervised learning tasks. A benchmark dataset has experimented and the results are compared by applying popular classifiers over varying missing mechanisms and rates on this benchmark dataset.

This work presents a new method for latent variable mixed models with missing data and extends the regression methods to obtain factor scores, as well as, letting covariates affect the latent variable directly. Maximum likelihood and least square methods are used to estimate model parameters and factor scores. The new model is applied to gross motor development data and the results are compared with two-stage factor analysis and structural equation models.

BACKGROUND AND OBJECTIVE: Applying the growth curve is the most powerful way for monitoring the growth in children and through this method it would be possible to recognize in time the deviation from the natural growth pattern in children. Falling the data and missing values are general problems in analyzing the growth longitudinal data. Therefore, it is important that by computing the missing values, the data should be completed and directed towards the proper path for analysis. METHODS: This two year longitudinal study was done on 317 infants (153 boys and 164 girls) in Shiraz during 1996. The information related to growth (weight, height, round the head, round the arm, and round the chest) at the birth time was collected and 11 visits from the infants living houses were done. In order to influence the missing values on the growth charts, four methods (ignoring the missing values, general and individual models of growth curve and multiple imputation) were considered to study. Mean, 3rd, 50th, 97th centiles of raw and smooth weight were computed in boys and the smooth growth charts of their weight were determined and compared based on the four methods.FINDINGS: There was no noticeable difference in the boys mean weight at age under study according to growth curve methods and multiple imputation while missing values were ignored. However, the smooth growth charts showed that applying the individual growth curve model (second level) and multiple imputation causes the noticeable difference between the values of 3rd, 97th centiles and the traditional analysis (ignoring missing values). CONCLUSION: Regarding the existence of missing values in growth longitudinal studies, ignoring the missing values for analyzing is not acceptable. Applying the growth curve model method could be considered important in making desirable the analysis and the proper growth path.

When the comprehensive information about a topic is scattered among two or more data sets, using only one of those data sets would lead to information loss available in other data sets. Hence, it is necessary to integrate scattered information to a comprehensive unique data set. On the other hand, sometimes we are interested in recognition of duplications in a data set. The identification of duplications in a data set or the same identities in different data sets is called record linkage. Linkage of data sets that their information is registered in the context of Persian language has special difficulties due to particular writing characteristics of the Persian language such as connectedness of letters in words, existence of different writing versions for some letters and dependency of writing shape of letters to their position in words.In this paper, usual difficulties in linkage of data sets that their information is registered in the context of the Persian language are studied and some solutions are presented. We introduced some compatible methods for preparing and preprocessing of files through standardization, blocking and selection of identifier variables. A new method is proposed for dealing with missing data that is a major problem in real world applications of record linkage theory.The proposed method takes into account the probability of occurrence of missing data. We also proposed an algorithm for increasing the number of comparable fields based on partitioning of .composite fields such as address. Finally, the proposed methods are used to link records of establishing censuses in a geographical region in Iran. The results show that taking into account the probability of the occurrence of missing data increases the efficiency of the record linkage process. In addition, using different codes and notations for data registration in different times, leads to information loss. Specially, it is necessary to design a general pattern for writing addresses in Iran, considering geographical and environmental situations.