A cautionary note on Clark Winsorization Section 1. Introduction
Recently we studied methods of detecting and treating verified influential values with the goal of finding an objective method for identification and treatment of influential values in a highly skewed business population (Mulry et al. 2014). An observation is considered influential if its value is correct but its weighted contribution has an excessive effect on the estimated total or period-to-period change. Although influential values occur infrequently in economic surveys, if one appears and is not “treated,” it may introduce substantial over- or under-estimation of survey totals or period-to-period change. In turn, this can impact other measures of the economy. For example, monthly estimates of sales and inventories from the U.S. Census Bureau’s Monthly Retail Trade Survey (MRTS) are inputs to the Gross Domestic Product (GDP). With any outlier detection and treatment method, one aspect of particular interest is the range of values that methods designate as influential, called the detection region. The size of the region and its boundary directly impact the number of identified values and the minimum amount by which the value(s) will be adjusted. Consequently, it is important to understand how to “manipulate” the method used, to ensure that (1) true influential values are always identified and receive the minimum treatment needed to ameliorate their impact on totals without overly perturbing the sample’s distribution and (2) values that are not influential are rarely identified and are consistently associated with trivial adjustments.
One approach for detecting and treating influential values is called Winsorization. These procedures replace extreme values with other, less extreme values, effectively moving the original extreme values toward the center of the distribution. Winsorization procedures may be one-sided by treating only extreme values that are too high, or they may be two-sided by simultaneously treating high and low values. Values designated as influential are modified (“treated”) by replacing them with values chosen to minimize the mean squared error (MSE) of the estimate of the total. For further discussion, see Chambers (1986), Chambers et al. (2000), and Martinoz, Haziza and Beaumont (2015).
In this note, we focus on the Clark Winsorization, a one-sided method developed by Clark (1995) and described by Chambers et al. (2000). The Clark Winsorization method assumes a data model and then uses an algorithm to detect and treat influential values. The detected and treated values form the detection region. Our studies found the Clark Winsorization algorithm can be effective, but the resultant detection region is highly dependent on the number of influential values in the sample. If the sample contains no influential values, the procedure is anti-conservative, meaning it makes very small changes to several values not considered influential thus reducing the variance and mean square error but essentially leaving the estimated total unchanged (trimming). On the other hand, the procedure can become very conservative if the sample contains a single influential value, depending on the distance of the value from the remainder of the distribution. When the sample contains two or more influential values, Clark Winsorization detects and adjusts only the influential values and does not trim any values that are not influential. However, the procedure can be prone to masking (Barnett and Lewis 1994). Trimming observations when no influential value is present does not appeal to subject matter analysts in a production setting where time is limited. The cost of examining a “false positive” can be prohibitive and treated values might be categorized as imputed in response rate computations. However, the algorithm has the advantage of being straightforward to implement and not requiring prior knowledge of the population. Certainly there are situations where these advantages of Clark Winsorization may outweigh the disadvantages.
We examine the influential value detection regions from Clark Winsorization using a simulated dataset that realistically reflects the population of the MRTS and was first used in (Mulry et al. 2014). We illustrate how the presence of one versus two high influential values can affect the detection region under several scenarios. Our objective is not to advocate for or against this method; the purpose of this note is to make potential users aware of aspects of this procedure that can affect its outcome.
Section 2 contains background on monthly business surveys including an overview of the sample design and weighting. A description of the Clark Winsorization methodology and its implementation using MRTS data appears in Section 3. The discussion in Section 4 concentrates on the detection region for influential values with Section 4.1 addressing the scenario of one influential value in a sample and Section 4.2 focusing on the scenario when two influential values are present. Section 5 contains a summary.
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