Econometric Issues To Consider and Model Selection for Some Hypothesis Tests

Insurance loss data are usually in the form of left-truncation and right-censoring due to deductibles and policy limits, respectively. This paper investigates the model uncertainty and selection procedure when various parametric models are constructed to accommodate such left-truncated and right-censored data. The joint asymptotic properties of the estimators have been established using the Delta method along with Maximum Likelihood Estimation when the model is specified. We conduct the simulation studies using Fisk, Lognormal, Lomax, Paralogistic, and Weibull distributions with various proportions of loss data below deductibles and above policy limits. A variety of graphic tools, hypothesis tests, and penalized likelihood criteria are employed to validate the models, and their performances on the model selection are evaluated through the probability of each parent distribution being correctly selected. The effectiveness of each tool on model selection is also illustrated using well-studied data that represent Wisconsin property losses in the United States from 2007 to 2010.

In order to have confidence in model-based phylogenetic analysis, the model of nucleotide substitution adopted must be selected in a statistically rigorous manner. Several model-selection methods are applicable to maximum likelihood (ML) analysis, including the hierarchical likelihood-ratio test (hLRT), Akaike information criterion (AIC), Bayesian information criterion (BIC), and decision theory (DT), but their performance relative to empirical data has not been investigated thoroughly. In this study, we use 250 phylogenetic data sets obtained from TreeBASE to examine the effects that choice in model selection has on ML estimation of phylogeny, with an emphasis on optimal topology, bootstrap support, and hypothesis testing. We show that the use of different methods leads to the selection of two or more models for approximately 80% of the data sets and that the AIC typically selects more complex models than alternative approaches. Although ML estimation with different best-fit models results in incongruent tree topologies approximately 50% of the time, these differences are primarily attributable to alternative resolutions of poorly supported nodes. Furthermore, topologies and bootstrap values estimated with ML using alternative statistically supported models are more similar to each other than to topologies and bootstrap values estimated with ML under the Kimura two-parameter (K2P) model or maximum parsimony (MP). In addition, Swofford-Olsen-Waddell-Hillis (SOWH) tests indicate that ML trees estimated with alternative best-fit models are usually not significantly different from each other when evaluated with the same model. However, ML trees estimated with statistically supported models are often significantly suboptimal to ML trees made with the K2P model when both are evaluated with K2P, indicating that not all models perform in an equivalent manner. Nevertheless, the use of alternative statistically supported models generally does not affect tests of monophyletic relationships under either the Shimodaira-Hasegawa (S-H) or SOWH methods. Our results suggest that although choice in model selection has a strong impact on optimal tree topology, it rarely affects evolutionary inferences drawn from the data because differences are mainly confined to poorly supported nodes. Moreover, since ML with alternative best-fit models tends to produce more similar estimates of phylogeny than ML under the K2P model or MP, the use of any statistically based model-selection method is vastly preferable to forgoing the model-selection process altogether.

기존의 frequentist 추론에 비해 Bayesian 추론에서의 가설 검정 및 모형 선택 문제는 학자들 간에 일치된 견해를 보이지 못하고 있으며 아직도 논란이 되는 것들이 많다. Bayesian 추론에서 가설 검정 및 모형 선택의 기준으로 널리 쓰이는 Bayes factor는 이해하기 쉬우나 여러 경우에 구하기 어려운 단점이 존재한다. 그 외에 다른 기준으로 Spiegelhalter 등 (2002)가 제시한 DIC(Deviance Information Criterion)과 frequentist 추론에서의 P-value에 대비되는 Bayesian P-value가 있다. 본 논문에서는 Swiss banknote 자료를 Bayesian 로지스틱 회귀모형으로 분석하고 관련 기준들을 구하여 각 기준들이 일관성 있는 결론을 보이는지 확인하고자 한다. Model selection and hypothesis testing problems in Bayesian inference are still debated between scholars. Bayesian factors traditionally used as a criterion in Bayesian hypothesis testing and model selection, are easy to understand but sometimes hard to compute. In addition, there are other model selection criterions such as DIC(Deviance Information Criterion) by Spiegelhalter et al. (2002) and Bayesian P-values for testing. In this paper, we briefly introduce the Bayesian hypothesis testing and model selection procedure. In addition we have applied a Bayesian inference to Swiss banknote data by a fitting logistic regression model and computing several test statistics to see if they provide consistent results.

Model selection is an omnipresent problem in signal processing applications. The Akaike information criterion (AIC) and the Bayesian information criterion (BIC) are the most commonly used solutions to this problem. These criteria have been found to have satisfactory performance in many cases and had a dominant role in the model selection literature since their introduction several decades ago, despite numerous attempts to dethrone them. Model selection can be viewed as a multiple hypothesis testing problem. This simple observation makes it possible to use for model selection a number of powerful hypothesis testing procedures that control the false discovery rate (FDR) or the familywise error rate (FER). This is precisely what we do in this paper in which we follow the lead of the proposers of the said procedures and introduce two <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">general</i> rules for model selection based on FDR and FER, respectively. We show in a numerical performance study that the FDR and FER rules are serious competitors of AIC and BIC with significant performance gains in more demanding cases, essentially at the same computational effort.

In many engineering disciplines the interesting model parameters are estimated from a large number of heterogeneous and redundant observations by a least-squares adjustment. The significance of the model parameters, outlier detection and the model selection itself are checked within statistical hypothesis tests. The acceptance and the rejection of the hypothesis are strongly related with two types of errors. A type I error occurs if the null hypothesis is rejected, although it is true. A type II error occurs if the null hypothesis is accepted, although it is false. This paper proposes a general procedure to hypothesis testing in linear parameter estimation, if the uncertainty is considered by random variability and interval/fuzzy errors. The study focuses on the probability of type I and type II errors. The applied procedure is outlined in detail showing both theory and numerical examples for the parameterisation of a geodetic monitoring network (deformation analysis).

Geodetic deformation analysis can be interpreted as a model selection problem. The null model indicates that no deformation has occurred. It is opposed to a number of alternative models, which stipulate different deformation patterns. A common way to select the right model is the usage of a statistical hypothesis test. However, since we have to test a series of deformation patterns, this must be a multiple test. As an alternative solution for the test problem, we propose the p-value approach. Another approach arises from information theory. Here, the Akaike information criterion (AIC) or some alternative is used to select an appropriate model for a given set of observations. Both approaches are discussed and applied to two test scenarios: A synthetic levelling network and the Delft test data set. It is demonstrated that they work but behave differently, sometimes even producing different results. Hypothesis tests are well-established in geodesy, but may suffer from an unfavourable choice of the decision error rates. The multiple test also suffers from statistical dependencies between the test statistics, which are neglected. Both problems are overcome by applying information criterions like AIC.

Teaching and learning process to determine student learning outcomes requires the selection of appropriate learning models so that it can provide maximum learning impact. This study aims to determine the effectiveness of better learning models for the ability to understand mathematical concepts. This type of research is quantitative using the Quasi-experimental design method. Data collection in this study uses a description test with the type of questions based on indicators of mathematical concept understanding ability. Hypothesis testing uses a non-correlated 2-sample t test with decisions taken through the left-side test. This shows that the Flipped Classroom learning model is more effective than the Auditory Intellectually Repetition learning model in influencing students' mathematical concepts

Comparing Distributions refers to the statistical data analysis that encompasses the traditional goodness-of-fit testing. Whereas the latter includes only formal statistical hypothesis tests for the one-sample and the K-sample problems, this book presents a more general and informative treatment by also considering graphical and estimation methods. A procedure is said to be informative when it provides information on the reason for rejecting the null hypothesis. Despite the historically seemingly different development of methods, this book emphasises the similarities between the methods by linking them to a common theory backbone. This book consists of two parts. In the first part statistical methods for the one-sample problem are discussed. The second part of the book treats the K-sample problem. Many sections of this second part of the book may be of interest to every statistician who is involved in comparative studies. The book gives a self-contained theoretical treatment of a wide range of goodness-of-fit methods, including graphical methods, hypothesis tests, model selection and density estimation. It relies on parametric, semiparametric and nonparametric theory, which is kept at an intermediate level; the intuition and heuristics behind the methods are usually provided as well. The book contains many data examples that are analysed with the cd R-package that is written by the author. All examples include the R-code. Because many methods described in this book belong to the basic toolbox of almost every statistician, the book should be of interest to a wide audience. In particular, the book may be useful for researchers, graduate students and PhD students who need a starting point for doing research in the area of goodness-of-fit testing. Practitioners and applied statisticians may also be interested because of the many examples, the R-code and the stress on the informative nature of the procedures.

When using maximum likelihood methods to estimate genetic and environmental components of (co)variance, it is common to test hypotheses using likelihood ratio tests, since such tests have desirable asymptotic properties. In particular, the standard likelihood ratio test statistic is assumed asymptotically to follow a χ2distribution with degrees of freedom equal to the number of parameters tested. Using the relationship between least squares and maximum likelihood estimators for balanced designs, it is shown why the asymptotic distribution of the likelihood ratio test for variance components does not follow a χ2distribution with degrees of freedom equal to the number of parameters tested when the null hypothesis is true. Instead, the distribution of the likelihood ratio test is a mixture of χ2distributions with different degrees of freedom. Implications for testing variance components in twin designs and for quantitative trait loci mapping are discussed. The appropriate distribution of the likelihood ratio test statistic should be used in hypothesis testing and model selection.

This chapter covers the discussions of model selection tests in empirical asset pricing models with the asymptotic properties developed in Chap. 4. In particular, model selection with forward selection for variables in empirical asset pricing models is introduced. The purpose of this chapter is to consider the sequential model search where model selection tests (or criteria) with additional asymptotic properties for common factors of asset returns are used. Differing from the other empirical studies, the emphasis is on the cross-sectional commonality of these presumed variables or factors when the asset returns are projected onto these variables. Given that the underlying intrinsic mechanism of asset returns is unknown, the sequential model search is to pursue the optimality in approximation that the basic requirement for these presumed variables or factors will satisfy the coherence condition where cross-sectional dependence is persistent.

Consider the simple normal linear regression model for estimation/prediction at a new design point. When the slope parameter is not obviously nonzero, hypothesis testing and information criteria can be used for identifying the right model. We compare the performances of such methods both theoretically and empirically from different perspectives for more insight. The testing approach at the conventional size of 0.05, in spite of being the “standard approach,” performs poorly in estimation. We also found that the frequently told story “the Bayesian information criterion (BIC) is good when the true model is finite-dimensional, and the Akaike information criterion (AIC) is good when the true model is infinite-dimensional” is far from being accurate. In addition, despite some successes in the effort to go beyond the debate between AIC and BIC by adaptive model selection, it turns out that it is not possible to share the pointwise adaptation property of BIC and the minimax-rate adaptation property of AIC by any model selection method. When model selection methods have difficulty in selection, model combining is a better alternative in terms of estimation accuracy.This work was completed when the author was on leave from Iowa State University and was a New Direction Visiting Professor at the Institute for Mathematics and its Applications (IMA) at the University of Minnesota. The fundings from both IMA and ISU are greatly appreciated. The work was also partly supported by NSF CAREER grant DMS0094323. The author thanks Xiaotong Shen and Hannes Leeb for very helpful discussions. The paper also benefited from the questions and comments from the participants at the statistics seminars the author gave at the University of Minnesota and Duke University. The author is very grateful to the anonymous reviewers and the co-editor Benedikt Potscher for carefully reading earlier versions of the paper, bringing my attention to several closely related previous and current results, and making many very valuable suggestions, which significantly improved the paper in both content and presentation.

Application of a sigmoid E max model is described for the assessment of dose-response with designs containing a small number of doses (typically, three to six). The expanded model is a common E max model with a power (Hill) parameter applied to dose and the ED 50 parameter. The model will be evaluated following a strategy proposed by Bretz et al. (2005). The sigmoid E max model is used to create several contrasts that have high power to detect an increasing trend from placebo. Alpha level for the hypothesis of no dose-response is controlled using multiple comparison methods applied to the p-values obtained from the contrasts. Subsequent to establishing drug activity, Bayesian methods are used to estimate the dose-response curve from the sparse dosing design. Bayesian estimation applied to the sigmoid model represents uncertainty in model selection that is missed when a single simpler model is selected from a collection of non-nested models. The goal is to base model selection on substantive knowledge and broad experience with dose-response relationships rather than criteria selected to ensure convergence of estimators. Bayesian estimation also addresses deficiencies in confidence intervals and tests derived from asymptotic-based maximum likelihood estimation when some parameters are poorly determined, which is typical for data from common dose-response designs.

Aims: This study investigates whether corporate social responsibility (CSR) mediates the effect of firm reputation on firm value in publicly listed companies in Indonesia. Study Design: This study adopts a quantitative descriptive approach employing a panel data regression design to analyze the effect of firm reputation on firm value and to examine the mediating role of Corporate Social Responsibility (CSR) activities. Statistical analyses were conducted using secondary data derived from publicly available reports. This methodological approach was chosen to ensure a rigorous examination of causal relationships across firms and over time, enhancing both internal validity and generalizability. The sample was selected using a purposive sampling technique based on specific criteria: (1) companies that consistently published annual and sustainability reports (CSR disclosures) during the observation period; (2) firms providing complete data for the variables of firm reputation. Firm reputation is proxied by brand image (awards and recognition) and Big-4 auditor affiliation, while firm value is measured using Economic Value Added (EVA). CSR is measured using a CSR disclosure score, which represents an index calculated as the ratio between the number of items disclosed by the company and the total number of items required to be disclosed. Control variables include Return on Assets (ROA) and firm size. Applying these criteria resulted in a final sample of 51 companies, yielding 306 firm-year observations included in the empirical analysis. Place and Duration of Study: This study examines companies listed on the Indonesia Stock Exchange (IDX) over a six year period, spanning from 2017 to 2022. Methodology: This study employed a panel data regression approach using observations from 51 firms over six years. The analysis began with descriptive statistics to capture the general characteristics of all variables. Model selection was then conducted through the Chow, Hausman, and Lagrange Multiplier (LM) tests to determine the most suitable estimation model. Afterward, hypothesis testing was performed to evaluate the relationships among variables, followed by a Sobel test to examine the mediating role of Corporate Social Responsibility (CSR) in linking firm reputation and firm value. Results: Empirical findings indicate that corporate reputation has a positive and significant influence on firm value (EVA). Furthermore, corporate reputation exhibits a significant influence on the level of Corporate Social Responsibility (CSR) disclosure, while CSR itself significantly increases firm value. Mediation analysis using the Sobel test confirms that CSR acts as a statistically significant mediator in the relationship between corporate reputation and firm value. These findings suggest that CSR serves as a strategic translation mechanism through which reputation assets are converted into economic value, underscoring the important role of CSR in linking intangible reputation factors to tangible financial performance among public companies in Indonesia. Conclusion: Corporate reputation has a significant positive effect on corporate value, both directly and indirectly through disclosure of Corporate Social Responsibility (CSR) activities. Corporate reputation, reflected in external awards and auditor affiliations, contributes to increased transparency and credibility of CSR, ultimately increasing the company's economic value. CSR is not only a moral or legal obligation, but also a strategic tool to actualize the power of reputation into financial added value. The implications of this study emphasize the strategic importance of reputation management through the implementation of high-quality audit mechanisms and the company's active involvement in sustainable business practices. And capital market authorities are encouraged to improve the quality of supervision related to corporate reporting and to promote greater transparency through comprehensive information disclosure.

There are different confirmatory techniques to compare means, like hypothesis testing and (Bayesian) model selection. However, there is no software package in which these techniques are available. A Fortran 90 program is written, which enables researchers to apply these techniques to their data. Besides traditional hypotheses, like <em>H₀ : µ_{1 = µ₂ = µ₃}</em> and <em>H_u : µ₁, µ₂, µ₃</em>, order-restricted hypotheses, like <em>µ₁ > µ_{2 > µ₃}</em> or <em>µ₁ > µ₂ = µ₃ or µ₁ > µ₂ < µ₃</em>, can be evaluated.

The aim of the research is to determine the effect of gender diversity and green accounting on CSR disclosure in LQ45 companies from 2015 to 2022. This research is included in the quantitative research category. The company population that is the focus of this research is the LQ45 companies listed on the Indonesia Stock Exchange between 2015 and 2022. There are 45 companies included in this research population. The total number of samples used was 9 companies with a total of 72 observations, which were selected based on the purposive sampling method. Gender diversity as measured by dummy variables and green accounting as measured by PROPER are independent variables in this research. The control variable, displayed by company size, is measured using size. What is meant by the dependent variable is to reveal the company's CSR which is measured using GRI 4 guidelines. Data collection is carried out using the documentation method. The data used comes from secondary sources obtained through annual reports and company sustainability reports which can be accessed via the website www.idx.co.id and the official websites of each company. The testing technique used is the panel data regression method. Eviews 12 is software used to process data in testing research samples. In data testing, the probability methods used include descriptive statistical analysis, model selection test, classical assumption test, and hypothesis testing. "The model selection in this research used the Chow test, Hausman test, and LM test, with the results selecting the common effect model." The results of this research reveal that gender diversity does not have a significant influence on the level of CSR closure, while green accounting has a positive and significant influence on the level of CSR closure in LQ45 companies from 2015 to 2022.