Statistical Papers最新文献

High placebo responses could significantly reduce the treatment effect in a parallel randomized trial. To combat that challenge, several approaches were developed, including the sequential parallel comparison design (SPCD) that was shown to increase the statistical power as compared to the traditional randomized trial. A linear combination of the response rate differences from two phases per the SPCD is commonly used to measure the overall treatment effect size. The traditional approach to calculate the confidence interval for the overall rate difference is based on the delta method using the variance–covariance matrix of all outcomes. As outcomes from a multinomial distribution are correlated, we suggest utilizing a constrained variance–covariance matrix in the delta method. In the observation of anti-conservative coverages from asymptotic intervals, we further propose using importance sampling to develop accurate intervals. Simulation studies show that accurate intervals have better coverage probabilities than others and the interval width of accurate intervals is similar to the interval width of others. Two real trials to treat major depressive disorder are used to illustrate the application of the proposed intervals.

Using statistical methods to analyze data requires considering the data set to be randomly generated from a probability distribution that is unknown but idealized according to a mathematical model consisting of constraints, assumptions about the distribution. Since the choice of such a model is up to the scientist, there is an understandable bias toward choosing models that make scientific conclusions appear more certain than they really are. There is a similar bias in the scientist’s choice of whether to use Bayesian or frequentist methods. This article provides tools to mitigate both of those biases on the basis of a principle of information theory. It is found that the same principle unifies Bayesianism with the fiducial version of frequentism. The principle arguably overcomes not only the main objections against fiducial inference but also the main Bayesian objection against the use of confidence intervals.

Analysis of binary matched pairs data is problematic due to infinite maximum likelihood estimates of the log odds ratio and potentially biased estimates, especially for small samples. We propose a penalised version of the log-likelihood function based on adjusted responses which always results in a finite estimator of the log odds ratio. The probability limit of the adjusted log-likelihood estimator is derived and it is shown that in certain settings the maximum likelihood, conditional and modified profile log-likelihood estimators drop out as special cases of the former estimator. We implement indirect inference to the adjusted log-likelihood estimator. It is shown, through a complete enumeration study, that the indirect inference estimator is competitive in terms of bias and variance in comparison to the maximum likelihood, conditional, modified profile log-likelihood and Firth’s penalised log-likelihood estimators.

In this short note, we reevaluate the run-length performance of the EWMA and exponentiated EWMA (Exp-EWMA) charts using the conditional expected delay metric. It is found that the enhancements offered by the Exp-EWMA chart over the EWMA chart in the zero-state setup are marginal. Given its simplicity in implementation and its ability to encompass the functionality of the Exp-EWMA chart in detecting delayed shifts in the process mean, the EWMA chart remains the preferred choice over the Exp-EWMA chart.

The symbolic partitioning of the Pearson chi-square statistic with unequal cell probabilities into asymptotically independent component tests is revisited. We introduce Hadamard-like matrices whose resulting component tests compares the full vector of cell counts. This contributes to making these component tests intuitively interpretable. We present a simple way to construct the Hadamard-like matrices when the number of cell counts is 2, 4 or 8 without assuming any relations between cell probabilities. For higher powers of 2, the theory of orthogonal designs is used to set a priori relations between cell probabilities, in order to establish the construction. Simulations are given to illustrate the sensitivity of various components to changes in location, scale, skewness and tail probability, as well as to illustrate the potential improvement in power when the cell probabilities are changed.

Similar to usual lower records, Bottom-(k)-lists (Kozan and Tanil, İstatistik J Turk Stat Assoc 13:73–79, 2013) have a wide range of practical applications in meteorology, hydrology, sports, etc. Also, exceedance statistics can be viewed as a close relative to tolerance limits—an important field of statistical science. In this study, an idea of combining these two important subjects together is studied and an exceedance statistic is defined based on bottom-(k)-lists in an independent and identically distributed (iid) continuous random sequence. Probability mass function (pmf) of a selected exceedance statistic is obtained. Also, an illustrative application of the exceedance statistic is given.

In analyzing bivariate data sets, data with common observations are frequently encountered and, in this case, existing absolutely continuous bivariate distributions are not applicable. Only a few models, such as the bivariate distribution proposed by Marshall and Olkin (J Am Stat Assoc 62(317):30–44, 1967), have been developed to model such data sets and the choice of models to fit data sets having common observations is very limited. In this paper, three general classes of bivariate distributions for modeling data with common observations are developed. To develop the bivariate distributions, we employ a probability model in reliability. Considering a system with two components, it is assumed that, when the first failure of the components occurs, with some probability, it immediately causes the failure of the remaining component, and, with complementary probability, the residual lifetime of the remaining component is shortened according to some stochastic order. It will be shown that, by specifying the underlying distributions contained in the joint distribution, numerous families of bivariate distributions can be generated. Therefore, this work provides substantially increased flexibility in modeling data sets with common observations. The developed models are fitted to two real-life data sets and it is shown that these models outperform the existing models in terms of fitting performance and their performances are satisfactory.

We consider the Hotelling (T^2) test in low sample size, high dimensional setting. We partition the p variables into (b>1) blocks of p/b variables and use the union-intersection principle to propose a testing procedure that computes the (T^2) test in each block. We show that the proposed method is more powerful than Hotelling (T^2) test. We also consider Wilks method of outlier detection and use the union-intersection principle to search for outliers in blocks of variables. The significance level and the power function of the new test are investigated. We show that the new outlier detection method produces more power compared to Wilks test.

The problem of linearly predicting a scalar response Y from a functional (random) explanatory variable (X=X(t), tin I) is considered. It is argued that the term “linearly” can be interpreted in several meaningful ways. Thus, one could interpret that (up to a random noise) Y could be expressed as a linear combination of a finite family of marginals (X(t_i)) of the process X, or a limit of a sequence of such linear combinations. This simple point of view (which has some precedents in the literature) leads to a formulation of the linear model in terms of the RKHS space generated by the covariance function of the process X(t). It turns out that such RKHS-based formulation includes the standard functional linear model, based on the inner product in the space (L^2[0,1]), as a particular case. It includes as well all models in which Y is assumed to be (up to an additive noise) a linear combination of a finite number of linear projections of X. Some consistency results are proved which, in particular, lead to an asymptotic approximation of the predictions derived from the general (functional) linear model in terms of finite-dimensional models based on a finite family of marginals (X(t_i)), for an increasing grid of points (t_j) in I. We also include a discussion on the crucial notion of coefficient of determination (aimed at assessing the fit of the model) in this setting. A few experimental results are given.

Additive partial linear models with symmetric autoregressive errors of order p are proposed in this paper for modeling time series data. Specifically, we apply this model class to explain the weekly hospitalization for respiratory diseases in Sorocaba, São Paulo, Brazil, by incorporating climate and pollution as covariates, trend and seasonality. The main feature of this model class is its capability of considering a set of explanatory variables with linear and nonlinear structures, which allows, for example, to model jointly trend and seasonality of a time series with additive functions for the nonlinear explanatory variables and a predictor to accommodate discrete and linear explanatory variables. Additionally, the conditional symmetric errors allow the possibility of fitting data with high correlation order, as well as error distributions with heavier or lighter tails than the normal ones. We present the model class and a novel iterative process is derived by combining a P-GAM type algorithm with a quasi-Newton procedure for the parameter estimation. The inferential results, diagnostic procedures, including conditional quantile residual analysis and local influence analysis for sensitivity, are discussed. Simulation studies are performed to assess finite sample properties of parametric and nonparametric estimators. Finally, the data set analysis and concluding remarks are given.