JournalTOCs

METRON
Journal Prestige (SJR): 0.311

Citation Impact (citeScore): 1
Number of Followers: 2

Hybrid journal (It can contain Open Access articles)
ISSN (Print) 0026-1424 - ISSN (Online) 2281-695X
Published by Springer-Verlag

[2467 journals]

Simulation comparisons between Bayesian and de-biased estimators in
low-rank matrix completion
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  Abstract: Abstract In this paper, we study the low-rank matrix completion problem, a class of machine learning problems, that aims at the prediction of missing entries in a partially observed matrix. Such problems appear in several challenging applications such as collaborative filtering, image processing, and genotype imputation. We compare the Bayesian approaches and a recently introduced de-biased estimator which provides a useful way to build confidence intervals of interest. From a theoretical viewpoint, the de-biased estimator comes with a sharp minimax-optimal rate of estimation error whereas the Bayesian approach reaches this rate with an additional logarithmic factor. Our simulation studies show originally interesting results that the de-biased estimator is just as good as the Bayesian estimators. Moreover, Bayesian approaches are much more stable and can outperform the de-biased estimator in the case of small samples. In addition, we also find that the empirical coverage rate of the confidence intervals obtained by the de-biased estimator for an entry is absolutely lower than of the considered credible interval. These results suggest further theoretical studies on the estimation error and the concentration of Bayesian methods as they are quite limited up to present.
  PubDate: 2023-02-09
Multivariate gaussian processes: definitions, examples and applications
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  Abstract: Abstract Gaussian processes occupy one of the leading places in modern statistics and probability theory due to their importance and a wealth of strong results. The common use of Gaussian processes is in connection with problems related to estimation, detection, and many statistical or machine learning models. In this paper, we propose a precise definition of multivariate Gaussian processes based on Gaussian measures on vector-valued function spaces, and provide an existence proof. In addition, several fundamental properties of multivariate Gaussian processes, such as stationarity and independence, are introduced. We further derive two special cases of multivariate Gaussian processes, including multivariate Gaussian white noise and multivariate Brownian motion, and present a brief introduction to multivariate Gaussian process regression as a useful statistical learning method for multi-output prediction problems.
  PubDate: 2023-01-27
Theoretical evaluation of partial credit scoring of the multiple-choice
test item
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  Abstract: Abstract In multiple-choice tests, guessing is a source of test error which can be suppressed if its expected score is made negative by either penalizing wrong answers or rewarding expressions of partial knowledge. Starting from the most general formulation of the necessary and sufficient scoring conditions for guessing to lead to an expected loss beyond the test-taker’s knowledge, we formulate a class of optimal scoring functions, including the proposal by Zapechelnyuk (Econ. Lett. 132, 24–27 (2015)) as a special case. We then consider an arbitrary multiple-choice test taken by a rational test-taker whose knowledge of a test item is defined by the fraction of the answer options which can be ruled out. For this model, we study the statistical properties of the obtained score for both standard marking (where guessing is not penalized), and marking where guessing is suppressed either by expensive score penalties for incorrect answers or by different marking schemes that reward partial knowledge.
  PubDate: 2023-01-06
  DOI: 10.1007/s40300-022-00237-w
Non-parametric test of recurrent cumulative incidence functions for
competing risks models
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  Abstract: Abstract Recurrent competing risks data are common in survival studies. In such contexts the effects of competing risks on lifetime outcomes are important problem of study. In this work we introduce recurrent cumulative incidence function and then propose a non-parametric test for comparing recurrent cumulative incidence functions. Asymptotic distribution of the test statistic is derived. A simulation study is carried out to assess the performance of the proposed test statistic. The proposed method is applied to an auto-mobile warranty data.
  PubDate: 2022-12-01
  DOI: 10.1007/s40300-022-00228-x
A fair comparison of credible and confidence intervals: an example with
binomial proportions
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  Abstract: Abstract Comparison between confidence and credible intervals is complicated in view of their different nature: confidence intervals are random and credible intervals are numeric. A fair comparison should take this difference into account. Motivated by the similarity of a confidence interval proposed by Agresti and Coull (Am Stat 52:119–126, 1998) and a Bayesian credible interval based on a Beta(2,2) prior distribution for a Binomial proportion, we design algorithms where the comparison is conducted under the same paradigm, i.e., considering the Bayesian intervals (central and HPD) as realizations of random intervals and treating confidence intervals as numeric. In our example, intervals are compared via simulation studies that show a better performance of the Wilson (score) and HPD uniform prior intervals with some advantages of Bayesian intervals with respect to the expected and posterior length.
  PubDate: 2022-12-01
  DOI: 10.1007/s40300-021-00225-6
Integrated likelihood inference in multinomial distributions
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  Abstract: Abstract Consider a random vector \((N_1, N_2, \ldots , N_m)\) with a multinomial distribution such that \({{\,\textrm{E}\,}}\left( N_j ; \theta \right) = n p_j(\theta )\) , \( j=1, \ldots , m\) , where \(p_1, \cdots , p_m\) are known functions of an unknown d-dimensional parameter, satisfying \(p_1(\theta ) + \cdots + p_m(\theta ) = 1\) . This paper considers non-Bayesian likelihood inference for a real-valued parameter of interest \(\psi = g(\theta )\) , for a known function g, using an integrated likelihood function. The integrated likelihood function is constructed using the zero-score expectation (ZSE) parameter, proposed by Severini (Biometrika 94:529–524, 2007); thus, the integrated likelihood function has a number of important properties, such as approximate score- and information-unbiasedness. The methodology is illustrated on the problem of inference for the entropy of the distribution.
  PubDate: 2022-11-08
  DOI: 10.1007/s40300-022-00236-x
A weighted distance metric for assessing ranking dissimilarity and
inter-group heterogeneity
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  Abstract: Abstract In this paper, a weighted variant of the normalized pairwise angular distance metric is proposed. The inclusion of position weights aims at penalizing inversions in the top of the ranking more than inversions in the tail of the ranking. The performance of the proposed weighted distance metric for assessing ranking dissimilarity and its impact on a procedure for testing inter-group heterogeneity have been investigated via a Monte Carlo simulation study under several scenarios—differing for group size, number of ranked alternatives and system of hypotheses—and compared against those obtained for the unweighted variant.
  PubDate: 2022-08-01
  DOI: 10.1007/s40300-021-00198-6
Optimal forecasting accuracy using Lp-norm combination
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  Abstract: Abstract A well-known result in statistics is that a linear combination of two-point forecasts has a smaller Mean Square Error (MSE) than the two competing forecasts themselves (Bates and Granger in J Oper Res Soc 20(4):451–468, 1969). The only case in which no improvements are possible is when one of the single forecasts is already the optimal one in terms of MSE. The kinds of combination methods are various, ranging from the simple average (SA) to more robust methods such as the one based on median or Trimmed Average (TA) or Least Absolute Deviations or optimization techniques (Stock and Watson in J Forecast 23(6):405–430, 2004). Standard regression-based combination approaches may fail to get a realistic result if the forecasts show high collinearity in several situations or the data distribution is not Gaussian. Therefore, we propose a forecast combination method based on Lp-norm estimators. These estimators are based on the Generalized Error Distribution, which is a generalization of the Gaussian distribution, and they can be used to solve the cases of multicollinearity and non-Gaussianity. In order to demonstrate the potential of Lp-norms, we conducted a simulated and an empirical study, comparing its performance with other standard-regression combination approaches. We carried out the simulation study with different values of the autoregressive parameter, by alternating heteroskedasticity and homoskedasticity. On the other hand, the real data application is based on the daily Bitfinex historical series of bitcoins (2014–2020) and the 25 historical series relating to companies included in the Dow Jonson, were subsequently considered. We showed that, by combining different GARCH and the ARIMA models, assuming both Gaussian and non-Gaussian distributions, the Lp-norm scheme improves the forecasting accuracy with respect to other regression-based combination procedures.
  PubDate: 2022-08-01
  DOI: 10.1007/s40300-021-00218-5
Missing value or behaviour: how to increase the signal of social media
data
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  Abstract: Abstract Social media has become a widespread element of people’s everyday life, which is used to communicate and generate contents. Among the several ways to express a reaction to social media contents, the “Likes” are critical. Indeed, they convey preferences, which drive existing markets or allow the creation of new ones. Nevertheless, the appreciation indicators have some complex features, as for example the interpretation of the absence of “Likes”. In this case, the lack of approval may be considered as a specific behaviour. The present study aimed to define whether the absence of Likes may indicate the presence of a specific behaviour through the contextualization of the treatment of missing data applied to real cases. We provided a practical strategy for extracting more knowledge from social media data, whose synthesis raises several measurement problems. We proposed an approach based on the disambiguation of missing data in two modalities: “Dislike” and “Nothing”. Finally, a data pre-processing technique was suggested to increase the signal of social media data.
  PubDate: 2022-08-01
  DOI: 10.1007/s40300-021-00216-7
Plateau proposal distributions for adaptive component-wise multiple-try
metropolis
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  Abstract: Abstract Markov chain Monte Carlo (MCMC) methods are sampling methods that have become a commonly used tool in statistics, for example to perform Monte Carlo integration. As a consequence of the increase in computational power, many variations of MCMC methods exist for generating samples from arbitrary, possibly complex, target distributions. The performance of an MCMC method, in particular that of a Metropolis–Hastings MCMC method, is predominately governed by the choice of the so-called proposal distribution used. In this paper, we introduce a new type of proposal distribution for the use in Metropolis–Hastings MCMC methods that operates component-wise and with multiple trials per iteration. Specifically, the novel class of proposal distributions, called Plateau distributions, does not overlap, thus ensuring that the multiple trials are drawn from different regions of the state space. Furthermore, the Plateau proposal distributions allow for a bespoke adaptation procedure that lends itself to a Markov chain with efficient problem dependent state space exploration and favourable burn-in properties. Simulation studies show that our novel MCMC algorithm outperforms competitors when sampling from distributions with a complex shape, highly correlated components or multiple modes.
  PubDate: 2022-07-15
  DOI: 10.1007/s40300-022-00235-y
Robustness of lognormal confidence regions for means of symmetric positive
definite matrices when applied to mixtures of lognormal distributions
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  Abstract: Abstract Symmetric positive definite (SPD) matrices arise in a wide range of applications including diffusion tensor imaging (DTI), cosmic background radiation, and as covariance matrices. A complication when working with such data is that the space of SPD matrices is a manifold, so traditional statistical methods may not be directly applied. However, there are nonparametric procedures based on resampling for statistical inference for such data, but these can be slow and computationally tedious. Schwartzman (Int Stat Rev 84(3):456–486, 2016). introduced a lognormal distribution on the space of SPD matrices, providing a convenient framework for parametric inference on this space. Our goal is to check how robust confidence regions based on this distributional assumption are to a lack of lognormality. The methods are illustrated in a simulation study by examining the coverage probability of various mixtures of distributions.
  PubDate: 2022-05-26
  DOI: 10.1007/s40300-022-00234-z
Correction to: A multi-group higher-order factor analysis for studying the
gender-effect in Teacher Job Satisfaction
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  Abstract: A correction to this paper has been published: https://doi.org/10.1007/s40300-021-00209-6
  PubDate: 2022-04-01
  DOI: 10.1007/s40300-021-00209-6
The generalized Taguchi’s statistic: a passenger satisfaction
evaluation
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  Abstract: Abstract Judgments are usually expressed in ordinal scale and the main aim of this analysis is to identify characteristics that affect the satisfaction. Taguchi’s and Hirotsu’s statistics are simple alternatives to Pearson’s Chi-squared test for contingency tables with ordered categorical variables. A different approach is developed in this paper. In particular, a new measure of the association between a nominal explanatory variable and an ordered categorical response variable is introduced. The new measure is called Generalized Cumulative Chi-Squared Statistic (GCCS) and a class of GCCS-type statistics is also introduced. Moreover, a generalized singular value decomposition of GCCS is provided and an empirical study is developed. A study on the evaluation of the passengers’ satisfaction is performed on a strategy based on the conjoint use of the Generalized Taguchi’s statistic and the Logistic Model. An optimal combination of factors and levels has been obtained to improve service quality.
  PubDate: 2022-04-01
  DOI: 10.1007/s40300-021-00202-z
Analysis of ordinal and continuous longitudinal responses using pair
copula construction
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  Abstract: Abstract In this paper, we present a model based on pair copula construction for bivariate longitudinal mixed ordinal and continuous responses. The temporal association of each response is separately modeled using pair copula construction with a D-vine structure and the contemporaneous association of bivariate responses is then joined by a bivariate copula. We employ a sequential approach for inference and its performance is investigated by a simulation study. Moreover, the proposed model is applied to Peabody Individual Achievement Test (PIAT) dataset which examines the relationship between reading capability and antisocial behavior of children. The result is that, children with low levels of antisocial behavior have better reading ability than that of children with high levels of antisocial behavior.
  PubDate: 2022-03-23
  DOI: 10.1007/s40300-022-00231-2
Giovanni Maria Giorgi (1947–2021) OBITUARY
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  PubDate: 2022-03-17
  DOI: 10.1007/s40300-022-00232-1
Handling multicollinearity in quantile regression through the use of
principal component regression
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  Abstract: Abstract In many fields of applications, linear regression is the most widely used statistical method to analyze the effect of a set of explanatory variables on a response variable of interest. Classical least squares regression focuses on the conditional mean of the response, while quantile regression extends the view to conditional quantiles. Quantile regression is very convenient, whereas classical parametric assumptions do not hold and/or when relevant information lies in the tails and therefore the interest is in modeling the conditional distribution of the response at locations different from the mean. A situation common to most regression applications is the presence of strong correlations between predictors. This leads to the well-known problem of collinearity. While the effects of collinearity on least squares estimates are well investigated, this is not the case for quantile regression estimates. This paper aims to explore the collinearity problem in quantile regression. First, a simulation study analyses the problem concerning different degrees of collinearity and various response distributions. Then the paper proposes using regression on latent components as a possible solution to collinearity in quantile regression. Finally, a case study shows the assessment of the quality of service in the presence of highly correlated predictors.
  PubDate: 2022-02-16
  DOI: 10.1007/s40300-022-00230-3
Ordinal response variation of the polytomous Rasch model
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  Abstract: Abstract Polytomous Rasch model (PRM) is a general probabilistic measurement model widely used in psychometrics, social science and educational measurement. It describes the probability of certain ordinal response of an object under test as a function of its ability, given, so called thresholds, characterizing the specific test item. The model was also adapted to business and industry applications. In contrast to the behavior of the median PRM outcome value, monotonically increasing as the ability increases, the ordinal variation behavior, as shown in the article, can be very diverse and it is rather determined by the mutual position of the threshold values of the model. The article studies ordinal variation of the response vs. ability for different thresholds locations arrangements and different amounts of ordered response categories. It is shown under what circumstances this function becomes multimodal. If several objects are involved in the test, attention is paid to the possibility of the total variation decomposition into intra and inter components. Considering the intra object variation helps to avoid overestimation of the real variation between the tested objects as it is demonstrated by illustrative example.
  PubDate: 2022-02-03
  DOI: 10.1007/s40300-022-00229-w
On continuity correction for RSS-structured cluster randomized designs
with binary outcomes
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  Abstract: Abstract Correction for continuity is commonly used to improve the inference for binary data when the event of interest is rare or the sample size is small. A standard approach to reduce the bias in logit estimation is to add a small constant to both event and nonevent counts. The 0.5 adjustment is known as a correction rendering the estimation unbiased up to the order of \(K^{-1}\) , where K is the size of a simple random sample. However, for general designs beyond simple random sampling, the bias in estimating the logit is no longer zero in order \(K^{-1}\) . In this paper, we derive the formula of the correction factor that makes the first-order term of the bias vanish for general designs. We then apply it to estimate the logit when data are from ranked set sampling (RSS) embedded in a cluster randomized design (CRD). An RSS-structured CRD (RSS-CRD), introduced by Wang et al. (J Am Stat Assoc 111: 1576–1590, 2016), is a new two-stage design for more efficient estimation of treatment effect. We propose two methods to estimate the correction factors derived for RSS-CRDs. We numerically compare the proposed methods to those with the default factor 0.5 in terms of bias and mean squared error for estimating the treatment effect, and finally make recommendations to practitioners.
  PubDate: 2022-01-28
  DOI: 10.1007/s40300-021-00226-5
An EM algorithm for estimating the parameters of the multivariate
skew-normal distribution with censored responses
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  Abstract: Abstract Limited or censored data are collected in many studies. This occurs for many reasons in several practical situations, such as limitations in measuring equipment or from an experimental design. Consequently, the true value is recorded only if it falls within an interval range so that the responses can be either left, interval, or right-censored. Missing values can be seen just as a particular case. Linear and nonlinear regression models are routinely used to analyze these types of data. Most of these models are based on the normality assumption for the error term. However, such analyses might not provide robust inference when the normality assumption (or symmetry) is questionable. The need for asymmetric distributions for the random errors motivates us to develop a likelihood-based inference for linear models with censored responses based on the multivariate skew-normal distribution, where the missing/censoring mechanism is assumed to be “missing at random” (MAR). The proposed EM-type algorithm for maximum likelihood estimation uses closed-form expressions at the E-step based on formulas for the mean and variance of a truncated multivariate skew-normal distribution, available in the R package MomTrunc. Three datasets with censored and/or missing observations are analyzed and discussed.
  PubDate: 2022-01-28
  DOI: 10.1007/s40300-021-00227-4
The association in two-way ordinal contingency tables through global odds
ratios
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  Abstract: Abstract Hirotsu’s statistic is a suitable measure for studying the association between two variables on an ordinal scale. For visualizing the nature of the association, such a statistic can be decomposed by performing doubly ordered cumulative correspondence analysis. An alternative measure for describing the association between two ordered variables could be global odds ratios. In this paper we consider a generalization of the doubly ordered cumulative correspondence analysis in order to represent the global odds ratios in the two-dimensional plot.
  PubDate: 2021-11-23
  DOI: 10.1007/s40300-021-00224-7