Li’s pHd method uses an asymptotic chi-squared test statistic to evaluate a hypothesized dimensionality of a reduceddimension space in a largely nonparametric setting. This statistic is based on an assumed normal distribution of the predictors. When the distributional assumption is violated, a mixture chi-squared test proposed by Cook is theoretically more appropriate. However, both tests may n...

The Gap statistic is a standard method for determining the number of clusters in a set of data. The Gap statistic standardizes the graph of log(Wk), where Wk is the within-cluster dispersion, by comparing it to its expectation under an appropriate null reference distribution of the data. We suggest to use Wk instead of log(Wk), and to compare it to the expectation of Wk under a null reference d...

Abstract. Structural break is one of the important concerns in non-stationary time series prediction. The cumulative sum of square (CUSUMS) statistic proposed by Brown et al (1975) has been developed as a general method for detecting a structural break. To better understand CUSUMS, this paper analyses the relationship among the bias of the break location estimation, pre-break data size and the ...

We present a new CuSum chart for monitoring shifts in the mean of autocorrelated data. The monitoring statistic is the plain cumulative sum of differences between the observations and the target value, and the control limits are a function of the asymptotic variance constant and target in-control average run length. Our method uses a variety of non-parametric techniques that are popular in the ...

Often a screening or selection experiment targets a cell or tissue, which presents many possible molecular targets and identifies a correspondingly large number of ligands. We describe a statistical method to extract an estimate of the complexity or richness of the set of molecular targets from competition experiments between distinguishable ligands, including aptamers derived from combinatoria...

A nonparametric smoothing method for assessing the adequacy of generalized linear mixed models (GLMMs) is developed. The proposed method is based on smoothing the residuals over continuous covariates to avoid the partition of continuous covariates on model checking. The global test statistic has a quadratic form and its formulae of expectation as well as variance are derived. The sampling distr...

It is a common practice to complement a forecasting method such as simple exponential smoothing with a monitoring scheme to detect those situations where forecasts have failed to adapt to structural change. It will be suggested in this paper that the equations for simple exponential smoothing can be augmented by a common monitoring statistic to provide a method that automatically adapts to stru...

Genetic mapping of quantitative trait loci (QTLs) is performed typically by using a parametric approach, based on the assumption that the phenotype follows a normal distribution. Many traits of interest, however, are not normally distributed. In this paper, we present a nonparametric approach to QTL mapping applicable to any phenotypic distribution. The method is based on a statistic ZW, which ...

Data created in a controlled laboratory setting are a relatively new phenomenon to economists. Traditional data analysis methods using either parametric or nonparametric tests are not necessarily the best option available to economists analyzing laboratory data. In 1935, Fisher proposed the randomization technique as an alternative data analysis method when examining treatment effects. The obse...