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Given a random sample X1,…,Xn in $\mathbb {R}^{p}$ from some distribution F and real weights w1, n,…,wn, n adding to n, define the weighted partial sum empirical distribution as $$ \begin{array}{@{}rcl@{}} \displaystyle G_{n} (\textbf{x}, t) = n^{-1} \sum\limits_{i=1}^{[nt]} w_{i, n} I \left( \textbf{X}_{i} \leq \textbf{x} \right) \end{array} $$ for x in $\mathbb {R}^{p}$ , 0 ≤ t ≤ 1. We give Cornish-Fisher expansions for smooth functionals of Gn, following up on Withers and Nadarajah (Statistical Methodology 12:1–15, 2013) who gave expansions for the unweighted version. Applications to sequential analysis include weighted cusum-type functionals for monitoring variance, and a Studentized weighted cusum-type functional for monitoring the mean.

This paper studies the properties of the wild bootstrap-based test proposed in Cameron et al. (2008) for testing hypotheses about the coefficients in a linear regression model with clustered data. Cameron et al. (2008) provide simulations that suggest this test works well even in settings with as few as five clusters, but existing theoretical analyses of its properties all rely on an asymptotic framework in which the number of clusters is “large." In contrast to these analyses, we employ an asymptotic framework in which the number of clusters is “small," but the number of observations per cluster is “large." In this framework, we provide conditions under which an unstudentized version of the test is valid in the sense that it has limiting rejection probability under the null hypothesis that does not exceed the nominal level. Importantly, these conditions require, among other things, certain homogeneity restrictions on the distribution of covariates. In contrast, we establish that a studentized version of the test may only over-reject the null hypothesis by a “small" amount in the sense that it has limiting rejection probability under the null hypothesis that does not exceed the nominal level by more than an amount that decreases exponentially with the number of clusters. We obtain results qualitatively similar to those for the studentized version of the test for closely related \score" bootstrap-based tests, which permit testing hypotheses about parameters in nonlinear models. We illustrate the relevance of our theoretical results for applied work via a simulation study and empirical application.

Conditions are considered under which studentization does not change the limiting distribution of the normalized intermediate order statistics. A similar problem is considered by Berman as applied to a limiting distribution of extreme order statistics.

In this work, we developed a robust permutation test for the concordance correlation coefficient (ρ c) for testing the general hypothesis H 0 : ρ c = ρ c(0). The proposed test is based on an appropriately studentized statistic. Theoretically, the test is proven to be asymptotically valid in the general setting when two paired variables are uncorrelated but dependent. This desired property was demonstrated across a range of distributional assumptions and sample sizes in simulation studies, where the test exhibits robust type I error control in all settings tested, even when the sample size is small. We demonstrated the application of this test in two real world examples across cardiac output measurements and endocardiographic imaging.

Accurate forecast of aggregate end-users electric load profiles is becoming a hot topic in research for those main issues addressed in many fields such as the electricity services market. Hence, load forecast is an extremely important task which should be understood more in depth. In this research paper, the dependency of the day-ahead load forecast accuracy on the basis of the data typology employed in the training of LSTM has been inspected. A real case study of an Italian industrial load with samples recorded every 15 min for the year 2017 and 2018 was studied. The effect in the load forecast accuracy of different dataset cleaning approaches was investigated. In addition, the Generalised Extreme Studentized Deviate hypothesis testing was introduced to identify the outliers present in the dataset. The populations were constructed on the basis of an autocorrelation analysis that allowed for identifying a weekly correlation of the samples. The accuracy of the prediction obtained from different input dataset has been therefore investigated by calculating the most commonly used error metrics, showing the importance of data processing before employing them for load forecast.

In the new era of big data, numerous information and technology systems can store huge amounts of streaming data in real time, for example, in server-access logs on web application servers. The importance of anomaly detection in voluminous quantities of streaming data from such systems is rapidly increasing. One of the biggest challenges in the detection task is to carry out real-time contextual anomaly detection in streaming data with varying patterns that are visually detectable but unsuitable for a parametric model. Most anomaly detection algorithms have weaknesses in dealing with streaming time-series data containing such patterns. In this paper, we propose a novel method for online contextual anomaly detection in streaming time-series data using generalized extreme studentized deviates (GESD) tests. The GESD test is relatively accurate and efficient because it performs statistical hypothesis testing but it is unable to handle streaming time-series data. Thus, focusing on streaming time-series data, we propose an online version of the test capable of detecting outliers under varying patterns. We perform extensive experiments with simulated data, syntactic data, and real online traffic data from Yahoo Webscope, showing a clear advantage of the proposed method, particularly for analyzing streaming data with varying patterns.

The Federal Office for Economic Affairs and Export Control (BAFA) of Germany promotes digital concepts for increasing energy efficiency as part of the “Pilotprogramm Einsparzahler”. Within this program, Limon GmbH is developing software solutions in cooperation with the University of Kassel to identify efficiency potentials in load profiles by means of automated anomaly detection. Therefore, in this study two strategies for anomaly detection in load profiles are evaluated. To estimate the monthly load profile, strategy 1 uses the artificial neural network LSTM (Long Short-Term Memory), with a data period of one month (1 M) or three months (3 M), and strategy 2 uses the smoothing method PEWMA (Probalistic Exponential Weighted Moving Average). By comparing with original load profile data, residuals or summed residuals of the sequence lengths of two, four, six and eight hours are identified as an anomaly by exceeding a predefined threshold. The thresholds are defined by the Z-Score test, i.e., residuals greater than 2, 2.5 or 3 standard deviations are considered anomalous. Furthermore, the ESD (Extreme Studentized Deviate) test is used to set thresholds by means of three significance level values of 0.05, 0.10 and 0.15, with a maximum of k = 40 iterations. Five load profiles are examined, which were obtained by the cluster method k-Means as a representative sample from all available data sets of the Limon GmbH. The evaluation shows that for strategy 1 a maximum F1-value of 0.4 (1 M) and for all examined companies an average F1-value of maximum 0.24 and standard deviation of 0.09 (1 M) could be achieved for the investigation on single residuals. In variant 3 M the highest F1-value could be achieved with an average F1-value of 0.21 and standard deviation of 0.06 (3 M) for summed residuals of the partial sequence length of four hours. The PEWMA-based strategy 2 did not show a higher anomaly detection efficacy compared to strategy 1 in any of the investigated companies.

We consider one-sided Grubbs's statistics for a normal sample of the size n. These statistics are extreme studentized deviations of the observations from the sample mean. One abnormal observation (outlier) is assumed in the sample, its number is unknown. We consider the case when the outlier differs from other observations in values of population mean and dispersion, i. e., shift and scale parameters. We construct a copula-function by an inversion method from the joint distribution of Grubbs's statistics, it depends on three parameters: shift and scale parameters and n. It is proved that for Grubbs's copula-function, the coefficients of the upper-left and lower-right tail dependencies are equal each other. Moreover, their value is independent of the shift and scale parameters but it depends on parameter n. The dependence in the tails of the distribution of the three-parameter Grubbs's copula coincides with the dependence in the tails of the joint distribution of one-sided Grubbs's statistics calculated from the normal sample without outlier.

Two sample mean vectors comparison hypothesis testing problems often emerge in modern biostatistics. Many tests are proposed for detecting relatively dense signals with somewhat dense nonzero components in mean vectors differences. One kind of these tests is based on some quadratic forms about two sample mean vectors differences. Another kind of these tests is based on some quadratic forms about studentized version of two sample mean vectors differences. In this article, we propose a bootstrap test by adopting stationary bootstrap scheme to calculate p value of a typical test which is based on a quadratic form about studentized version of two sample mean vectors differences. Extensive simulations are conducted to compare performances of the bootstrap test with other existing typical tests. We also apply the bootstrap test to a real genetic data analysis about breast cancer.

Although many methodologists and professional organizations have urged applied researchers to compute and report effect size measures accompanying tests of statistical significance, discussions on obtaining confidence intervals (CIs) for effect size with clustered/multilevel data have been scarce. In this paper, I explore the bootstrap as a viable and accessible alternative for obtaining CIs for multilevel standardized mean difference effect size for cluster-randomized trials. A simulation was carried out to compare 17 analytic and bootstrap procedures for constructing CIs for multilevel effect size, in terms of empirical coverage rate and width, for both normal and nonnormal data. Results showed that, overall, the residual bootstrap with studentized CI had the best coverage rates (94.75% on average), whereas the residual bootstrap with basic CI had better coverage in small samples. These two procedures for constructing CIs showed better coverage than using analytic methods for both normal and nonnormal data. In addition, I provide an illustrative example showing how bootstrap CIs for multilevel effect size can be easily obtained using the statistical software R and the R package bootmlm. I strongly encourage applied researchers to report CIs to adequately convey the uncertainty of their effect size estimates.

In a linear regression model, testing for uniformity of the variance of the residuals is a significant integral part of statistical analysis. This is a crucial assumption that requires statistical confirmation via the use of some statistical tests mostly before carrying out the Analysis of Variance (ANOVA) technique. Many academic researchers have published series of papers (articles) on some tests for detecting variance heterogeneity assumption in multiple linear regression models. So many comparisons on these tests have been made using various statistical techniques like biases, error rates as well as powers. Aside comparisons, modifications of some of these statistical tests for detecting variance heterogeneity have been reported in some literatures in recent years. In a multiple linear regression situation, much work has not been done on comparing some selected statistical tests for homoscedasticity assumption when linear, quadratic, square root, and exponential forms of heteroscedasticity are injected into the residuals. As a result of this fact, the present study intends to work extensively on all these areas of interest with a view to filling the gap. The paper aims at providing a comprehensive comparative analysis of asymptotic behaviour of some selected statistical tests for homoscedasticity assumption in order to hunt for the best statistical test for detecting heteroscedasticity in a multiple linear regression scenario with varying variances and levels of significance. In the literature, several tests for homoscedasticity are available but only nine: Breusch-Godfrey test, studentized Breusch-Pagan test, White’s test, Nonconstant Variance Score test, Park test, Spearman Rank, Glejser test, Goldfeld-Quandt test, Harrison-McCabe test were considered for this study; this is with a view to examining, by Monte Carlo simulations, their asymptotic behaviours. However, four different forms of heteroscedastic structures: exponential and linear (generalize of square-root and quadratic structures) were injected into the residual part of the multiple linear regression models at different categories of sample sizes: 30, 50, 100, 200, 500 and 1000. Evaluations of the performances were done within R environment. Among other findings, our investigations revealed that Glejser and Park tests returned the best test to employ to check for heteroscedasticity in EHS and LHS respectively also White and Harrison-McCabe tests returned the best test to employ to check for homoscedasticity in EHS and LHS respectively for sample size less than 50.

Influential observations (IOs), which are outliers in the x direction, y direction or both, remain a problem in the classical regression model fitting. Spatial regression models have a peculiar kind of outliers because they are local in nature. Spatial regression models are also not free from the effect of influential observations. Researchers have adapted some classical regression techniques to spatial models and obtained satisfactory results. However, masking or/and swamping remains a stumbling block for such methods. In this article, we obtain a measure of spatial Studentized prediction residuals that incorporate spatial information on the dependent variable and the residuals. We propose a robust spatial diagnostic plot to classify observations into regular observations, vertical outliers, good and bad leverage points using a classification based on spatial Studentized prediction residuals and spatial diagnostic potentials, which we refer to as ISRs−Posi and ESRs−Posi. Observations that fall into the vertical outliers and bad leverage points categories are referred to as IOs. Representations of some classical regression measures of diagnostic in general spatial models are presented. The commonly used diagnostic measure in spatial diagnostics, the Cook’s distance, is compared to some robust methods, Hi2 (using robust and non-robust measures), and our proposed ISRs−Posi and ESRs−Posi plots. Results of our simulation study and applications to real data showed that the Cook’s distance, non-robust Hsi12 and robust Hsi22 were not very successful in detecting IOs. The Hsi12 suffered from the masking effect, and the robust Hsi22 suffered from swamping in general spatial models. Interestingly, the results showed that the proposed ESRs−Posi plot, followed by the ISRs−Posi plot, was very successful in classifying observations into the correct groups, hence correctly detecting the real IOs.

Outlier detection is challenging for time series with seasonality and trend due to the presence of local outliers. In this paper, we propose an online unsupervised deep learning based algorithm for outlier detection utilizing temporal convolutional neural network (TCN). In the proposed algorithm, firstly, the TCN network is trained using a novel loss function designed to address time series with seasonality and trend. Secondly, instead of a single global threshold for outlier detection for the entire time series, we define a set of thresholds computed based on the output of the TCN network, leading to robust detection of local outliers caused by the seasonality and the trend. The performance of the proposed algorithm is evaluated using synthetic time series. The results show that given 99% Precision, the proposed algorithm achieves at least 70% Recall and 80% F-score, which is much better than 43% Recall and 60% F-score achieved by the statistics-based seasonal extreme studentized deviate test (S-ESD) algorithm. Our algorithm also demonstrates better performance than that of the TCN based detection algorithm trained by the conventional loss function.

Purpose – to investigate the relationship between job security and labor productivity among 45,506 companies from the Czech Republic, Slovakia, Croatia, Slovenia, and Latvia. Design/Method/Approach. This article uses linear regression analysis based on data from the period of 2013-2017. Findings. The study indicates an inverse U-shaped relationship between employment volatility, as measured by the coefficient of variation, and labor productivity. Labor productivity increases along with employment fluctuation up to a certain point; however, when employees feel insecure, their labor productivity deteriorates. Surprisingly, for most companies, the relationship between employment fluctuation and labor productivity remains positive. Labor productivity gets affected positively by the security feeling rather than by guaranteeing the job position. Originality/Value. The results are consistent within the subsamples of the five individual countries in the sample and robust to two alternative measures of fluctuation, the mean absolute deviation, and the studentized range. Paper type – empirical.

We consider six variants of (local) Whittle estimators of the fractional order of integration d. They follow a limiting normal distribution under stationarity as well as under (a certain degree of) nonstationarity. Experimentally, we observe a lack of continuity of the objective functions of the two fully extended versions at $$d=1/2$$ that has not been reported before. It results in a pileup of the estimates at $$d=1/2$$ when the true value is in a neighborhood to this half point. Consequently, studentized test statistics may be heavily oversized. The other four versions suffer from size distortions, too, although of a different pattern and to a different extent.

© 2019 American Statistical Association. A fundamental limitation of causal inference in observational studies is that perceived evidence for an effect might instead be explained by factors not accounted for in the primary analysis. Methods for assessing the sensitivity of a study’s conclusions to unmeasured confounding have been established under the assumption that the treatment effect is constant across all individuals. In the potential presence of unmeasured confounding, it has been argued that certain patterns of effect heterogeneity may conspire with unobserved covariates to render the performed sensitivity analysis inadequate. We present a new method for conducting a sensitivity analysis for the sample average treatment effect in the presence of effect heterogeneity in paired observational studies. Our recommended procedure, called the studentized sensitivity analysis, represents an extension of recent work on studentized permutation tests to the case of observational studies, where randomizations are no longer drawn uniformly. The method naturally extends conventional tests for the sample average treatment effect in paired experiments to the case of unknown, but bounded, probabilities of assignment to treatment. In so doing, we illustrate that concerns about certain sensitivity analyses operating under the presumption of constant effects are largely unwarranted.

We propose two methods to approximate the distribution function of a Studentized linear combination of order statistics for a simple random sample drawn without replacement from a finite population. Using auxiliary data available for the population units, the first method modifies a nonparametric bootstrap approximation, and the second one corrects an empirical saddlepoint approximation based on the bootstrap. We conclude from simulations that, on the tails of distribution of interest, both approximations improve their initial versions and alternative Edgeworth approximations.

The objective of this study is to analyze and foresee potential outliers in pulp and handsheet properties for larger data sets. The method is divided into two parts comprising a generalized Extreme Studentized Deviate (ESD) procedure for laboratory data followed by an analysis of the findings using a multivariable model based on internal variables (i. e. process variables like consistency and fiber residence time inside the refiner) as predictors. The process data used in this has been obtained from CD-82 refiners and from a laboratory test program perspective, the test series were extensive. In the procedure more than 290 samples were analyzed to get a stable outlier detection. Note, this set was obtained from pulp at one specific operating condition. When comparing such “secured data sets” with process data it is shown that an extended procedure must be performed to get data sets which cover different operating points. Here 100 pulp samples at different process conditions were analyzed. It is shown that only about 60 percent of all tensile index measurements were accepted in the procedure which indicates the need to oversample when performing extensive trials to get reliable pulp and handsheet properties in TMP and CTMP processes.

We study one-sided Grubbs’ statistics for a normal sample, i.e., extreme studentized deviations of observations from the mean, computed from a normally distributed sample. We consider the case when the sample has an abnormal observation (outlier) with unknown number. The outlier differs from other observations in mean value and dispersion. We investigate the properties of the joint distribution of Grubbs’ statistics. We prove the existence of domain in which the joint distribution function of Grubbs’ statistics is a linear function of their marginal distribution functions. We construct a three-parameter Grubbs’ copula from the joint distribution of Grubbs’ statistics. We prove the existence of a domain in which Grubbs’ copula coincides with the Frechet-Hoeffding lower bound. We investigate the influence of the copulas parameters on the shape of this domain.

A short Edgeworth expansion is approximated for the distribution function of a Studentized linear combination of order statistics computed on a random sample drawn without replacement from a finite...

The Ryan-Einot-Gabriel-Welsch and Quiot (REGWQ) test allows one to compare vast amounts of data while monitoring the likelihood of having at least one Type I or Family wise mistake. The REGWQ multiple comparisons test for qualitative data was used in this investigation. For multiple comparisons of the means, okra characterisation data was utilised and submitted to ANOVA (P_0.05) with REGWQ. When variances are heterogeneous, the findings of this study define a summary technique of following a significant ANOVA F with REGWQ test on several comparisons of means in summation of a broad entries/treatments to the small classes. Cluster analysis could be particularly helpful for categorising qualitative treatments and should also be used in combination with REFWQ multiple generates. The research will be developed in REGWQ multiple producers in SAS alternative for distributing a large number of treatments to a small population with summering the best treatment preference. The use of REGWQ for multiple comparisons of qualitative data typically produce overlapping group of means, unless access multiple comparison of gaulatitive data need new approaches in computer program to calculate exact studentized range values.

This study is aimed to determine the factors contributing to the prediction of the total Consumer Price Index (CPI) in Malaysia through model selection using LASSO regression. The outliers are identified using the leverage values and studentized deleted residuals while the multicollinearity variables will undergo progressive elimination based on Variance Inflation Factor (VIF) values. K-fold Cross-Validation (CV) method and Mean Square Error of Prediction (MSE(P)) were used to identify the best model. Model-building without removal of outliers (Set A), model-building with the remove outliers based on leverage points and studentized deleted residuals (Set B), model-building after removal of extreme outliers based on the boxplot (Set C) were carried out. The multicollinearity variables were removed for all the three sets. The results showed that the MSE(P) of the best LASSO model in Set C is the smallest compared to the other two sets. The nine major categories such as food and non-alcoholic beverages, alcoholic beverages and tobacco, clothing and footwear, transport, communication, recreation service and culture, education, restaurants and hotels, miscellaneous goods and services have significant contribution in prediction of the total CPI in Malaysia.

Suppose that we are interested in the effect of four different types of chemical fertilizers on the yield of rice, measured in pounds per acre. If there is no difference between the different types of fertilizers, then we would expect all the mean yields to be approximately equal. Otherwise, we would expect the mean yields to differ. The different types of fertilizers are called treatments and their effects are the treatment effects. The yield is called the response. Typically, we have a model with a response variable that is possibly affected by one or more treatments. The study of these types of models falls under the purview of design of experiments, which we discussed in Chapter 9 . In this chapter, we concentrate on the analysis aspect of the data obtained from the designed experiments. If the data came from one or two populations, we could use the techniques learned in Chapters 6 and 7 . Here, we introduce some tests that are used to analyze the data from more than two populations. These tests are used to deal with treatment effects, including tests that take into account other factors that may affect the response. The hypothesis that the population means are equal is considered equivalent to the hypothesis that there is no difference in treatment effects. The analytical method we will use in such problems is called the analysis of variance (ANOVA). Initial development of this method could be credited to Sir Ronald A. Fisher who introduced this technique for the analysis of agricultural field experiments. The “green revolution” in agriculture would have been impossible without the development of theory of experimental design and the methods of ANOVA.

Analysis of x-ray absorption spectroscopy (XAS) data often involves the removal of artifacts or glitches from the acquired signal, a process commonly known as deglitching. Glitches result either from specific orientations of monochromator crystals or from scattering by crystallites in the sample itself. Since the precise energy or wavelength location and the intensity of glitches in a spectrum cannot always be predicted, deglitching is often performed on a per spectrum basis by the analyst. Some routines have been proposed, but they are prone to arbitrary selection of spectral artifacts and are often inadequate for processing large data sets. Here we present a statistically robust algorithm, implemented as a Python program, for the automatic detection and removal of glitches that can be applied to a large number of spectra. It uses a Savitzky-Golay filter to smooth spectra and the generalized extreme Studentized deviate test to identify outliers. We achieve robust, repeatable, and selective removal of glitches using this algorithm., 13 pages, 2 figures

In order to search for an ideal test for multiple comparison procedures, this study aimed to develop two tests, similar to the Tukey and SNK tests, based on the distribution of the externally studentized amplitude. The test names are Tukey Midrange (TM) and SNK Midrange (SNKM). The tests were evaluated based on the experimentwise error rate and power, using Monte Carlo simulation. The results showed that the TM test could be an alternative to the Tukey test, since it presented superior performances in some simulated scenarios. On the other hand, the SNKM test performed less than the SNK test. RESUMO Em face de ainda haver a busca de um teste ideal aos procedimentos de comparações múltiplas, esse trabalho teve como objetivo desenvolver dois testes de comparações múltiplas, similares aos testes Tukey e SNK, porém, baseados na distribuição da amplitude estudentizada externamente. Os nomes dos testes são Tukey Midrange (TM) e SNK Midrange (SNKM). Os testes foram avaliados baseados na taxa de erro por experimento e no poder, usando simulação Monte Carlo. Os resultados mostraram que o teste TM pode ser uma alternativa ao teste Tukey, uma vez que apresentou desempenho superior em alguns cenários simulados. Ao passo que o teste SNKM apresentou desempenho inferior ao teste SNK.

The eigenvalue based spectrum sensing is a low-cost spectrum sensing method that detects the presence of the licensed user signal in desired frequency. Traditional single-threshold eigenvalue sensing methods, which are widely used in the literature, can exhibit inadequate performance under low SNR and noise uncertainty. Therefore, in this study an eigenvalue-based spectrum sensing method is proposed using a double threshold with the studentized extreme eigenvalue distribution function. The results that threshold values obtained for the proposed method were simulated in Rayleigh fading channels. The results were compared with traditional methods and they were observed to be more accurate.

We examine the performance of asymptotic inference as well as bootstrap tests for the Alphabeta and Kobus&ndash, Miłoś family of inequality indices for ordered response data. We use Monte Carlo experiments to compare the empirical size and statistical power of asymptotic inference and the Studentized bootstrap test. In a broad variety of settings, both tests are found to have similar rejection probabilities of true null hypotheses, and similar power. Nonetheless, the asymptotic test remains correctly sized in the presence of certain types of severe class imbalances exhibiting very low or very high levels of inequality, whereas the bootstrap test becomes somewhat oversized in these extreme settings.

In this chapter we present a general theory of approximation of scale-mixed distributions or distributions of scale mixtures, including simple examples of Student’s t-distribution and F-distribution as a scale mixtures of the normal and chi-square distribution, respectively. Such scale mixtures appear as sampling distributions of various statistics such as the studentized version of some estimators. Errors of the approximation are evaluated in \(\sup \) and \(L_1\)-norms. Extension to multivariate scale mixtures with error bounds evaluated in \(L_1\)-norm shall be discussed in Chap. 3.

The present paper intends to revisit the distribution of the ratio of the range to the sample standard deviation, known as the distribution of the internally studentized range, in the normal case. This distribution has its importance recognized in several areas, as quality control and inference, for testing the lack of homogeneity of the data or kurtosis. An alternative distribution to the one presented by David et al. (1954), based on the distribution of the maximum, is proposed. We exhibit a detailed proof for the distribution of the internally studentized range in the normal case and sample size 3. We also provide a new result: the distribution for the uniform case with sample of size 3.

Count data are common endpoints in clinical trials, for example magnetic resonance imaging lesion counts in multiple sclerosis. They often exhibit high levels of overdispersion, that is variances are larger than the means. Inference is regularly based on negative binomial regression along with maximum-likelihood estimators. Although this approach can account for heterogeneity it postulates a common overdispersion parameter across groups. Such parametric assumptions are usually difficult to verify, especially in small trials. Therefore, novel procedures that are based on asymptotic results for newly developed rate and variance estimators are proposed in a general framework. Moreover, in case of small samples the procedures are carried out using permutation techniques. Here, the usual assumption of exchangeability under the null hypothesis is not met due to varying follow-up times and unequal overdispersion parameters. This problem is solved by the use of studentized permutations leading to valid inference methods for situations with (i) varying follow-up times, (ii) different overdispersion parameters, and (iii) small sample sizes. peerReviewed

Permutation tests are very useful when parametric assumptions are violated or distributions of test statistics are mathematically intractable. The major advantage of permutation tests is that the procedure is so general that it is applicable to most test statistics. The computational expense is, however, impractical in high-dimensional settings such as genomewide association studies. This study provides a comprehensive review of existing methods that can compute very small p-values efficiently. A common issue with existing methods is that they can only be applied to a specific test statistic. To fill in the knowledge gap, we propose a hybrid method of the sequential Monte Carlo and the Edgeworth expansion approximation for a studentized statistic, which is applicable to a variety of test statistics. The simulation results show that the proposed method performs better than competing methods. Furthermore, applications of the proposed method are demonstrated by statistical analysis on the genomewide association studies data from the Study of Addiction: Genetics and Environment (SAGE).

International audience; Asymptotic and bootstrap tests for inequality measures are known to perform poorly in finite samples when the underlying distribution is heavy-tailed. We propose Monte Carlo permutation and bootstrap methods for the problem of testing the equality of inequality measures between two samples. Results cover the Generalized Entropy class, which includes Theil’s index, the Atkinson class of indices, and the Gini index. We analyze finite-sample and asymptotic conditions for the validity of the proposed methods, and we introduce a convenient rescaling to improve finite-sample performance. Simulation results show that size correct inference can be obtained with our proposed methods despite heavy tails if the underlying distributions are sufficiently close in the upper tails. Substantial reduction in size distortion is achieved more generally. Studentized rescaled Monte Carlo permutation tests outperform the competing methods we consider in terms of power.

Hotelling's T 2 and Mahalanobis distance are widely used in the statistical analysis of multivariate data. When either of these quantities is large, a natural question is: How do individual variables contribute to its size? The Garthwaite–Koch partition has been proposed as a means of assessing the contribution of each variable. This yields point estimates of each variable's contribution and here we consider bootstrap methods for forming interval estimates of these contributions. New bootstrap methods are proposed and compared with the percentile, bias-corrected percentile, non-studentized pivotal and studentized pivotal methods via a large simulation study. The new methods enable use of a broader range of pivotal quantities than with standard pivotal methods, including vector pivotal quantities. In the context considered here, this obviates the need for transformations and leads to intervals that have higher coverage, and yet are narrower, than intervals given by the standard pivotal methods. These results held both when the population distributions were multivariate normal and when they were skew with heavy tails. Both equal-tailed intervals and shortest intervals are constructed; the latter are particularly attractive when (as here) squared quantities are of interest.

SUMMARYVolatility functionals are widely used in financial econometrics. In the literature, they are estimated with realized volatility functionals using high-frequency data. In this paper we introduce a nonparametric local bootstrap method that resamples the high-frequency returns with replacement in local windows shrinking to zero. While the block bootstrap in time series (Hall et al., 1995) aims to reduce correlation, the local bootstrap is intended to eliminate the heterogeneity of volatility. We prove that the local bootstrap distribution of the studentized realized volatility functional is first-order accurate. We present Edgeworth expansions of the studentized realized variance with and without local bootstrapping in the absence of the leverage effect and jumps. The expansions show that the local bootstrap distribution of the studentized realized variance is second-order accurate. Extensive simulation studies verify the theory.

Clinical study endpoints, including some biomarkers, are frequently analyzed after a log transformation. To calculate study power for detecting a between-treatment difference in the log scale, an e...

The two-sample problem for Cronbach's coefficient [Formula: see text], as an estimate of test or composite score reliability, has attracted little attention compared to the extensive treatment of the one-sample case. It is necessary to compare the reliability of a test for different subgroups, for different tests or the short and long forms of a test. In this paper, we study statistical procedures of comparing two coefficients [Formula: see text] and [Formula: see text]. The null hypothesis of interest is [Formula: see text], which we test against one-or two-sided alternatives. For this purpose, resampling-based permutation and bootstrap tests are proposed for two-group multivariate non-normal models under the general asymptotically distribution-free (ADF) setting. These statistical tests ensure a better control of the type-I error, in finite or very small sample sizes, when the state-of-affairs ADF large-sample test may fail to properly attain the nominal significance level. By proper choice of a studentized test statistic, the resampling tests are modified in order to be valid asymptotically even in non-exchangeable data frameworks. Moreover, extensions of this approach to other designs and reliability measures are discussed as well. Finally, the usefulness of the proposed resampling-based testing strategies is demonstrated in an extensive simulation study and illustrated by real data applications.

A new test is proposed for testing the equality of two sample means in high dimensional data in which the sample sizes may be much less than the dimension. The test is constructed based on a studentized average of squared component-wise t-statistics. Asymptotic normality of the test statistic was derived under H 0 . Theoretical properties of the power function were given under local alternatives. The new test has much better type I error control and power compared to a similarly constructed competing test in recent literature as a result of a more efficient scaling parameter estimate in the test statistic. Monte Carlo experiments show that the new test outperforms several popular competing tests under various data settings, especially when components of the data vector have high correlations. The results are established under the condition that there exists a permutation of the component indices such that the correlation decays suitably fast (at least with polynomial rate). The test is further evaluated with a real-data task of identifying differently expressed Gene Ontology terms with the acute lymphoblastic leukemia gene expression data. The new test provides more consistent results on random samples of the dataset.

We study the properties of tests constructed by a simple modification of the studentized range of the sample from a symmetric stable population in the problem of testing the hypothesis $$ \mathrm{\mathscr{H}} $$ α (the stability index equals α, α ∈ (1, 2)) against the alternative $$ \mathrm{\mathscr{H}} $$ 2. We obtain approximate formulas for the calculation of critical values and estimation of the test power and develop a method for the estimation of the accuracy of these approximations. The major part of the paper deals with the construction of the approximations to the distribution function of the normalized sum of squares of symmetric stable random variables and estimation of the accuracy of approximations.

A test based on the studentized empirical characteristic function calculated in a single point is derived. An empirical power comparison is made between this test and tests like the Epps–Pulley, Shapiro–Wilks, Anderson–Darling and other tests for normality. It is shown to outperform the more complicated Epps-Pulley test based on the empirical characteristic function and a Cramer-von Mises type expression in a simulation study. The test performs especially good in large samples and the derived test statistic has an asymptotic normal distribution which is easy to apply.

The paper presents the econometric procedures of identifying specific transactions, in which atypical conditions or attributes may occur. These procedures are based on studentized and predictive residuals of the accordingly specified econometric models. The dependent variable is a unit transactional price, and explanatory variables are both the real properties’ attributes and accordingly defined artificial binary variables. The utility of the proposed method has been verified by means of a real market data base. The proposed procedures can be helpful during the property valuation process, making it possible to reject real properties that are specific (both from the point of view of the transaction conditions and the properties’ attributes) and, consequently, to select an appropriate set of similar attributes that are essential for the valuation process.

Mineral prospectivity mapping (MPM) is a multi-step process that ranks promising target areas for further exploration. Fuzzy logic and fuzzy analytical hierarchy process (AHP) are knowledge-driven MPM approaches. In this study, both approaches were used for data processing, based on which MPM was performed for porphyry and hydrothermal vein copper deposits in the Dananhu-Tousuquan island arc, Xinjiang. The results of the two methods were then compared. The two methods combined expert experience and the Studentized contrast (S(C)) values of the weights-of-evidence approach to calculate the weights of 15 layers, and these layers were then integrated by the gamma operator (γ). Through prediction-area (P-A) plot analysis, the optimal γ for fuzzy logic and fuzzy AHP was determined as 0.95 and 0.93, respectively. The thresholds corresponding to different levels of metallogenic probability were defined via concentration-area (C-A) fractal analysis. The prediction performances of the two methods were compared on this basis. The results showed that in MPM based on fuzzy logic, the area under the receiver operating characteristic (ROC) curve was 0.806 and 81.48% of the known deposits were predicted, whereas in MPM based on fuzzy AHP, the area under the ROC curve was 0.862 and 92.59% of the known deposits were predicted. Therefore, prediction based on fuzzy AHP is more accurate and can provide directions for future prospecting.

Sequentially crosslinked and annealed polyethylene (SXL) is a second generation highly crosslinked polyethylene that has been available for joint replacement with clinical success. The purpose of this study is to characterize SXL cups through an analysis of almost 14 years of historical in vitro wear simulation data. Three characteristics were evaluated in this study (1) Wear rate, (2) linear penetration and (3) shelf-life effect on wear. Specimens were SXL acetabular cups with internal diameters ranging from 22 mm to 44 mm, and thicknesses ranging from 3.9 mm to 19.6 mm. All cups were tested for 1–5 million cycles. Wear rates were tested for normality and suspected outliers were tested using the generalized extreme studentized deviate (ESD). A total of 290 samples were evaluated, which included suspected outliers. After ESD statistical outlier removal, distribution was non-normal and the range of wear rates was −4.3 to 8.2 mm3/mc, with a mean of 1.8±1.6 mm3/mc and median of 1.6 mm3/mc. Individual bearing sizes and thicknesses reveal non-normal distributions for the 22 mm, 32 mm, and 40mm groups and for the 10 mm thickness group. The sample with the highest calculated linear penetration rate, 22.2 μm/mc, was for a 22 mm bearing size with 19.6 mm thickness. Before and after outlier removal, regression results of bearing size, thickness, and shelf age produce linear coefficients of correlation, R2 Published clinical data performance at 5 years documented with 32 mm bearings show clinical values ranging from 0.008 mm/yr to 0.015 mm/yr. The 32 mm bearing size represents 127 samples in this data set, and the mean calculated linear penetration is 0.008 mm/mc. This value compares favorably to the reported penetration values, assuming that 1 million hip wear simulation cycles approximates closely to one year of in-vivo cycles. In addition, wear analysis showed no effect of shelf-life on wear and maintained its low wear characteristics regardless of polyethylene thickness or head size.

We investigate one-sided Grubbs’ statistics for a normal sample. Those statistics are standardized maximum and standardized minimum, i.e., studentized extreme deviation statistics. We consider the case of the sample when there is one abnormal observation (outlier), unknown to what number according. The outlier differs from other observations in values of population mean and dispersion. We obtain recursive relationships for the marginal distribution function of one-sided Grubbs’ statistics. We find asymptotic formulas for marginal distribution functions. We obtain recursive relationships for the joint distribution function of one-sided Grubbs’ statistics and investigate its properties.

We consider inference for the mean of a general stationary process based on standardizing the sample mean by a frequency domain estimator of the long run variance. Here, the main novelty is that we consider alternative asymptotics in which the bandwidth is kept fixed. This does not yield a consistent estimator of the long run variance, but, for the weakly dependent case, the studentized sample mean has a Student- limit distribution, which, for any given bandwidth, appears to be more precise than the traditional Gaussian limit. When data are fractionally integrated, the fixed bandwidth limit distribution of the studentized mean is not standard, and we derive critical values for various bandwidths. By a Monte Carlo experiment of finite sample performance we find that this asymptotic result provides a better approximation than other proposals like the test statistic based on the Memory Autocorrelation Consistent (MAC) estimator of the variance of the sample mean. Javier Hualde’s research is supported by the Spanish Ministerio de Economía y Competitividad through project ECO2015-64330-P.