Mirta Benšić

Modelling small-business credit scoring by using logistic regression, neural networks and decision trees

Previous research on credit scoring that used statistical and intelligent methods was mostly focused on commercial and consumer lending. The main purpose of this paper is to extract important features for credit scoring in small-business lending on a dataset with specific transitional economic conditions using a relatively small dataset. To do this, we compare the accuracy of the best models extracted by different methodologies, such as logistic regression, neural networks (NNs), and CART decision trees. Four different NN algorithms are tested, including backpropagation, radial basis function network, probabilistic and learning vector quantization, by using the forward nonlinear variable selection strategy. Although the test of differences in proportion and McNemars test do not show a statistically significant difference in the models tested, the probabilistic NN model produces the highest hit rate and the lowest type I error. According to the measures of association, the best NN model also shows the highest degree of association with the data, and it yields the lowest total relative cost of misclassification for all scenarios examined. The best model extracts a set of important features for small-business credit scoring for the observed sample, emphasizing credit programme characteristics, as well as entrepreneurs personal and business characteristics as the most important ones. Copyright

Small business credit scoring: a comparison of logistic regression, neural network, and decision tree models

The paper compares the models for small business credit scoring developed by logistic regression, neural networks, and CART decision trees on a Croatian bank dataset. The models obtained by all three methodologies were estimated; then validated on the same hold-out sample, and their performance is compared. There is an evident significant difference among the best neural network model, decision tree model, and logistic regression model. The most successful neural network model was obtained by the probabilistic algorithm. The best model extracted the most important features for small business credit scoring from the observed data

Diagnostic value of US, MR and MR arthrography in shoulder instability.

INTRODUCTION The aim of our study was to compare US, conventional MRI and MR arthrography findings in patients with anterior shoulder instability and with a clinical diagnosis of labral capsular ligamentous complex lesion. At the same time we evaluated the accuracy of MR arthrography in the diagnosis of this lesion. METHODS After approval of the local Ethics Committee, our departments Trauma Registry from July 2008 up to February 2012 was retrospectively reviewed to identify all eligible patients. Eligibility criteria included: 1)history of acute or chronic shoulder instability (more than three dislocations over a period of more than two months); 2) diagnosis of labroligamentous lesion. All patients were investigated with plain radiographs, Ultrasound Scans (US), Magnetic Resonance Imaging (MRI) and MR arthrography. Finally, all patients underwent an arthroscopy that confirmed the diagnosis. RESULTS A total of 200 consecutive patients who met the inclusion criteria were included in this study. The mean age was 39 years (range 15 to 83); 147 were male and 133 involved the right shoulder. Chronic instability was documented in 133 patients, whereas acute instability was documented in 67 patients. We detected a statistically significant difference between US and MR arthrography in SLAP (Superior Labrum Anterior to Posterior) lesions (TypeII, III and IV), in Bankart lesions, in glenohumeral ligament lesions (superior, middle, anterior-inferior and anterior inferior glenohumeral ligament) in Hill-Sachs lesions, in diagnosing internal subacromial impingement and in normal findings. MR arthrography was superior to the US. A statistically significant difference was evident between MRI and MR arthrography findings in SLAP lesions (III and IV Type lesions), in glenohumeral ligament lesions (anterior inferior and posterior inferior glenohumeral ligament), in partial rotator cuff ruptures and in normal findings. MR arthrography diagnosed this lesion better than MRI without contrast. We also found a statistically significant difference between US and MRI findings in SLAP Type II lesions, in partial rotator cuff ruptures, in Hill-Sachs lesions and in diagnosing internal subacromial impingement. CONCLUSION The US scan is a valuable diagnostic technique for rotator cuff complete or incomplete ruptures. For evaluating Hill-Sachs lesions or bony Bankart lesions, MRI is more accurate. In the case of labral capsular ligamentous complex lesions, MR arthrography is superior.

On the existence of the nonlinear weighted least squares estimate for a three-parameter Weibull distribution

The problem of nonlinear weighted least squares fitting of the three-parameter Weibull distribution to the given data (wi,ti,yi), i=1,...,n, is considered. The part wi>0 of the data stands for the data weights. It is shown that the best least squares estimate exists provided that the data satisfy just the following two natural conditions: (i) 0

Estimating the width of a uniform distribution when data are measured with additive normal errors with known variance

The problem of estimating the width of the symmetric uniform distribution on the line when data are measured with normal additive error is considered. The main purpose is to discuss the efficiency of the maximum likelihood estimator and the moment method estimator. It is shown that the model is regular and that the maximum likelihood estimator is more efficient than the moment method estimator. A sufficient condition is also given for the existence of both estimators.

Border estimation of a two-dimensional uniform distribution if data are measured with additive error

The paper considers estimation of the boundary of an elliptical domain when the data without a measurement error are distributed uniformly on this domain but are superimposed by random errors. The problem is solved in two phases. In the first phase the domain is subdivided into thin slices and the endpoints of these slices are estimated within the framework of a corresponding one-dimensional problem. In the second phase the estimated endpoints are used to estimate the boundary using the total least-squares curve fitting procedure.

Fitting distribution to data by a generalized nonlinear least squares method

The primary concern is to introduce and illustrate the way of using a generalized nonlinear regression method for the purpose of parameter estimation in the classical parametric independent and identically distributed sample model. It is shown by simulation that the presented estimator has a root-mean-square error comparable to the maximum likelihood estimator in the model for which it is known that maximum likelihood has excellent properties. As this estimator is based on an empirical distribution function, it is also compared to the maximum goodness-of-fit estimators that minimize Cramer-von Mises and Anderson–Darling empirical distribution statistics and it is shown that it outperforms them in most cases.

Estimating a uniform distribution when data are measured with a normal additive error with unknown variance

The problem of estimating the width of a symmetric uniform distribution on the line together with the error variance, when data are measured with normal additive error, is considered. The main purpose is to analyse the maximum-likelihood (ML) estimator and to compare it with the moment-method estimator. It is shown that this two-parameter model is regular so that the ML estimator is asymptotically efficient. Necessary and sufficient conditions are given for the existence of the ML estimator. As numerical problems are known to frequently occur while computing the ML estimator in this model, useful suggestions for computing the ML estimator are also given.

Side distinct sciatic nerve recovery differences between rats and mice

The Sciatic Functional Index (SFI) is widely used to evaluate functional recovery after sciatic nerve injury, primarily in the rat, and more recently shown useful in the mouse. This quantitative, non-invasive method allows tracking of regeneration capability, visible in the gait of the animal. Using a Martin micro needle holder, carrying a force measured to be 49.2 N, the left sciatic nerve was crushed for 60 s. We accumulated data from walking tracks collected preoperatively and 1, 7, 14, 21, and 28 days after injury. SFI values were first calculated in the traditional manner. Then using the preoperative values as the normal value in the postoperative calculations, SFI was again calculated; this isolated the calculations to either injured or contra lateral leg giving a “split” plot. The traditional SFI calculations resulted in typical shaped graphs for both rats and mice. However, the “split” SFI calculations showed how rats and mice differ in their recovery from sciatic nerve injury. The mouse graph shows the intact leg remaining stable and the injured leg having functional impairment, which then recovers. The rat graph showed functional impairment of the injured leg, however, the intact leg had an increase in SFI values as if to compensate until the injured leg showed recovery.

Estimating the size of an object captured with error

In many applications we are faced with the problem of estimating object dimensions from a noisy image. Some devices like a fluorescent microscope, X-ray or ultrasound machines, etc., produce imperfect images. Image noise comes from a variety of sources. It can be produced by the physical processes of imaging, or may be caused by the presence of some unwanted structures (e.g. soft tissue captured in images of bones). In the proposed models we suppose that the data are drawn from uniform distribution on the object of interest, but contaminated by an additive error. Here we use two one-dimensional parametric models to construct confidence intervals and statistical tests pertaining to the object size and suggest the possibility of application in two-dimensional problems. Normal and Laplace distributions are used as error distributions. Finally, we illustrate ability of the R-programs we created for these problems on a real-world example.