Robust statistical method

An extensive introduction into robust statistical methods is given in Ref. 134 a discussion of non-linear robust regression is found in Ref. 135. An example is worked in Section 3.4. 

The validity of the results is a central issue, and it is confirmed by comparing traditional methods with their robust counterparts. Robust statistical methods are less common in chemometrics, although they are easy to access and compute quickly. Thus, several robust methods are included. 

In the last years the robust statistical methods got more and more important. In all new relevant standards the use of these methods are now highly recommended. 

Robust statistical methods (see Section 6.3), which may well represent the best current approach to the problems of suspect values, despite their requirement for iterative calculations. 

Robust statistical method Significance tests Standard uncertainty True value Type 1 error Type II error Uncertainty j -Residuals... 

Rey, W. J. J., 1983. Introduction to Robust and Quasi-Robust Statistical Methods. Springer-Verlang, Berlin/ new York. 

A note about outliers is appropriate here. Many data analysis methods, including least-squares regression and backpropagation ANNs, are sensitive to outliers that is, the methods are not robust. This is because they rely on minimizing a function of squared errors, so the outliers are too influential. Some recent work attempts to make backpropagation methods robust.218-221 (There are also robust statistical methods.) Nonetheless, we strongly encourage you to study your data and make appropriate transformations. 

The outlier tests described above assume that the sample comes from a normal population. It is important to realize that a result that seems to be an outlier on the assumption of a normal population distribution may well not be an outlier if the sample actually comes from (for example) a log-normal distribution (Section 2.3). Therefore outlier tests should not be used if there is a suspicion that the population may not have a normal distribution. This difficulty, along with the extra complications arising in cases of multiple outliers, explains the increasing use of the non-parametric and robust statistical methods described in Chapter 6. Such methods are either insensitive to extreme values, or at least give them less weight in calculations, so the problem of whether or not to reject outliers is avoided. 

Robust statistical methods can be applied to samples from symmetrical but heavy-tailed distributions, or when outliers may occur. They should not be applied in situations where the underlying distribution is bi-modal, multimodal, or very asymmetrical, e.g. log-normal distributions. 

To gain the most predictive utility as well as conceptual understanding from the sequence and structure data available, careful statistical analysis will be required. The statistical methods needed must be robust to the variation in amounts and quality of data in different protein families and for structural features. They must be updatable as new data become available. And they should help us generate as much understanding of the determinants of protein sequence, structure, dynamics, and functional relationships as possible. 

Hoskuldsson A (1988) PLS regression methods. Chemom 2 211 Huber PJ (1981) Robust statistics. Wiley, New York... 

Robust system identification and estimation has been an important area of research since the 1990s in order to get more advanced and robust identification and estimation schemes, but it is still in its initial stages compared with the classical identification and estimation methods (Wu and Cinar, 1996). With the classical approach we assume that the measurement errors follow a certain statistical distribution, and all statistical inferences are based on that distribution. However, departures from all ideal distributions, such as outliers, can invalidate these inferences. In robust statistics, rather than assuming an ideal distribution, we construct an estimator that will give unbiased results in the presence of this ideal distribution, but will be insensitive to deviation from ideality to a certain degree (Alburquerque and Biegler, 1996). 

If the errors are normally distributed, the OLS estimates are the maximum likelihood estimates of 9 and the estimates are unbiased and efficient (minimum variance estimates) in the statistical sense. However, if there are outliers in the data, the underlying distribution is not normal and the OLS will be biased. To solve this problem, a more robust estimation methods is needed. 

Peter Filzmoser was bom in 1968 in Weis, Austria. He studied applied mathematics at the Vienna University of Technology, Austria, where he wrote his doctoral thesis and habilitation, devoted to the field of multivariate statistics. His research led him to the area of robust statistics, resulting in many international collaborations and various scientific papers in this area. His interest in applications of robust methods resulted in the development of R software packages. J ( He was and is involved in the organization of several y scientific events devoted to robust statistics. Since... 

The focus is on multivariate statistical methods typically needed in chemo-metrics. In addition to classical statistical methods, also robust alternatives are introduced which are important for dealing with noisy data or with data including outliers. Practical examples are used to demonstrate how the methods can be applied and results can be interpreted however, in general the methodical part is separated from application examples. 

Maronna, R., Martin, D., Yohai, V. Robust Statistics Theory and Methods. Wiley, Toronto, ON, Canada, 2006. 

Accommodation. The philosophy of this strategy is to include the outlying observations in the analysis. Methods are then used to define the final actions which are only slightly influenced by the presence of outliers (Figure le). Such statistical methods are developed under the name of "robust statistics. ... 

Most frequently, the design results, or more specifically the factor effects, are analyzed graphically and/or statistically, to decide on method robustness. A method is considered robust when no significant effects are found on responses describing the quantitative aspects. When significant effects are found on quantitative responses, non-significance intervals for the significant quantitative factors can be defined, to obtain a robust response. However, no case studies were found in CE where such intervals actually were determined. 

Methods for robust statistics have been developed that deliver good results (i.e. estimation of the population mean) even with a relatively large number of outliers or with a skewed distributiom For more detailed descriptions of these methods please refer to the relevant textbooks. 

Due to plate-to-plate variations from different days or runs a normalizing step is necessary to render the data comparable across entire screens. We have developed several KNIME nodes for popular normalization methods in HTS such as POC, normalized percentage inhibition (NPI), standard score (z-score), and 5-score (26). For all nodes, robust statistics, grouping, negative control, and parameters can be chosen. The method chosen for normalization is dependent on the screening results and the normality of the data. A fiill discussion on this issue is beyond the scope of this chapter and the reader is referred to excellent reviews (27, 28). 

AMC (2001) Robust statistics a method of coping with outliers. AMC Technical Brief No. 6 (April 2001). Analytical... 

This general introduction will continue with a summary of application areas covered in the following chapters and the related robustness questions which have to be solved. Then the different statistical methods that play a role in solving the questions and which are discussed in the following chapters will be put in a general framework. 

However, if not enough experimental data are available to allow a robust statistical correlation, it is not possible to rely on group contribution methods, van Krevelen subsequently published an extensive, very useful review article on the power and limitations of group contribution methods. ... 

Recently, major developments in statistical methods have been made particularly in the areas of collaborative studies and method validation and robustness testing. In addition, analytical method development and validation have assumed a new importance. However, this handbook is not intended to be a list of statistical procedures but rather a framework of approaches and an indication of where detailed statistical methods may be found. Whilst it is recognised that much of the information required is available in the scientific literature, it is scattered and not in a readily accessible format. In addition, many of the requirements are written in the language of the statistician and it was felt that a clear concise collation was needed which has been specifically written for the practising analytical chemist. This garnering of existing information is intended to provide an indication of current best practices in these areas. Where examples are given the intent is to illustrate important points of principle and best practice. 

Initially, these claims raised quite a lot of interest—but it soon became apparent that the claimed effects were deeply problematical from the point of view of prevailing cosmology and, very conveniently, that Tifft s own statistical methods were very far from being robust. This latter fact made it very easy for the community to ignore a potentially very difficult problem for the status quo. 

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