A unified approach for estimation and detection of outliers

Two two-stage procedures RD_M-ESD and RD_M-KUR to detect outliers from normal samples are considered. Their powers for n=20 (10)60, k=2(1)(n/5) are computed and compared. Percentage points of these procedures are presented.Two examples to illustrate the use of these procedures are also given.     

A procedure for estimating the number of outliers

A new type of procedure for estimating the number of outliers in a sample is presented and compared with existing procedures. The probabilities of exact, under-, and overestimation with the different procedures are examined for two different contamination schemes.     

Multiple outlier test for upper outliers in an exponential sample

In this paper, a test statistic for testing upper outliers with a slippage alternative, in an exponential sample is proposed. No tables for critical values are required as they can be calculated easily for any sample size. A simulation study is also carried out to compare the performance of the test with the maximum likelihood ratio test and other existing tests.     

Testing for multiple upper and lower outliers in an exponential sample

Due to wide applicability and simplicity, the exponential distribution is the most commonly used distribution in reliability engineering and other life testing experiments. In this paper a test statistic for testing upper and lower outliers simultaneously in an exponential sample is proposed. However, the distribution of test statistic under the alternative is rather intricate, the null distribution is derived and critical values are obtained. A simulation study is also carried out to compare the performance of test and is found that the test based on this statistic is more powerful than the other two selected tests.     

On the power of the t-test and some rank tests when outliers may be present

The power of some rank tests, used for testing the hypothesis of shift, is found when the underlying distributions contain outliers. The outliers are assumed to occur as the result of mixing two normal distributions with common variance. A small sample case shows how the scores for the rank tests are found and the exact power is computed for each of these rank tests. A Monte Carlo study provides an estimate of the power of the usual two sample t-test.     

Masking and swamping effects on tests for multiple outliers in normal sample

A study of some commonly used multiple outlier tests in case of normal samples is presented. When the number of outliers in the sample is unknown, two phenomena, namely, the masking and the swamping effect can occur. The performance of the tests is studied using the measures of masking and swamping effects proposed by Bendre and Kale (1985) and Bendre (1985). The effects are illustrated in case of the Murphy test, Tietjen—Moore test and Dixon test. A small simulation study is carried out to indicate these effects.     

On the power of some tests for examining the stability of regression coefficients

The main objective of the study is to compare four different procedures to test for the stability of regression coefficients. The comparisons are based on a numerical study and are with respect to their abilities to detect various simple forms of parameter instabilities. Besides the power comparisons a special interest is directed towards the choice of “window length” in the tests based on moving sums of squared recursive and ordinary least-squares residuals.     

Testing purchasing power parity: some evidence of the effects of transaction costs

Empirical tests of purchasing power parity often recognize the problems created by simultaneous equations, but seldom recognize the effects of measurement error or transaction costs. Presumably because most researchers believe that they are unimportant. We present evidence that shows that measurement error and transaction costs and create serious econometric problems for testing purchasing power parity. One effect of these problems is that conventional tests of purchasing power parity can accept PPP when predictive errors are relatively large and reject it when predictive errors are relatively small. Another effect is to bias test of cointegration toward accepting the null of no cointegration between exchange rates and relative price indexes. We also construct a simple model of the determination of exchange rates that shows how transaction costs lead to regression switiching.     

Detecting and identifying interventions with the Whittle spectral approach in a long memory panel data model

This article provides a procedure for the detection and identification of outliers in the spectral domain where the Whittle maximum likelihood estimator of the panel data model proposed by Chen [W.D. Chen, Testing for spurious regression in a panel data model with the individual number and time length growing, J. Appl. Stat. 33(88) (2006b), pp. 759–772] is implemented. We extend the approach of Chang and co-workers [I. Chang, G.C. Tiao, and C. Chen, Estimation of time series parameters in the presence of outliers, Technometrics 30 (2) (1988), pp. 193–204] to the spectral domain and through the Whittle approach we can quickly detect and identify the type of outliers. A fixed effects panel data model is used, in which the remainder disturbance is assumed to be a fractional autoregressive integrated moving-average (ARFIMA) process and the likelihood ratio criterion is obtained directly through the modified inverse Fourier transform. This saves much time, especially when the estimated model implements a huge data-set.

Through Monte Carlo experiments, the consistency of the estimator is examined by growing the individual number N and time length T, in which the long memory remainder disturbances are contaminated with two types of outliers: additive outlier and innovation outlier. From the power tests, we see that the estimators are quite successful and powerful.

In the empirical study, we apply the model on Taiwan's computer motherboard industry. Weekly data from 1 January 2000 to 31 October 2006 of nine familiar companies are used. The proposed model has a smaller mean square error and shows more distinctive aggressive properties than the raw data model does.     

Bayesian predictive power: choice of prior and some recommendations for its use as probability of success in drug development

Bayesian predictive power, the expectation of the power function with respect to a prior distribution for the true underlying effect size, is routinely used in drug development to quantify the probability of success of a clinical trial. Choosing the prior is crucial for the properties and interpretability of Bayesian predictive power. We review recommendations on the choice of prior for Bayesian predictive power and explore its features as a function of the prior. The density of power values induced by a given prior is derived analytically and its shape characterized. We find that for a typical clinical trial scenario, this density has a u‐shape very similar, but not equal, to a β‐distribution. Alternative priors are discussed, and practical recommendations to assess the sensitivity of Bayesian predictive power to its input parameters are provided. Copyright © 2016 John Wiley & Sons, Ltd.     

Outlier detection for multivariate skew-normal data: a comparative study

A general way of detecting multivariate outliers involves using robust depth functions, or, equivalently, the corresponding ‘outlyingness’ functions; the more outlying an observation, the more extreme (less deep) it is in the data cloud and thus potentially an outlier. Most outlier detection studies in the literature assume that the underlying distribution is multivariate normal. This paper deals with the case of multivariate skewed data, specifically when the data follow the multivariate skew-normal [1] distribution. We compare the outlier detection capabilities of four robust outlier detection methods through their outlyingness functions in a simulation study. Two scenarios are considered for the occurrence of outliers: ‘the cluster’ and ‘the radial’. Conclusions and recommendations are offered for each scenario.     

Identification and classification of multiple outliers,high leverage points and influential observations in linear regression

Detection of multiple unusual observations such as outliers, high leverage points and influential observations (IOs) in regression is still a challenging task for statisticians due to the well-known masking and swamping effects. In this paper we introduce a robust influence distance that can identify multiple IOs, and propose a sixfold plotting technique based on the well-known group deletion approach to classify regular observations, outliers, high leverage points and IOs simultaneously in linear regression. Experiments through several well-referred data sets and simulation studies demonstrate that the proposed algorithm performs successfully in the presence of multiple unusual observations and can avoid masking and/or swamping effects.     

Size and power of some cointegration tests under structural breaks and heteroskedastic noise

In this paper we examine the power and size distortions of a number of representative cointegration tests in some large-scale Monte Carlo simulations, when the underlying system is subjected to regime shifts and conditional (ARCH-type) heteroskedasticity. Following the suggestion by Gregory and Hansen, we select the minimum (maximum for the Johansen test) value for the statistics evaluated over a set of tentative break points for the regime shifts. The performance of these statistics is compared to the corresponding ordinary statistics in the presence of regime shifts. We demonstrate that the size of the cointegration tests is severely distorted by conditional heteroskedasticity.     

Computation of the percentage points and the power for the two-sided Kolmogorov-Smirnov one sample test

Two recursive schemes are presented for the calculation of the probabilityP(g(x)≤S _n (x)≤h(x) for allx∈®), whereS _n is the empirical distribution function of a sample from a continuous distribution andh, g are continuous and isotone functions. The results are specialized for the calculation of the distribution and the corresponding percentage points of the test statistic of the two-sided Kolmogorov-Smirnov one sample test. The schemes allow the calculation of the power of the test too. Finally an extensive tabulation of percentage points for the Kolmogorov-Smirnov test is given.     

Local power of some tests in exponential family nonlinear models

In this paper we obtain asymptotic expansions up to order n^−1/2 for the nonnull distribution functions of the likelihood ratio, Wald, score and gradient test statistics in exponential family nonlinear models (Cordeiro and Paula, 1989), under a sequence of Pitman alternatives. The asymptotic distributions of all four statistics are obtained for testing a subset of regression parameters and for testing the dispersion parameter, thus generalising the results given in Cordeiro et al. (1994) and Ferrari et al. (1997). We also present Monte Carlo simulations in order to compare the finite-sample performance of these tests.     

The power of some tests of normality against weibull alternatives

The powers of the Kolmogorov-Smirnov, Weisberg-Bingham and Anderson-Darling tests of normality are determined by Monte Carlo sampling ror Weibull alternatives with 10 shape parameters ranging from 1.0 to 10.0 and seven sample sizes from 10 to 100. There is, in general, good agreement at the relatively few points for which power values have previously been published. The usefulness of examining the power as a function of the parameter(s) of an alternate distribution family is outlined.