The Multiple Adaptations of Multiple Imputation

Support vector machine is a machine learning algorithm developed by Vapnik from the statistical learning theory for data classification via study from a small sample of fault data. For fault data it can isolate the fault categories accurately even though only has the small sample of data. In the present work, support vector machine's classification mechanism and its application in mechanical fault diagnosis are introduced. Therefore, give an instance the support vector machine makes fault classification for the coal mine scraper conveyor's faults. Last but not the least, put forward some of the shortcomings of the support vector machine and look forward to the direction of development of the support vector machine fault diagnosis in the future.

Bootstrapped artificial neural networks for synthetic flow generation with a small data sample

Multiple imputation is a popular technique for analysing incomplete data. Given the imputed data and a particular model, Rubin's rules (RR) for estimating parameters and standard errors are well established. However, there are currently no guidelines for variable selection in multiply imputed data sets. The usual practice is to perform variable selection amongst the complete cases, a simple but inefficient and potentially biased procedure. Alternatively, variable selection can be performed by repeated use of RR, which is more computationally demanding. An approximation can be obtained by a simple 'stacked' method that combines the multiply imputed data sets into one and uses a weighting scheme to account for the fraction of missing data in each covariate. We compare these and other approaches using simulations based around a trial in community psychiatry. Most methods improve on the naïve complete-case analysis for variable selection, but importantly the type 1 error is only preserved if selection is based on RR, which is our recommended approach.

This paper proposes a weakly supervised cross-domain person re-identification (Re-ID) method based on small sample data. In order to reduce the cost of data collection and annotation, the model design focuses on extracting and abstracting the information contained in the data under limited conditions. In this paper, we focus on the problems of strong data dependence, weak cross-domain capability and low accuracy in Re-ID in weakly supervised scenarios. Our contributions are as follows: first, we implement a joint training framework with the help of small sample learning and cross-domain migration for Re-ID. Second, with the help of residual compensation and fusion attention module, the RCFA module is designed, and the model framework is built on this basis to improve the cross-domain ability of the model. Third, to solve the problem of low accuracy caused by insufficient data coverage of small samples, a fusion of shallow features and deep features is designed to enable the model to weighted fusion of shallow detail information and deep semantic information. Finally, by selecting different camera images in Market1501 dataset and DukeMTMC-reID dataset as small samples, respectively, and introducing another dataset data for joint training, we demonstrate the feasibility of this joint training framework, which can perform weakly supervised cross-domain Re-ID based on small sample data.

The prerequisites for reducing the test sample chi-square Pearson test size from 400 to 32 or fewer examples while maintaining its power are considered. The urgency of the problem results from the fact that when learning and testing the biometric identification means to identify the personality, it is not possible to use large volumes of learning and test samples. The conditions under which the chi-square test on small samples from the continuous distribution of values becomes a discrete distribution of values are formalized. Normal and uniform laws of values distribution use histograms with uniform intervals, which accurately relate the central intervals of the histogram to the mathematical expectation calculated on the test sample. 16 experiments shown that the chi-square-synchronized test built on histograms with four equal intervals has a discrete probability spectrum consisting of only 20 significant spectral lines. A simple method for estimating the informativity of each of the important spectral components is proposed. Traditional statistical assessments can be strengthened by the following deeper level of the spectral components analysis of small samples of biometric data. The second deeper level of statistical processing should be substantially more powerful. Under the same conditions, the computational informativity increases from 2.22 bits to 24.95 bits due to the transition from simple continual calculations to discrete calculations of high computational complexity.

In order to solve the problem of predicting the residual life of mechanical products accurately based on small-sample data, this paper proposes a small-sample adaptive residual life prediction model of mechanical products based on feature matching preprocessor-LSTM. First, aiming at the problem of low accuracy of remaining life prediction for small samples of mechanical products caused by multiple time scales and multiple fault states, the failure time data and performance degradation data are fused, and the failure rate and standard deviation are used as the remaining life prediction criteria to intuitively reflect The possibility of failure of a component or system at a certain point in time. Considering the demand of adaptive small-sample residual life prediction data, this paper establishes the adaptive matching pre-processor model of life characteristics. On this basis, the LSTM neural network is used to establish a small-sample adaptive residual life prediction model. Then, the XJTU-SY bearing life data set and the test data of the small-sample life characteristics measured by the RV reducer are used as the research objects, and a small amount of the data set is randomly selected. The remaining life expectancy is predicted from the sample data and compared with its standard remaining life, respectively. The comparison results show that the overall prediction error is small. This study shows that the remaining life prediction model established can better predict the remaining life of mechanical product sub-sample data and provides a feasible method for predicting the remaining life of mechanical product sub-samples.

We propose improvements to existing degrees of freedom used for significance testing of multivariate hypotheses in small samples when missing data are handled using multiple imputation. The improvements are for 1) tests based on unrestricted fractions of missing information and 2) tests based on equal fractions of missing information with M ( p - 1) ≤ 4, where M is the number of imputations and p is the number of tested parameters. Using the mi command available as of Stata 11, we demonstrate via simulation that using these adjustments can result in a more sensible degrees of freedom (and hence closer-to-nominal rejection rates) than existing degrees of freedom.

Missing data are nearly always a problem in research, and missing values represent a serious threat to the validity of inferences drawn from findings. Increasingly, social science researchers are turning to multiple imputation to handle missing data. Multiple imputation, in which missing values are replaced by values repeatedly drawn from conditional probability distributions, is an appropriate method for handling missing data when values are not missing completely at random. However, use of this method requires developing an imputation model from the observed data. This is typically a rigorous and time-consuming process. To encourage wider adoption of multiple imputation in social work research, a simple framework for designing imputation models is presented. The framework and its ability to generate unbiased estimates are demonstrated in a simulation study. KEY WORDS: missing data; multiple imputation; nonresponse ********** Missing data are ubiquitous in social research, and missingness or nonresponse can represent a threat to the validity of inferences because of undue effects on efficiency, power, and parameter bias (Shadish, Cook, & Campbell, 2002). Social work researchers are now addressing missing data in a more rigorous manner. Recently, Saunders et al. (2006) and Choi, Golder, Gillmore, and Morrison (2005) described important data imputation methods and dispelled misunderstandings regarding popular imputation methods, such as mean substitution. Recent advances in analytic methods, such as multiple imputation (MI), are taking hold in social work research. With MI, missing values are replaced with values repeatedly drawn from simulated conditional probability distributions (Schafer, 1997), thus creating multiple versions of the data set. Each version of the data set is analyzed according to the data analysis model, and the multiple results are combined into point estimates (Rubin, 1996). A critical task in MI is to devise an imputation model (Allison, 2002) or missing data model (Graham, Olchowski, & Gilreath, 2007), which involves specifying the measures that are putatively associated with the missing values. Although this process adds additional steps, the specification of an imputation model and the creation of multiple data sets can produce less-biased estimates in the presence of missing data across a wide variety of data analysis techniques (Schafer, 1997). Besides MI, there are many other methods for addressing missing data (Schafer, 1999; Schafer & Graham, 2002). An equally rigorous method known as direct or full information maximum likelihood (FIML) estimation can produce unbiased estimates and correct standard errors in the presence of missing data. When the number of imputations is sufficiently large, identical missing data models will produce the same estimates under MI and FIML (Graham et al., 2007). Unlike MI, FIML is limited to maximum likelihood analytic techniques and the missing data model must be included in the analysis model. Although we focus on MI, the steps we describe for developing an imputation model are equally appropriate for use in the missing data model for FIML. On the basis of the MI literature, this article describes a framework for developing an imputation model for use with any free or commercial software package that performs MI. BRIEF REVIEW OF MISSING DATA CONCEPTS Generally, both MI and a broad range of missing data issues have received ample attention in the applied literature (Graham et al., 2007). We briefly discuss the three types of distributions that describe the randomness of nonresponse given that this property has consequences for the development of an imputation model. For a discussion of general missing data concepts that are not critical to understanding our discussion of imputation model development, we refer readers to Schafer and Graham (2002). Distribution of Nonresponse The probability distribution of nonresponse--more frequently referred to as the missing data or nonresponse mechanism (Rubin, 1976)--is both an important factor in the decision to impute with MI and a context for the development of an imputation model. …

The greater part of Legendre & Dutilleul (1991)'s comments are devoted to illustrating the problems involved in estimating confidence intervals for small samples of autocorrelated data. I do not disagree; rather that is why I wrote an article (Boyle, 1991) proposing an alternative approach. As Legendre & Dutilleul thoroughly demonstrate, the problems are greatly reduced if sample size is large. So rather than estimate variance from a small sample, I propose estimating it from a large sample of similar data, and assuming this figure to be valid for the smaller sample. There are obvious dangers with this approach, but it does permit realistic estimation of confidence interval when sample size is very small. The direct approach advocated by Legendre & Dutilleul results in greatly exaggerated confidence intervals for such samples because of the uncertainty about the variance estimate. In considering which transformation should be used, I looked only at the two commonly used forms (log-transformation and no transformation). I do not disagree with Legendre & Dutilleul's contention that for any specific study, a normalizing function which fits better could be found. Demonstrating that such a transformation is more appropriate would be harder. In reply to some specific objections by Legendre & Dutilleul: I use chi-square and K-S distance only to compare degree of fit; I did not test for normality hence no reference to tables. I stated that weekly sampled data showed significant autocorrelation; I did not claim that autocorrelation coefficients of 0.40 ad 0.52 are negligible. I pointed out that because of the relatively large sample sizes, the consequences even of the statistically significant autocorrelations were minor; Legendre & Dutilleul's calculations support this. The monthly sampled data have smaller autocorrelations and less bias. I used z instead of t in the confidence interval equation because a population parameter is assumed. Legendre & Dutilleul's inappropriate use of t in this equation results in a gross overestimation of the confidence interval.

In the evaluation of system effectiveness, the factors affecting system effectiveness are becoming more and more complex and the relationship between them is obviously nonlinear. The Genetic Algorithm-Error Back Propagation(GA-BP) neural network evaluation method has a wide application space due to its good nonlinear fitting ability and good convergence. However, the sample data for system effectiveness evaluation is usually small sample data, which increases the randomness of the evaluation results of the GA-BP neural network evaluation method with sample dependence. The accuracy of the assessment is reduced. In view of this, based on the bootstrap method and the non-replacement sampling method, two GA-BP-based system effectiveness evaluation methods under the condition of small sample are proposed, which are verified by using the sample data. Compared with the GA-BP neural network evaluation method, the two evaluation methods have significantly improved evaluation accuracy, and the evaluation method optimized based on the non-replacement sampling method has better performance.

Good control of experiment variability is critical to experiment success, and many methods are available for quantifying variation in data. Popular methods for measuring variability in data typically uses a statistical distribution such as a standard normal distribution, but these distributions are designed for large sample size with n > 30. However, experiments typically generate less than 5 replicates (n < 5). Thus, the key requirement for the use of standard normal distribution is not satisfied, which bring forth the need for the development of alternative ways of quantifying the variation in collected data for small sample size. This abstract describes a new statistic, average deviation, that aims to quantify the variation of repeated measurements of a variable. By taking an average of the sum of the differences between the mean and all measurements, average deviation provides a better representation of the variation in data around a mean, while capturing the impact of significant deviation from the mean by individual measurement. However, division of the sum of deviation of all measurements from the mean by the sample size meant that the presence of outlier measurement may not be fully represented by the calculated average deviation. Thus, the new statistic is better used with a small sample size of less than 5, which helps reduce the extent in which an outlier’s influence on the average deviation would be diluted. In summary, for small sample size, average deviation better represents the deviation between each measurement and the mean compared to statistical distribution-based approaches such as standard error. However, desire to not dilute the impact of outlier measurement on the calculated average deviation meant that the new statistic is only suitable for sample size less than 5.

This study develops an insolvency model to predict the possible wilful non-payment of debt obligations that turn into bad assets. This paper reveals that financially weak firms have been in deep financial distress somewhere between two to three years prior to their declaration as a wilful defaulter by the initial credit institution and its reporting on the same to the credit information companies. The Cox proportional hazards model (PHM) has been employed, which is a well-known and profusely applied approach not just in medical science but also in forecasting firm bankruptcy. This widely recognized model has been utilized to estimate the effects of different covariates influencing the times-to-event data. The application of Bayesian methods has the benefit in dealing with censored data in small sample over frequentists’ approach. Herein, Bayesian survival framework is applied incorporating normal priors that generally performs better than the traditional likelihood estimation to forecast wilful default. Subsequently, Markov Chain Monte Carlo (MCMC) sampling enables to provide the Bayesian estimator. In the Bayesian structure, the Survival model is used with the help of hazard function. The gamma distribution is selected as the prior for the standard hazard equation in PHM. In order to solve for posterior distribution, the Metropolis Hastings scheme is followed that avoids solving complicated equations with OpenBugs platform.

The occurrence of missing data due to protocol deviations is inevitable in clinical trials. When missing data exist, analyses rely on assumptions about the behaviour of the individuals after dropping out. As a result, sensitivity analysis, which is now advocated by regulatory bodies, should be performed to explore the robustness of the inference to those assumptions. These assumptions should be relevant to the estimand of the study and be practically accessible by all parties. The aim of this document is twofold: to assess the statistical validity of a new method for sensitivity analysis, and apply this method to a published Alzheimer’s study. At the beginning of the thesis, a description of the Alzheimer’s study and issues with missing data encountered therein, take place. This study was mainly set up to investigate the effect rosiglitazone, as an adjunct therapy in Alzheimer’s patients. Two different doses of the drug were compared to placebo. The study suffered from a moderate degree of missing data in each treatment arm. The thesis proceeds with a critique on the per-protocol and intention-to-treat estimands, and revisits their meaning when missing data occur. Two new estimands are introduced, which are particularly amenable to studies with missing data. They are termed de-jure and de-facto. Following that, the main methods for dealing with missing data are introduced, with a particular emphasis on multiple imputation, and how it can easily incorporate missing not at random (MNAR) analyses. A thorough presentation of the new methodology is given. This is built around a set of assumptions, that reflect possible distributional behaviours of the subjects after protocol deviation. The assumptions are Randomised-treatment Missing at Random (MAR), Jump to Reference, Last Mean Carried Forward, Copy Increments in Reference, and Copy Reference. Estimation and inference is achieved via multiple imputation, and it is shown how the predictive distribution of the imputation model can be constructed from parameters borrowed from an MAR model and manipulated in a pattern-mixture model approach, to obtain the five assumptions for the 4 unobserved component of groups of individuals. A number of simulations whose aim is to explore the statistical properties of the new method, are carried out. The simulated datasets, which are based on the parameters from the Alzheimer’s study, focus on the estimator bias, the size and power of the methods, the bias of the variance estimator, and coverage. The results obtained from the simulations show the method has sensible properties; no bias for the estimator was detectable and the sizes and power of the methods agreed closely with their theoretical equivalents. The main result however, pertains to Rubin’s variance estimator, which proves to appropriately reflect the loss of information from missing data. It is therefore argued, it is the right estimator to use in this setting. The results from the application of the proposed method on the Alzheimer’s dataset are presented in tables. Inferences from the sensitivity analysis assumptions were consistent with those from the original MAR analyses. The comparison between high dose rosiglitazone and placebo did not show any evidence in favour of the treatment under any sensitivity assumption. Some evidence of treatment difference existed when the low dose treatment was compared to placebo. This finding though, should be interpreted with caution, as the differences were obtained from analyses not subjected to the rigorous inferential process that was used in the Harringtons study. It was further argued, this finding might have been due to chance, and it was not replicated in a different study.

BackgroundMissing data are a common problem in prospective studies with a long follow-up, and the volume, pattern and reasons for missing data may be relevant when estimating the cost of illness. We aimed to evaluate the effects of different methods for dealing with missing longitudinal cost data and for costing caregiver time on total societal costs in Alzheimer’s disease (AD).MethodsGERAS is an 18-month observational study of costs associated with AD. Total societal costs included patient health and social care costs, and caregiver health and informal care costs. Missing data were classified as missing completely at random (MCAR), missing at random (MAR) or missing not at random (MNAR). Simulation datasets were generated from baseline data with 10–40 % missing total cost data for each missing data mechanism. Datasets were also simulated to reflect the missing cost data pattern at 18 months using MAR and MNAR assumptions. Naïve and multiple imputation (MI) methods were applied to each dataset and results compared with complete GERAS 18-month cost data. Opportunity and replacement cost approaches were used for caregiver time, which was costed with and without supervision included and with time for working caregivers only being costed.ResultsTotal costs were available for 99.4 % of 1497 patients at baseline. For MCAR datasets, naïve methods performed as well as MI methods. For MAR, MI methods performed better than naïve methods. All imputation approaches were poor for MNAR data. For all approaches, percentage bias increased with missing data volume. For datasets reflecting 18-month patterns, a combination of imputation methods provided more accurate cost estimates (e.g. bias: −1 % vs −6 % for single MI method), although different approaches to costing caregiver time had a greater impact on estimated costs (29–43 % increase over base case estimate).ConclusionsMethods used to impute missing cost data in AD will impact on accuracy of cost estimates although varying approaches to costing informal caregiver time has the greatest impact on total costs. Tailoring imputation methods to the reason for missing data will further our understanding of the best analytical approach for studies involving cost outcomes.Electronic supplementary materialThe online version of this article (doi:10.1186/s12874-016-0188-1) contains supplementary material, which is available to authorized users.

Data of Social Survey and Economic National is a relatively small sample of data, so that data is called small area. Estimation of parameter in small area can be done in two ways, there are direct estimation and indirect estimation. Direct estimation is unbias estimation but give a high variance because from small sample of data. The technique that use to increase efectivity of sample size is indirect estimation or called Small Area Estimation (SAE). SAE is done by adding auxiliary variable. on estimating parameter. Assumed that auxiliary variable has a linear correlation with the direct estimation. If that assumption is incomplete, use an nonparametric approaching. This research is using Kernel Gaussian approaching to build a correlation between direct estimation which expenditure per capita and auxiliary variable which population density. Evaluation of estimation result is done by comparing the value of direct estimation variance with the value of indirect estimation variance using Kernel Gaussian approaching. The result of parameter estimation which approached by SAE is the best estimation, because it produce the small value of variance that is 5,31275, while the value of direct estimator variance is 6,380522. Keywords : Direct Estimation, Small Area Estimation (SAE), Kernel Gaussian