Asta-Advances in Statistical Analysis最新文献

We analyze issues related to estimation and inference for the constrained sum of squares estimator (CSS) of the k-factor Gegenbauer autoregressive moving average (GARMA) model. We present theoretical results for the estimator and show that the parameters that determine the cycle lengths are asymptotically independent, converging at rate T, the sample size, for finite cycles. The remaining parameters lack independence and converge at the standard rate. Analogous with existing literature, some challenges exist for testing the hypothesis of non-cyclical long memory, since the associated parameter lies on the boundary of the parameter space. We present simulation results to explore small sample properties of the estimator, which support most distributional results, while also highlighting areas that merit additional exploration. We demonstrate the applicability of the theory and estimator with an application to IBM trading volume.

In this paper measures of interrater absolute agreement for quantitative measurements based on the standard deviation are proposed. Such indices allow (i) to overcome the limits affecting the intraclass correlation index; (ii) to measure the interrater agreement on single targets. Estimators of the proposed measures are introduced and their sampling properties are investigated for normal and non-normal data. Simulated data are employed to demonstrate the accuracy and practical utility of the new indices for assessing agreement. Finally, an application to assess the consistency of measurements performed by radiologists evaluating tumor size of lung cancer is presented.

Non-response is a major problem for anyone collecting and processing data. A commonly used technique to deal with missing data is imputation, where missing values are estimated and filled in into the dataset. Imputation can become challenging if the variable to be imputed has to comply with a known total. Even more challenging is the case where several variables in the same dataset need to be imputed and, in addition to known totals, logical restrictions between variables have to be satisfied. In our paper, we develop an approach for a broad class of imputation methods for multivariate categorical data such that previously published totals are preserved while logical restrictions on the data are satisfied. The developed approach can be used in combination with any imputation model that estimates imputation probabilities, i.e. the probability that imputation of a certain category for a variable in a certain unit leads to the correct value for this variable and unit.

Black box machine learning models are currently being used for high-stakes decision making in various parts of society such as healthcare and criminal justice. While tree-based ensemble methods such as random forests typically outperform deep learning models on tabular data sets, their built-in variable importance algorithms are known to be strongly biased toward high-entropy features. It was recently shown that the increasingly popular SHAP (SHapley Additive exPlanations) values suffer from a similar bias. We propose debiased or "shrunk" SHAP scores based on sample splitting which additionally enable the detection of overfitting issues at the feature level.

A family of consistent tests, derived from a characterization of the probability generating function, is proposed for assessing Poissonity against a wide class of count distributions, which includes some of the most frequently adopted alternatives to the Poisson distribution. Actually, the family of test statistics is based on the difference between the plug-in estimator of the Poisson cumulative distribution function and the empirical cumulative distribution function. The test statistics have an intuitive and simple form and are asymptotically normally distributed, allowing a straightforward implementation of the test. The finite sample properties of the test are investigated by means of an extensive simulation study. The test shows satisfactory behaviour compared to other tests with known limit distribution.

This paper uses independence-type characterizations to propose a class of test statistics which can be used for testing goodness-of-fit with several classes of null distributions. The resulting tests are consistent against fixed alternatives. Some limiting and small sample properties of the test statistics are explored. In comparison with common universal goodness-of-fit tests, the new tests exhibit better power for most of the alternatives considered, while in comparison with another characterization-based procedure, the new tests provide competitive or comparable power in various simulation settings. The handiness of the proposed tests is demonstrated through several real-data examples.

Despite the popularity of feature importance (FI) measures in interpretable machine learning, the statistical adequacy of these methods is rarely discussed. From a statistical perspective, a major distinction is between analysing a variable’s importance before and after adjusting for covariates—i.e., between marginal and conditional measures. Our work draws attention to this rarely acknowledged, yet crucial distinction and showcases its implications. We find that few methods are available for testing conditional FI and practitioners have hitherto been severely restricted in method application due to mismatched data requirements. Most real-world data exhibits complex feature dependencies and incorporates both continuous and categorical features (i.e., mixed data). Both properties are oftentimes neglected by conditional FI measures. To fill this gap, we propose to combine the conditional predictive impact (CPI) framework with sequential knockoff sampling. The CPI enables conditional FI measurement that controls for any feature dependencies by sampling valid knockoffs—hence, generating synthetic data with similar statistical properties—for the data to be analysed. Sequential knockoffs were deliberately designed to handle mixed data and thus allow us to extend the CPI approach to such datasets. We demonstrate through numerous simulations and a real-world example that our proposed workflow controls type I error, achieves high power, and is in-line with results given by other conditional FI measures, whereas marginal FI metrics can result in misleading interpretations. Our findings highlight the necessity of developing statistically adequate, specialized methods for mixed data.

The extreme value theory (EVT) encompasses a set of methods that allow inferring about the risk inherent to various phenomena in the scope of economic, financial, actuarial, environmental, hydrological, climatic sciences, as well as various areas of engineering. In many situations the clustering effect of high values may have an impact on the risk of occurrence of extreme phenomena. For example, extreme temperatures that last over time and result in drought situations, the permanence of intense rains leading to floods, stock markets in successive falls and consequent catastrophic losses. The extremal index is a measure of EVT associated with the degree of clustering of extreme values. In many situations, and under certain conditions, it corresponds to the arithmetic inverse of the average size of high-value clusters. The estimation of the extremal index generally entails two sources of uncertainty: the level at which high observations are considered and the identification of clusters. There are several contributions in the literature on the estimation of the extremal index, including methodologies to overcome the aforementioned sources of uncertainty. In this work we will revisit several existing estimators, apply automatic choice methods, both for the threshold and for the clustering parameter, and compare the performance of the methods. We will end with an application to meteorological data.

This paper proposes an M-quantile regression approach to address the heterogeneity of the housing market in a modern European city. We show how M-quantile modelling is a rich and flexible tool for empirical market price data analysis, allowing us to obtain a robust estimation of the hedonic price function whilst accounting for different sources of heterogeneity in market prices. The suggested methodology can generally be used to analyse nonlinear interactions between prices and predictors. In particular, we develop a spatial semiparametric M-quantile model to capture both the potential nonlinear effects of the cultural environment on pricing and spatial trends. In both cases, nonlinearity is introduced into the model using appropriate bases functions. We show how the implicit price associated with the variable that measures cultural amenities can be determined in this semiparametric framework. Our findings show that the effect of several housing attributes and urban amenities differs significantly across the response distribution, suggesting that buyers of lower-priced properties behave differently than buyers of higher-priced properties.

Many real-life data sets can be analyzed using linear mixed models (LMMs). Since these are ordinarily based on normality assumptions, under small deviations from the model the inference can be highly unstable when the associated parameters are estimated by classical methods. On the other hand, the density power divergence (DPD) family, which measures the discrepancy between two probability density functions, has been successfully used to build robust estimators with high stability associated with minimal loss in efficiency. Here, we develop the minimum DPD estimator (MDPDE) for independent but non-identically distributed observations for LMMs according to the variance components model. We prove that the theoretical properties hold, including consistency and asymptotic normality of the estimators. The influence function and sensitivity measures are computed to explore the robustness properties. As a data-based choice of the MDPDE tuning parameter (alpha) is very important, we propose two candidates as “optimal” choices, where optimality is in the sense of choosing the strongest downweighting that is necessary for the particular data set. We conduct a simulation study comparing the proposed MDPDE, for different values of (alpha), with S-estimators, M-estimators and the classical maximum likelihood estimator, considering different levels of contamination. Finally, we illustrate the performance of our proposal on a real-data example.