Nikolai Gagunashvili
A self-contained Fortran-77 program for goodness of fit tests for histograms with weighted entries as well as with unweighted entries is presented. The code calculates test statistics for case of histogram with normalized weights of events and in case of unnormalized weights of events.
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Weighted histograms are used for the estimation of probability density functions. Computer simulation is the main domain of application of this type of histogram. A review of chi-square goodness of fit tests for weighted histograms is presented in this paper. Improvements are proposed to these tests that have size more close to its nominal value. Numerical examples are presented in this paper for evaluation of tests and to demonstrate various applications of tests.
Weighted histogram in Monte-Carlo simulations is often used for the estimation of a probability density function. It is obtained as a result of random experiment with random events that have weights. In this paper the bin contents of weighted histogram are considered as a sum of random variables with random number of terms. Goodness of fit tests for weighted histograms and for weighted histograms with unknown normalization are proposed. Sizes and powers of the tests are investigated numerically.
A self-contained Fortran-77 program for calculating test statistics to compare weighted histogram with unweighted histogram and two histograms with weighted entries is presented. The code calculates test statistics for cases of histograms with normalized weights of events and unnormalized weights of events.
A goodness-of-fit test for the logistic propensity score model under nonignorable missing data
本文提出了一种在非忽略缺失数据下用于逻辑倾向评分模型的拟合优度检验方法，通过构建未加权残差平方和并考虑结果的不完全可观测性，建立了检验统计量的渐近分布，并通过Bootstrap方法验证其有效性。
Two modifications of the chi square test for comparing usual(unweighted) and weighted histograms and two weighted histograms are proposed. Numerical examples illustrate an application of the tests for the histograms with different statistics of events. Proposed tests can be used for the comparison of experimental data histograms against simulated data histograms and two simulated data histograms.
In this paper we present a linear regression model for modal symbolic data. The observed variables are histogram variables according to the definition given in the framework of Symbolic Data Analysis and the parameters of the model are estimated using the classic Least Squares method. An appropriate metric is introduced in order to measure the error between the observed and the predicted distributions. In particular, the Wasserstein distance is proposed. Some properties of such metric are exploited to predict the response variable as direct linear combination of other independent histogram var…
The problem of testing the reliability of ensemble forecasting systems is revisited. A popular tool to assess the reliability of ensemble forecasting systems (for scalar verifications) is the rank histogram, this histogram is expected to be more or less flat, since for a reliable ensemble, the ranks are uniformly distributed among their possible outcomes. Quantitative tests for flatness (e.g.\ Pearson's goodness--of--fit test) have been suggested, without exception though, these tests assume the ranks to be a sequence of independent random variables, which is not the case in general as can be …
Weighted Extensions of the Kolmogorov-Smirnov, Cramer-von Mises, and Anderson-Darling Tests for Assessing Covariate Balance
研究针对因果推断中协变量平衡评估问题，扩展柯尔莫哥洛夫-斯米尔诺夫、克莱默-冯·米塞斯和安德森-达林检验以适应加权数据，通过共享程序控制I型错误，保留各检验优势，支持AD为通用默认方法，KS在特定情况有优势。
Maximum likelihood fits to data can be done using binned data (histograms) and unbinned data. With binned data, one gets not only the fitted parameters but also a measure of the goodness of fit. With unbinned data, currently, the fitted parameters are obtained but no measure of goodness of fit is available. This remains, to date, an unsolved problem in statistics. Using Bayes theorem and likelihood ratios, we provide a method by which both the fitted quantities and a measure of the goodness of fit are obtained for unbinned likelihood fits, as well as errors in the fitted quantities. We provide…
Maximum likelihood fits to data can be done using binned data (histograms) and unbinned data. With binned data, one gets not only the fitted parameters but also a measure of the goodness of fit. With unbinned data, currently, the fitted parameters are obtained but no measure of goodness of fit is available. This remains, to date, an unsolved problem in statistics. Using Bayes' theorem and likelihood ratios, we provide a method by which both the fitted quantities and a measure of the goodness of fit are obtained for unbinned likelihood fits, as well as errors in the fitted quantities. The quant…
In many analyses in high energy physics, attempts are made to remove the effects of detector smearing in data by techniques referred to as "unfolding" histograms, thus obtaining estimates of the true values of histogram bin contents. Such unfolded histograms are then compared to theoretical predictions, either to judge the goodness of fit of a theory, or to compare the abilities of two or more theories to describe the data. When doing this, even informally, one is testing hypotheses. However, a more fundamentally sound way to test hypotheses is to smear the theoretical predictions by simulatin…
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