Statistical Microcomputing—Like it is

A statistical software package is a collaborative effort between a program's authors and users. When statistical analysis took place exclusively on mainframe computers, the entire statistical community was served by some three to six major packages, which helped to ensure that program errors would be quickly uncovered and corrected. The current trend toward performing statistical analysis on microcomputers has resulted in an explosion of software of varying quality, with more than 200 packages for the IBM PC alone. Since all of these programs are competing for the same base of knowledgeable users, the number of sophisticated users per package is dramatically less than for mainframe packages; the net result is that problems in any particular package are more likely to go unnoticed and uncorrected. For example, the most widely used shareware package contains major errors that should cause it to be rejected out of hand, and three best-selling packages analyze unbalanced two-factor experiments using an approximate technique originally developed for hand calculation. Several strategies are offered to help author and user reveal any problems that might be present in their software.     

Will the ASA's Efforts to Improve Statistical Practice be Successful? Some Evidence to the Contrary

ABSTRACT

Recent efforts by the American Statistical Association to improve statistical practice, especially in countering the misuse and abuse of null hypothesis significance testing (NHST) and p-values, are to be welcomed. But will they be successful? The present study offers compelling evidence that this will be an extraordinarily difficult task. Dramatic citation-count data on 25 articles and books severely critical of NHST's negative impact on good science, underlining that this issue was/is well known, did nothing to stem its usage over the period 1960–2007. On the contrary, employment of NHST increased during this time. To be successful in this endeavor, as well as restoring the relevance of the statistics profession to the scientific community in the 21st century, the ASA must be prepared to dispense detailed advice. This includes specifying those situations, if they can be identified, in which the p-value plays a clearly valuable role in data analysis and interpretation. The ASA might also consider a statement that recommends abandoning the use of p-values.     

Comparison of Statistical Methods for Pretest–Posttest Designs in Terms of Type I Error Probability and Statistical Power

The pretest–posttest design is widely used to investigate the effect of an experimental treatment in biomedical research. The treatment effect may be assessed using analysis of variance (ANOVA) or analysis of covariance (ANCOVA). The normality assumption for parametric ANOVA and ANCOVA may be violated due to outliers and skewness of data. Nonparametric methods, robust statistics, and data transformation may be used to address the nonnormality issue. However, there is no simultaneous comparison for the four statistical approaches in terms of empirical type I error probability and statistical power. We studied 13 ANOVA and ANCOVA models based on parametric approach, rank and normal score-based nonparametric approach, Huber M-estimation, and Box–Cox transformation using normal data with and without outliers and lognormal data. We found that ANCOVA models preserve the nominal significance level better and are more powerful than their ANOVA counterparts when the dependent variable and covariate are correlated. Huber M-estimation is the most liberal method. Nonparametric ANCOVA, especially ANCOVA based on normal score transformation, preserves the nominal significance level, has good statistical power, and is robust for data distribution.     

Statistical analysis of firm interdependence using duration data—parametric approach

A pioneer first enters the market as the monopolist and later experiences the competition when a similar product is brought to the market by the competitor. In 2012, Wang and Xie suggested to decompose the pioneer survival to “monopoly” and “competition” durations and estimate the two survivals of the pioneer individually with the competitor's survival via regression analysis. In their article, several regression analyses were performed to study the effect of order entry to the pioneer and the later entrant in different market status. Using the same datasets from their study, our main interest is to investigate the interdependent relationship between two competitive firms and study whether the market pioneer and the later entrant can benefit from the competition. The major contribution of this article is that the interdependence between two competitive firms is explicitly expressed and three survival durations can be estimated in one model. The proposed method relates the survival times of two competitive firms to pioneer's monopoly time and some observable covariates via proportional hazard model, and incorporates frailty variables to capture the interdependence in the competition. This article demonstrates a new method that formulates the interdependence between competitive firms and shows data analyses in the industries of newspapers and high technology.     

Statistical choice of extreme value domains of attraction — a comparative analysis

In recent years there has been a significant development of several procedures to infer about the extremal model that most conveniently describes the distribution function of the underlying population from a data set. The problem of choosing one of the three extremal types, giving preference to the Gumbel model for the null hypothesis, has frequently received the general designation of statistical choice of extremal models and has been handled under different set-ups by numerous authors. Recently, a test procedure, referred by Hasofer and Wang (1992), gave place to a comparison with some of other connected perspectives. Such a topic, jointly with some suggestions for applicability to real data, is the theme of the present paper.     

New Developments in Statistical Computing: New Bias Evaluation Features of EXPLOR—A Program for Assessing Experimental Design Properties

Longitudinal investigations play an increasingly prominent role in biomedical research. Much of the literature on specifying and fitting linear models for serial measurements uses methods based on the standard multivariate linear model. This article proposes a more flexible approach that permits specification of the expected response as an arbitrary linear function of fixed and time-varying covariates so that mean-value functions can be derived from subject matter considerations rather than methodological constraints. Three families of models for the covariance function are discussed: multivariate, autoregressive, and random effects. Illustrations demonstrate the flexibility and utility of the proposed approach to longitudinal analysis.     

What Level of Statistical Model Should We Use in Small Area Estimation?

If unit‐level data are available, small area estimation (SAE) is usually based on models formulated at the unit level, but they are ultimately used to produce estimates at the area level and thus involve area‐level inferences. This paper investigates the circumstances under which using an area‐level model may be more effective. Linear mixed models (LMMs) fitted using different levels of data are applied in SAE to calculate synthetic estimators and empirical best linear unbiased predictors (EBLUPs). The performance of area‐level models is compared with unit‐level models when both individual and aggregate data are available. A key factor is whether there are substantial contextual effects. Ignoring these effects in unit‐level working models can cause biased estimates of regression parameters. The contextual effects can be automatically accounted for in the area‐level models. Using synthetic and EBLUP techniques, small area estimates based on different levels of LMMs are investigated in this paper by means of a simulation study.     

Estimating the Spot Covariation of Asset Prices—Statistical Theory and Empirical Evidence

ABSTRACT

We propose a new estimator for the spot covariance matrix of a multi-dimensional continuous semimartingale log asset price process, which is subject to noise and nonsynchronous observations. The estimator is constructed based on a local average of block-wise parametric spectral covariance estimates. The latter originate from a local method of moments (LMM), which recently has been introduced by Bibinger et al.. We prove consistency and a point-wise stable central limit theorem for the proposed spot covariance estimator in a very general setup with stochastic volatility, leverage effects, and general noise distributions. Moreover, we extend the LMM estimator to be robust against autocorrelated noise and propose a method to adaptively infer the autocorrelations from the data. Based on simulations we provide empirical guidance on the effective implementation of the estimator and apply it to high-frequency data of a cross-section of Nasdaq blue chip stocks. Employing the estimator to estimate spot covariances, correlations, and volatilities in normal but also unusual periods yields novel insights into intraday covariance and correlation dynamics. We show that intraday (co-)variations (i) follow underlying periodicity patterns, (ii) reveal substantial intraday variability associated with (co-)variation risk, and (iii) can increase strongly and nearly instantaneously if new information arrives. Supplementary materials for this article are available online.     

Some Statistical Methods in Assessing Linear Relational Agreement: An Empirical Comparative Study

Although multiple indices were introduced in the area of agreement measurements, the only documented index for linear relational agreement, which is for interval scale data, is the Pearson product-moment correlation coefficient. Despite its meaningfulness, the Pearson product-moment correlation coefficient does not convey the practical information such as what proportion of observations is within a certain boundary of the target value. To address this need, based on the inverse regression, we proposed the adjusted mean squared deviation (AMSD), adjusted coverage probability (ACP), and adjusted total deviation index (ATDI) for the measurement of the relational agreement. They can serve as reasonable and practically meaningful measurements for relational agreement. Real life data are considered to illustrate the performance of the methods.     

Statistical Analysis of Uncertainties in Deterministic Computational Modeling – Application to Composite Process Resin Infusion Flow Model

Deterministic physics-based flow modeling provides an effective way to simulate and understand the resin flow infusion process in liquid composite molding processes and its variants. These are effective to provide optimal injection time and locations prior to gelation for given process parameters of resin viscosity and preform permeability. However, there could be significant variations in these two parameters during actual manufacturing. This paper presents simulation-based statistical analysis of uncertainties of these process parameters involved in the resin flow infusion. Two key process parameters, viscosity and permeability, and their statistical variations are examined individually and subsequently in combination for their impact on the associated injection time. Values from statistical probability distribution of the process parameters were employed to find the solution space for this engineering application through deterministic physics-based process flow modeling simulations. A bivariate confidence envelope was developed using the appropriate Cumulative Density Function for a 95% probability of successfully completing resin infusion prior to physical resin gelation time. A logistic regression model for the influence of resin viscosity and permeability on the binary response of successful resin infusion is presented and conforms well to the sensitivity analysis inferences.     

Statistical analysis of the Lomax–Logarithmic distribution

In this paper we introduce a three-parameter lifetime distribution following the Marshall and Olkin [New method for adding a parameter to a family of distributions with application to the exponential and Weibull families. Biometrika. 1997;84(3):641–652] approach. The proposed distribution is a compound of the Lomax and Logarithmic distributions (LLD). We provide a comprehensive study of the mathematical properties of the LLD. In particular, the density function, the shape of the hazard rate function, a general expansion for moments, the density of the rth order statistics, and the mean and median deviations of the LLD are derived and studied in detail. The maximum likelihood estimators of the three unknown parameters of LLD are obtained. The asymptotic confidence intervals for the parameters are also obtained based on asymptotic variance–covariance matrix. Finally, a real data set is analysed to show the potential of the new proposed distribution.     

Statistical considerations in bioequivalence of two area under the concentration–time curves obtained from serial sampling data

In this paper, we study the bioequivalence (BE) inference problem motivated by pharmacokinetic data that were collected using the serial sampling technique. In serial sampling designs, subjects are independently assigned to one of the two drugs; each subject can be sampled only once, and data are collected at K distinct timepoints from multiple subjects. We consider design and hypothesis testing for the parameter of interest: the area under the concentration–time curve (AUC). Decision rules in demonstrating BE were established using an equivalence test for either the ratio or logarithmic difference of two AUCs. The proposed t-test can deal with cases where two AUCs have unequal variances. To control for the type I error rate, the involved degrees-of-freedom were adjusted using Satterthwaite's approximation. A power formula was derived to allow the determination of necessary sample sizes. Simulation results show that, when the two AUCs have unequal variances, the type I error rate is better controlled by the proposed method compared with a method that only handles equal variances. We also propose an unequal subject allocation method that improves the power relative to that of the equal and symmetric allocation. The methods are illustrated using practical examples.     

Do antidepressants work? Statistical significance versus clinical benefits

Ours has been called the Prozac generation but, earlier this year, newspaper front page headlines screamed Antidepressants don't work. Our authors' reanalysis of drug trials was widely reported as implying that antidepressant drugs such as Prozac are overprescribed and useless. The truth, as Blair T. Johnson and Irving Kirsch explain, is more complex, and more interesting.     

Statistical Modeling for the Evaluation of Consumers’ Preferences

In 2009 a survey was performed in Veneto, a region in the north-east of Italy, to study the demand for wine and specifically for Passito, a typical Italian wine. The main goal of the study consisted in analyzing how the preferences and consumption habits of Passito vary depending on consumers’ characteristics. Specifically two kinds of statistical methods were applied: Covariate Uniform Binomial (CUB) model, a statistical approach for ordinal data to study the feeling toward Passito and the uncertainty of the respondents; classical logistic regression analysis, to describe how the attitude toward passito can be modeled as function of consumers’ covariates. Gender and residence were the most important covariates, useful in defining segments of consumers with significant differences in terms of Passito's preferences and consumption behavior. The logistic regression analysis allowed to complete the statistical analysis based on CUB models validating the results of the CUB model and estimating a model useful to predict the attitude toward the considered product for specific sub-groups of consumers.     

Statistical inference for α-series process with the inverse Gaussian distribution

Statistical inferences for the geometric process (GP) are derived when the distribution of the first occurrence time is assumed to be inverse Gaussian (IG). An α-series process, as a possible alternative to the GP, is introduced since the GP is sometimes inappropriate to apply some reliability and scheduling problems. In this study, statistical inference problem for the α-series process is considered where the distribution of first occurrence time is IG. The estimators of the parameters α, μ, and σ² are obtained by using the maximum likelihood (ML) method. Asymptotic distributions and consistency properties of the ML estimators are derived. In order to compare the efficiencies of the ML estimators with the widely used nonparametric modified moment (MM) estimators, Monte Carlo simulations are performed. The results showed that the ML estimators are more efficient than the MM estimators. Moreover, two real life datasets are given for application purposes.     

Combinatorics and Statistical Issues Related to the Kruskal–Wallis Statistic

We explore criteria that data must meet in order for the Kruskal–Wallis test to reject the null hypothesis by computing the number of unique ranked datasets in the balanced case where each of the m alternatives has n observations. We show that the Kruskal–Wallis test tends to be conservative in rejecting the null hypothesis, and we offer a correction that improves its performance. We then compute the number of possible datasets producing unique rank-sums. The most commonly occurring data lead to an uncommonly small set of possible rank-sums. We extend prior findings about row- and column-ordered data structures.     

Statistical analysis for Kumaraswamy’s distribution based on record data

In this paper we review some results that have been derived on record values for some well known probability density functions and based on m records from Kumaraswamy’s distribution we obtain estimators for the two parameters and the future sth record value. These estimates are derived using the maximum likelihood and Bayesian approaches. In the Bayesian approach, the two parameters are assumed to be random variables and estimators for the parameters and for the future sth record value are obtained, when we have observed m past record values, using the well known squared error loss (SEL) function and a linear exponential (LINEX) loss function. The findings are illustrated with actual and computer generated data.