Related papers: Transforming variables to central normality
Transforming a random variable to improve its normality leads to a followup test for whether the transformed variable follows a normal distribution. Previous work has shown that the Anderson Darling test for normality suffers from…
Automatic detection of statistical outliers is facilitated through knowledge of the source distribution of regular observations. Since the population distribution is often unknown in practice, one approach is to apply a transformation to…
Many variables in the social, physical, and biosciences, including neuroscience, are non-normally distributed. To improve the statistical properties of such data, or to allow parametric testing, logarithmic or logit transformations are…
Modern data analysis frequently involves variables with highly non-Gaussian marginal distributions. However, commonly used analysis methods are most effective with roughly Gaussian data. This paper introduces an automatic transformation…
The scores of distance-based outlier detection methods are difficult to interpret, making it challenging to determine a cut-off threshold between normal and outlier data points without additional context. We describe a generic…
Box-Cox power transformation is a commonly used methodology to transform the distribution of a non-normal data into a normal one. Estimation of the transformation parameter is crucial in this methodology. In this study, the estimation…
The Box-Cox transformation is applied to the linear mixed models for analyzing positive and grouped data. The problem in using Box Cox transformation is that the maximum likelihood estimator of the transformation parameter is generally…
Outlier detection algorithms typically assign an outlier score to each observation in a dataset, indicating the degree to which an observation is an outlier. However, these scores are often not comparable across algorithms and can be…
Parameter estimation is one of the most important tasks in statistics, and is key to helping people understand the distribution behind a sample of observations. Traditionally parameter estimation is done either by closed-form solutions…
Meta-analysis is the aggregation of data from multiple studies to find patterns across a broad range relating to a particular subject. It is becoming increasingly useful to apply meta-analysis to summarize these studies being done across…
In many cases, the values of some model parameters are determined by maximising the likelihood of a set of data points given the parameter values. The presence of outliers in the data and correlations between data points complicate this…
Transformation models are a very important tool for applied statisticians and econometricians. In many applications, the dependent variable is transformed so that homogeneity or normal distribution of the error holds. In this paper, we…
Many common loss functions such as mean-squared-error, cross-entropy, and reconstruction loss are unnecessarily rigid. Under a probabilistic interpretation, these common losses correspond to distributions with fixed shapes and scales. We…
The problem of transformation selection is thoroughly treated from a Bayesian perspective. Several families of transformations are considered with a view to achieving normality: the Box-Cox, the Modulus, the Yeo & Johnson and the Dual…
In the real world, experimental data are rarely, if ever, distributed as a normal (Gaussian) distribution. As an example, a large set of data--such as the cross sections for particle scattering as a function of energy contained in the…
Normalization and outlier detection belong to the preprocessing of gene expression data. We propose a natural normalization procedure based on statistical data depth which normalizes to the distribution of gene expressions of the most…
Outliers widely occur in big-data applications and may severely affect statistical estimation and inference. In this paper, a framework of outlier-resistant estimation is introduced to robustify an arbitrarily given loss function. It has a…
The maximum likelihood principle is widely used in statistics, and the associated estimators often display good properties. indeed maximum likelihood estimators are guaranteed to be asymptotically efficient under mild conditions. However in…
Real data often contain anomalous cases, also known as outliers. These may spoil the resulting analysis but they may also contain valuable information. In either case, the ability to detect such anomalies is essential. A useful tool for…
Outlier detection has gained increasing interest in recent years, due to newly emerging technologies and the huge amount of high-dimensional data that are now available. Outlier detection can help practitioners to identify unwanted noise…