A Method for Measuring Distance From a Training Data Set

A new method is proposed for measuring the distance between a training data set and a single, new observation. The novel distance measure reflects the expected squared prediction error when a quantitative response variable is predicted on the basis of the training data set using the distance weighted k-nearest-neighbor method. The simulation presented here shows that the distance measure correlates well with the true expected squared prediction error in practice. The distance measure can be applied, for example, in assessing the uncertainty of prediction.     

Spatial Cluster Detection for Longitudinal Outcomes Using Administrative Regions

This article proposes a new spatial cluster detection method for longitudinal outcomes that detects neighborhoods and regions with elevated rates of disease while controlling for individual level confounders. The proposed method, CumResPerm, utilizes cumulative geographic residuals through a permutation test to detect potential clusters which are defined as sets of administrative regions, such as a town or group of administrative regions. Previous cluster detection methods are not able to incorporate individual level data including covariate adjustment, while still being able to define potential clusters using informative neighborhood or town boundaries. Often, it is of interest to detect such spatial clusters because individuals residing in a town may have similar environmental exposures or socioeconomic backgrounds due to administrative reasons, such as zoning laws. Therefore, these boundaries can be very informative and more relevant than arbitrary clusters such as the standard circle or square. Application of the CumResPerm method will be illustrated by the Home Allergens and Asthma prospective cohort study analyzing the relationship between area or neighborhood residence and repeated measured outcome, occurrence of wheeze in the last six months, while taking into account mobile locations.     

Infiuence functions for certain parameters in discriminant analysis when a single discriminant function is not adequate

The influence function introduced by Hampel (1968, 1973, 1974) i s a tool that can be used for outlier detection. Campbell (1978) has derived influence function for ~ahalanobis's distance between two populations which can be used for detecting outliers i n discriminant analysis. Radhakrishnan and Kshirsagar (1981) have obtained influence functions for a variety of parametric functions i n multivariate analysis. Radhakrishnan (1983) obtained influence functions for parameters corresponding to "residual" wilks's A and i t s "direction" and "collinearity" factors i n discriminant analysis when a single discriminant function is ade- quate while discriminating among several groups. In this paper influence functions for parameters that correspond to "residual" wilks's A and its "direction" and "coplanarity" factors used to test the goodness of f i t of s (s>l) assigned discriminant func- tions for discriminating among several groups are obtained. These influence functions can be used for outlier detection i n m u l t i -variate data when a single discriminant function is not adequate.     

Two tests for sequential detection of a change-point in a nonlinear model

In this paper, two tests, based on weighted CUSUM of the least squares residuals, are studied to detect in real time a change-point in a nonlinear model. A first test statistic is proposed by extension of a method already used in the literature but for the linear models. It is tested under the null hypothesis, at each sequential observation, that there is no change in the model against a change presence. The asymptotic distribution of the test statistic under the null hypothesis is given and its convergence in probability to infinity is proved when a change occurs. These results will allow to build an asymptotic critical region. Next, in order to decrease the type I error probability, a bootstrapped critical value is proposed and a modified test is studied in a similar way. A generalization of the Hájek–Rényi inequality is established.     

A Comparison of Multiple Outlier Detection Methods for Regression Data

The problem of outliers in statistical data has attracted many researchers for a long time. Consequently, numerous outlier detection methods have been proposed in the statistical literature. However, no consensus has emerged as to which method is uniformly better than the others or which one is recommended for use in practical situations. In this article, we perform an extensive comparative Monte Carlo simulation study to assess the performance of the multiple outlier detection methods that are either recently proposed or frequently cited in the outlier detection literature. Our simulation experiments include a wide variety of realistic and challenging regression scenarios. We give recommendations on which method is superior to others under what conditions.     

Estimation of the Proportion of Defective Units by Using Group Testing Under the Existence of a Threshold of Detection

Group testing procedures, in which groups containing several units are tested without testing each unit, are widely used as cost-effective procedures in estimating the proportion of defective units in a population. A problem arises when we apply these procedures to the detection of genetically modified organisms (GMOs), because the analytical instrument for detecting GMOs has a threshold of detection. If the group size (i.e., the number of units within a group) is large, the GMOs in a group are not detected due to the dilution even if the group contains one unit of GMOs. Thus, most people conventionally use a small group size (which we call conventional group size) so that they can surely detect the existence of defective units if at least one unit of GMOs is included in the group. However, we show that we can estimate the proportion of defective units for any group size even if a threshold of detection exists; the estimate of the proportion of defective units is easily obtained by using functions implemented in a spreadsheet. Then, we show that the conventional group size is not always optimal in controlling a consumer's risk, because such a group size requires a larger number of groups for testing.     

需求分布规律变化情况下的报童订货策略

在需求分布规律变化情况下，报童在进行订货决策时会因为错误判断需求分布规律而导致期望库存成本增加。为了解决这一问题，本文集成传统历史需求信息和非传统需求信息以正确地认知需求分布规律，在此基础上决策订货量。假设需求服从均值不同、方差相同的两种类型的正态分布，每一种正态分布的概率已知。利用信号检测理论构建基于历史需求信息与需求分布概率的报童最优订货策略，并与只基于需求分布概率的直觉规则订货策略进行对比。结果表明：只要排除需求分布概率很大或很小两种极端情况，最优订货策略比直觉规则订货策略在控制期望库存成本方面的作用更明显，即利用历史需求信息可以有效修正报童对实际需求分布的检测结果，从而提高实际订货决策的准确性。研究结果对传统历史需求信息和非传统需求信息的集成以及需求信息交换等有一定的管理学启示和应用价值。     

Two-stage approaches to the analysis of occupancy data I: the homogeneous case (analysis of occupancy data)

Abstract

Occupancy models are used in statistical ecology to estimate species dispersion. The two components of an occupancy model are the detection and occupancy probabilities, with the main interest being in the occupancy probabilities. We show that for the homogeneous occupancy model there is an orthogonal transformation of the parameters that gives a natural two-stage inference procedure based on a conditional likelihood. We then extend this to a partial likelihood that gives explicit estimators of the model parameters. By allowing the separate modeling of the detection and occupancy probabilities, the extension of the two-stage approach to more general models has the potential to simplify the computational routines used there.