A Rank-Invariant Method of Linear and Polynomial Regression Analysis
01 Jan 1992-pp 345-381
TL;DR: In most cases, the assumption that one of the variables is normally distributed with constant variance, its mean being a function of the other variables, is not always satisfied, and in most cases difficult to ascertain this paper.
Abstract: Regression analysis is usually carried out under the hypothesis that one of the variables is normally distributed with constant variance, its mean being a function of the other variables. This assumption is not always satisfied, and in most cases difficult to ascertain.
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TL;DR: In this paper, the median of the squared residuals is used to resist the effect of nearly 50% of contamination in the data in the special case of simple least square regression, which corresponds to finding the narrowest strip covering half of the observations.
Abstract: Classical least squares regression consists of minimizing the sum of the squared residuals. Many authors have produced more robust versions of this estimator by replacing the square by something else, such as the absolute value. In this article a different approach is introduced in which the sum is replaced by the median of the squared residuals. The resulting estimator can resist the effect of nearly 50% of contamination in the data. In the special case of simple regression, it corresponds to finding the narrowest strip covering half of the observations. Generalizations are possible to multivariate location, orthogonal regression, and hypothesis testing in linear models.
3,713 citations
TL;DR: The seasonal Kendall test as discussed by the authors is a nonparametric test for trend applicable to data sets with seasonality, missing values, or values reported as "less than" or values below the limit of detection.
Abstract: Some of the characteristics that complicate the analysis of water quality time series are non-normal distributions, seasonality, flow relatedness, missing values, values below the limit of detection, and serial correlation. Presented here are techniques that are suitable in the face of the complications listed above for the exploratory analysis of monthly water quality data for monotonie trends. The first procedure described is a nonparametric test for trend applicable to data sets with seasonality, missing values, or values reported as ‘less than’: the seasonal Kendall test. Under realistic stochastic processes (exhibiting seasonality, skewness, and serial correlation), it is robust in comparison to parametric alternatives, although neither the seasonal Kendall test nor the alternatives can be considered an exact test in the presence of serial correlation. The second procedure, the seasonal Kendall slope estimator, is an estimator of trend magnitude. It is an unbiased estimator of the slope of a linear trend and has considerably higher precision than a regression estimator where data are highly skewed but somewhat lower precision where the data are normal. The third procedure provides a means for testing for change over time in the relationship between constituent concentration and flow, thus avoiding the problem of identifying trends in water quality that are artifacts of the particular sequence of discharges observed (e.g., drought effects). In this method a flow-adjusted concentration is defined as the residual (actual minus conditional expectation) based on a regression of concentration on some function of discharge. These flow-adjusted concentrations, which may also be seasonal and non-normal, can then be tested for trend by using the seasonal Kendall test.
2,482 citations
TL;DR: In this article, the power of the Mann-Kendall test and Spearman's rho test for detecting monotonic trends in time series data is investigated by Monte Carlo simulation.
1,642 citations
TL;DR: In this article, the authors investigated the effect of serial correlation on the performance of the Mann-Kendall (MK) statistic and showed that the presence of a trend alters the estimate of the magnitude of serial correlations.
Abstract: This study investigated using Monte Carlo simulation the interaction between a linear trend and a lag-one autoregressive (AR(1)) process when both exist in a time series. Simulation experiments demonstrated that the existence of serial correlation alters the variance of the estimate of the Mann–Kendall (MK) statistic; and the presence of a trend alters the estimate of the magnitude of serial correlation. Furthermore, it was shown that removal of a positive serial correlation component from time series by pre-whitening resulted in a reduction in the magnitude of the existing trend; and the removal of a trend component from a time series as a first step prior to pre-whitening eliminates the influence of the trend on the serial correlation and does not seriously affect the estimate of the true AR(1). These results indicate that the commonly used pre-whitening procedure for eliminating the effect of serial correlation on the MK test leads to potentially inaccurate assessments of the significance of a trend; and certain procedures will be more appropriate for eliminating the impact of serial correlation on the MK test. In essence, it was advocated that a trend first be removed in a series prior to ascertaining the magnitude of serial correlation. This alternative approach and the previously existing approaches were employed to assess the significance of a trend in serially correlated annual mean and annual minimum streamflow data of some pristine river basins in Ontario, Canada. Results indicate that, with the previously existing procedures, researchers and practitioners may have incorrectly identified the possibility of significant trends. Copyright 2002 Environment Canada. Published by John Wiley & Sons, Ltd.
1,573 citations
TL;DR: Simpler models representing transport, limiting precursor pollutants, and gas-to-particle equilibrium should be used to understand where and when emission reductions will be effective, rather than large complex models that have insufficient input and validation measurements.
Abstract: The 1999 Regional Haze Rule provides a context for this review of visibility, the science that describes it, and the use of that science in regulatory guidance The scientific basis for the 1999 regulation is adequate The deciview metric that tracks progress is an imperfect but objective measure of what people see near the prevailing visual range The definition of natural visibility conditions is adequate for current planning, but it will need to be refined as visibility improves Emissions from other countries will set achievable levels above those produced by natural sources Some natural events, notably dust storms and wildfires, are episodic and cannot be represented by annual average background values or emission estimates Sulfur dioxide (SO2) emission reductions correspond with lower sulfate (SO4 2−) concentrations and visibility im-provements in the regions where these have occurred Non-road emissions have been growing more rapidly than emissions from other sources, which have remained
964 citations
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01 Jan 1948
TL;DR: The measurement of rank correlation was introduced in this paper, and rank correlation tied ranks tests of significance were applied to the problem of m ranking, and variate values were used to measure rank correlation.
Abstract: The measurement of rank correlation introduction to the general theory of rank correlation tied ranks tests of significance proof of the results of chapter 4 the problem of m ranking proof of the result of chapter 6 partial rank correlation ranks and variate values proof of the result of chapter 9 paired comparisons proof of the results of chapter 11 some further applications.
6,404 citations
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821 citations
TL;DR: In this article, a distinction is made between the linear regression equation of a variable y on a second variable x, and a linear functional relation between two variables Y and X masked by errors.
Abstract: (i) a distinction must be made between the linear regression equation of a variable y on a second variable x, and a linear functional relation between two variables Y and X masked by errors. The former equation is still available for prediction even if the variable x is subject to error, but is not necessarily appropriate for a functional relation when one exists. (ii) it is possible to set up maximum likelihood equations for the second problem, but they do not lead to a unique solution without further assumptions, such as an assumption about the relative magnitude of the errors in x and y.
385 citations