The Mean Squared Error of the Generalized Ridge Regression Estimator and the Orientation of β

Newhouse and Oman (1971) identified the orientations with respect to the eigenvectors of X'X of the true coefficient vector of the linear regression model for which the ordinary ridge regression estimator performs best and performs worse when mean squared error is the measure of performance. In this paper the corresponding result is derived for generalized ridge regression for two risk functions: mean squared error and mean squared error of prediction.     

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.     

Estimating the Parameters of the Generalized Lambda Distribution: Which Method Performs Best?

Generalized lambda distribution (GLD) is a flexible distribution that can represent a wide variety of distributional shapes. This property of the GLD has made it very popular in simulation input modeling in recent years, and several fitting methods for estimating the parameters of the GLD have been proposed. Nevertheless, there appears to be a lack of insights about the performances of these fitting methods in estimating the parameters of the GLD for a variety of distributional shapes and input data. Our primary goal in this article is to compare the goodness-of-fits of the popular fitting methods in estimating the parameters of the GLD introduced in Freimer et al. (1988 Freimer, M., Mudholkar, G., Kollia, G., Lin, C. (1988). A study of the Generalized Tukey Lambda family. Communications in Statistics-Theory and Methods 17:3547–3567.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]), i.e., Freimer–Mudholkar–Kollia–Lin (FMKL) GLD, and provide guidelines to the simulation practitioner about when to use each method. We further describe the use of the genetic algorithm for the FMKL GLD, and investigate the performances of the suggested methods in modeling the daily exchange rates of eight currencies.     

Measurement error correction for the cumulative average model in the survival analysis of nutritional data: application to Nurses’ Health Study

The use of the cumulative average model to investigate the association between disease incidence and repeated measurements of exposures in medical follow-up studies can be dated back to the 1960s (Kahn and Dawber, J Chron Dis 19:611–620, 1966). This model takes advantage of all prior data and thus should provide a statistically more powerful test of disease-exposure associations. Measurement error in covariates is common for medical follow-up studies. Many methods have been proposed to correct for measurement error. To the best of our knowledge, no methods have been proposed yet to correct for measurement error in the cumulative average model. In this article, we propose a regression calibration approach to correct relative risk estimates for measurement error. The approach is illustrated with data from the Nurses’ Health Study relating incident breast cancer between 1980 and 2002 to time-dependent measures of calorie-adjusted saturated fat intake, controlling for total caloric intake, alcohol intake, and baseline age.     

Deterministic Evolution of Strength in Multiple Comparisons Models: Who is the Greatest Golfer?

We present a statistical methodology for fitting time‐varying rankings, by estimating the strength parameters of the Plackett–Luce multiple comparisons model at regularly spaced times for each ranked item. We use the little‐known method of barycentric rational interpolation to interpolate between the strength parameters so that a competitor's strength can be evaluated at any time. We chose the time‐varying strengths to evolve deterministically rather than stochastically, a preference that we reason often has merit. There are many statistical and computational problems to overcome on fitting anything beyond ‘toy’ data sets. The methodological innovations here include a method for maximizing a likelihood function for many parameters, approximations for modelling tied data and an approach to the elimination of secular drift of the estimated ‘strengths’. The methodology has obvious applications to fields such as marketing, although we demonstrate our approach by analysing a large data set of golf tournament results, in search of an answer to the question ‘who is the greatest golfer of all time?’     

Authors’ responses to the discussion on “Predicting losses of residential structures in the state of Florida by the Public Hurricane Loss Evaluation Model”

Hurricanes threaten the Florida coast line every year and are capable of causing catastrophic losses. The Public Hurricane Loss Model was developed in response to the need for having an open transparent model to predict the above losses. The results were summarized in the paper “Predicting Losses of Residential Structures in the State of Florida by the Public Hurricane Loss Model” which was subsequently a subject of discussion by experts in Meteorology, Engineering, Actuarial Sciences and Statistics. The present paper presents a response to the discussions on the above mentioned article.     

Ridge Regression and Generalized Maximum Entropy: An improved version of the Ridge–GME parameter estimator

In this article, the Ridge–GME parameter estimator, which combines Ridge Regression and Generalized Maximum Entropy, is improved in order to eliminate the subjectivity in the analysis of the ridge trace. A serious concern with the visual inspection of the ridge trace to define the supports for the parameters in the Ridge–GME parameter estimator is the misinterpretation of some ridge traces, in particular where some of them are very close to the axes. A simulation study and two empirical applications are used to illustrate the performance of the improved estimator. A MATLAB code is provided as supplementary material.     

Principles and analysis of hematopoietic stem cell transplantation outcomes: the physician’s perspective

Hematopoietic stem cell transplantation (HSCT) is used widely for the treatment of malignant and non-malignant diseases. Advances in transplantation strategies such as modifications to existing transplant-conditioning regimens to lower morbidity and mortality, use of alternative donors and grafts, supportive care including graft-versus-host disease prophylaxis and antimicrobial therapy have led to increasing numbers of HSCT being performed. The procedure is now available to children, young and older adults with an ever increasing number of survivors from this procedure. Analysis of outcomes after HSCT giving consideration to existing strategies warrants using appropriate statistical methodology. This is critical not only in documenting the current success of HSCT but to plan future strategies to optimize accessibility to HSCT, donor and graft choices, patient selection, counsel potential HSCT candidates and long-term survivors and plan intervention trials for these persons. We describe concepts and principles of HSCT to better understand the complexities associated with outcome analysis.     

Authors’ response: on the role of data,statistics and decisions in a pandemic

AStA Advances in Statistical Analysis -     

Comparisons of the <Emphasis Type=Italic>r</Emphasis> − <Emphasis Type=Italic>k</Emphasis> class estimator to the ordinary least squares estimator under the Pitman’s closeness criterion

In the presence of multicollinearity, the r − k class estimator is proposed as an alternative to the ordinary least squares (OLS) estimator which is a general estimator including the ordinary ridge regression (ORR), the principal components regression (PCR) and the OLS estimators. Comparison of competing estimators of a parameter in the sense of mean square error (MSE) criterion is of central interest. An alternative criterion to the MSE criterion is the Pitman’s (1937) closeness (PC) criterion. In this paper, we compare the r − k class estimator to the OLS estimator in terms of PC criterion so that we can get the comparison of the ORR estimator to the OLS estimator under the PC criterion which was done by Mason et al. (1990) and also the comparison of the PCR estimator to the OLS estimator by means of the PC criterion which was done by Lin and Wei (2002).     

Integration of model-based recursive partitioning with bias reduction estimation: a case study assessing the impact of Oliver’s four factors on the probability of winning a basketball game

AStA Advances in Statistical Analysis - In this contribution, we investigate the importance of Oliver’s Four Factors, proposed in the literature to identify a basketball team’s...     

On estimating the distribution of data envelopment analysis efficiency scores: an application to nursing homes’ care planning process

Data envelopment analysis (DEA) is a deterministic econometric model for calculating efficiency by using data from an observed set of decision-making units (DMUs). We propose a method for calculating the distribution of efficiency scores. Our framework relies on estimating data from an unobserved set of DMUs. The model provides posterior predictive data for the unobserved DMUs to augment the frontier in the DEA that provides a posterior predictive distribution for the efficiency scores. We explore the method on a multiple-input and multiple-output DEA model. The data for the example are from a comprehensive examination of how nursing homes complete a standardized mandatory assessment of residents.