Methodological Variation in Empirical Corporate Finance

I document large variation in empirical methodology in corporate finance regressions in top finance journals. Although methodological variation allows for customization of empirical tests to fit specific theories, it can also enable excessive reporting of statistically significant results. For example, given discretion over 10 routine methodological decisions, a researcher could report that over 70% of randomly generated variables are statistically significant determinants of leverage at the 5% level. The methodological decisions that affect statistical significance the most are dependent variable selection, variable transformation, and outlier treatment. I discuss remedies that can mitigate the negative effects of methodological variation.

Painlevé Analysis, Soliton Molecule, and Lump Solution of the Higher-Order Boussinesq Equation

The Painlevé integrability of the higher-order Boussinesq equation is proved by using the standard Weiss-Tabor-Carnevale (WTC) method. The multisoliton solutions of the higher-order Boussinesq equation are obtained by introducing dependent variable transformation. The soliton molecule and asymmetric soliton of the higher-order Boussinesq equation can be constructed by the velocity resonance mechanism. Lump solution can be derived by solving the bilinear form of the higher-order Boussinesq equation. By some detailed calculations, the lump wave of the higher-order Boussinesq equation is just the bright form. These types of the localized excitations are exhibited by selecting suitable parameters.

Data transformation: a focus on the interpretation

Several assumptions such as normality, linear relationship, and homoscedasticity are frequently required in parametric statistical analysis methods. Data collected from the clinical situation or experiments often violate these assumptions. Variable transformation provides an opportunity to make data available for parametric statistical analysis without statistical errors. The purpose of variable transformation to enable parametric statistical analysis and its final goal is a perfect interpretation of the result with transformed variables. Variable transformation usually changes the original characteristics and nature of units of variables. Back-transformation is crucial for the interpretation of the estimated results. This article introduces general concepts about variable transformation, mainly focused on logarithmic transformation. Back-transformation and other important considerations are also described herein.

Lump-type solutions, interaction solutions, and periodic lump solutions of the generalized (3+1)-dimensional Burgers equation

In this paper, the lump-type solutions, interaction solutions, and periodic lump solutions of the generalized ([Formula: see text])-dimensional Burgers equation were obtained by using the ansatz method. Based on a variable transformation, the generalized ([Formula: see text])-dimensional Burgers equation was transformed into a bilinear equation. And then, lump-type solutions, two kinds of interaction solutions, and periodic lump solutions were obtained via solutions of the bilinear equation. Fission and fusion phenomena are found in the process of interaction between lump-type soliton and one stripe soliton, which can derive the lumpoff wave solution. The dynamic characteristics of these solutions were vividly displayed by graphics.

An Effective Variable Transformation Strategy in Multitasking Evolutionary Algorithms

Multitasking evolutionary algorithm (MTEA), which solves multiple optimization tasks simultaneously in a single run, has received considerable attention in the community of evolutionary computation, and several algorithms have been proposed in the literature. Unfortunately, knowledge transfer between constituent tasks may cause negative effect on algorithm performance, especially when the optimal solutions of all tasks are in different locations of the unified search space. To address this issue, an effective variable transformation strategy and the corresponding inverse transformation are proposed in multitasking optimization scenario. After using variable transformation strategy, the estimated optimal solutions of all tasks are both near the center point of the unified search space. More importantly, this strategy can enhance the task similarity, and then the effectiveness of knowledge transfer will probably be positive in this case, which can help us to improve the algorithm performance. Keeping this in mind, a multitasking evolutionary algorithm (named MTDE-VT) is realized as an instance by embedding the proposed variable transformation strategy into multitasking differential evolution. In MTDE-VT, the individuals in the original population are first transformed into new locations by the variable transformation strategy. Once the offspring is generated in the transformed unified search space, it must be transformed back to the original unified search space. The statistical analysis of experimental results on some multitasking optimization benchmark problems illustrates the superiority of the proposed MTDE-VT algorithm in terms of solution accuracy and robustness. Furthermore, the basic principle and the good parameter combination are also provided based on massive simulated data.

CANONICALIZATION OF CONSTRAINED HAMILTONIAN EQUATIONS IN A SINGULAR SYSTEM

In this paper, the canonicalization of constrained Hamiltonian system is discussed. Because the constrained Hamiltonian equations are non-canonical, they lead to many limitations in the research. For this purpose, variable transformation is constructed that satisfies the condition of canonical equation, and the new variables can be obtained by a series of derivations. Finally, two examples are given to illustrate the applications of the result.