Two advanced methods for adjusting the main coefficient in logistic regression

A binary disease outcome is commonly modeled with continuous covariates (e.g., biochemical concentration) in medical research, and the corresponding exploration may employ a normal discrimination approach. The covariate relationship affects the estimated association between binary outcome and the interesting covariate. The method of value deviated from a fitted value (fractional polynomial), which is abbreviated as VDFV, may reduce the estimation bias especially when the relationship between the covariates is nonlinear. However, when the extraneous variable relates to the outcome, the pooled data (cases and controls) are replaced by the control data only for the purpose of fitting values. Based on two association patterns, the extraneous variable unrelated to the outcome (I) and that related to the outcome (II), the simulation study reveals that VDFV-p (using pooled data) is reliable, with less bias and a smaller mean square error (MSE) in pattern (I) and that VDFV-c (using control data) shows less bias in pattern (II). The conventional covariate adjustment performs worse in (I) but fairly well in (II). Note that a huge MSE is never observed in VDFV-p or VDFV-c, while this is a common issue related to small sample size or sparse data in logistic regression. Two fetal studies are illustrated—one for pattern (I) and one for pattern (II).     

A Trait‐based framework for mutation bias as a driver of long‐term evolutionary trends

Previous work has shown that mutation bias can direct evolutionary trends in genotypic space under strong selection and rare mutation. We present an extension of this work to general traits of the organism. We do this by allowing many different genotypes, with different fitnesses, to have the same trait value. This approach makes novel predictions and shows that the outcome of evolution for a trait is influenced by mutation bias as well as the fitness distribution of the genotypes that have the same trait value. This distribution can alter evolution in interesting ways, depending on the likelihood of generating high fitness mutants. We also show that mutation bias can direct evolution when many mutants are present at any one time. We demonstrate that mutation bias can drive long‐term evolutionary trends when the environment is constantly changing. Under biologically realistic conditions, we show that mutation bias can counter strong gradients of environmental selection over time. We conclude that evolutionary trends can be quite independent of the environment, even when they depress population fitness. Finally, we show that entropy can be a powerful source of mutation bias and can drive evolutionary trends. © 2015 Wiley Periodicals, Inc. Complexity 21: 331–345, 2016     

On non-negligible bias of the first output byte of RC4 towards the first three bytes of the secret key

In this paper, we show that the first byte of the keystream output of RC4 has non-negligible bias towards the sum of the first three bytes of the secret key. This result is based on our observation that the index, where the first byte of the keystream output is chosen from, is approximately twice more likely to be 2 than any other value. Our technique is further used to theoretically prove Roos’s experimental observation (A class of weak keys in the RC4 stream cipher, 1995) related to weak keys.     

Rs中响应曲面模型的稳健设计

本文运用再生核Hhilbert空间方法研究R^s中响应曲面模型的稳健设计问题。我们假设模型偏差包括由多元Hermite多项式高阶项产生的效应，如果偏差大，设计点应该布于布点附近，否则，设计点应该适当散开，所求设计是正交不变的，而且关于模型偏差是稳健的。     

Contradictions and uncertainty in scientists’ mathematical modeling and interpretation of data

Contradictions have been recognized as important factors in learning (conceptual change), because they require students to engage in deep reflection that leads to accommodation and learning. However, in the face of uncertainty, confirmation bias and the theory-laden nature of observation may not allow the recognition of a situation as harboring a contradiction. In the present study, I analyze a meeting in which a scientific research team presents its results to an informed audience. I show that with hindsight, there are contradictions in the mathematical models that the scientists use and the graph interpretations that they produce. Because the contradictions went unnoticed, they could not become a determinant factor in the process. This has implications for thinking about the role of uncertainty and contradiction as factors in and of mathematical learning.     

THE MITRA‐WAN FORESTRY MODEL: A DISCRETE‐TIME OPTIMAL CONTROL PROBLEM

In this paper, we present some new properties of the Mitra‐Wan forestry model written as a discrete‐time optimal control problem. For this problem, the set of stationary states is characterized. For the optimal long‐run management, we consider the following optimality criteria: average optimality, good control policies, bias optimality, and overtaking optimality. We establish relationships between these criteria and show that the value of average optimal policies is constant and equals the value in the optimal stationary state.     

Reduced‐bias kernel estimators of a positive extreme value index

In this paper, we deal with the semi‐parametric estimation of the extreme value index, an important parameter in extreme value analysis. It is well known that many classic estimators, such as the Hill estimator, reveal a strong bias. This problem motivated the study of two classes of kernel estimators. Those classes generalize the classical Hill estimator and have a tuning parameter that enables us to modify the asymptotic mean squared error and eventually to improve their efficiency. Since the improvement in efficiency is not very expressive, we also study new reduced bias estimators based on the two classes of kernel statistics. Under suitable conditions, we prove their asymptotic normality. Moreover, an asymptotic comparison, at optimal levels, shows that the new classes of reduced bias estimators are more efficient than other reduced bias estimator from the literature. An illustration of the finite sample behaviour of the kernel reduced‐bias estimators is also provided through the analysis of a data set in the field of insurance.     

The impact of sampling methods on bias and variance in stochastic linear programs

Stochastic linear programs can be solved approximately by drawing a subset of all possible random scenarios and solving the problem based on this subset, an approach known as sample average approximation (SAA). The value of the objective function at the optimal solution obtained via SAA provides an estimate of the true optimal objective function value. This estimator is known to be optimistically biased; the expected optimal objective function value for the sampled problem is lower (for minimization problems) than the optimal objective function value for the true problem. We investigate how two alternative sampling methods, antithetic variates (AV) and Latin Hypercube (LH) sampling, affect both the bias and variance, and thus the mean squared error (MSE), of this estimator. For a simple example, we analytically express the reductions in bias and variance obtained by these two alternative sampling methods. For eight test problems from the literature, we computationally investigate the impact of these sampling methods on bias and variance. We find that both sampling methods are effective at reducing mean squared error, with Latin Hypercube sampling outperforming antithetic variates. For our analytic example and the eight test problems we derive or estimate the condition number as defined in Shapiro et al. (Math. Program. 94:1–19, 2002). We find that for ill-conditioned problems, bias plays a larger role in MSE, and AV and LH sampling methods are more likely to reduce bias.     

Attributed Grammatical Evolution with Lookahead for the Multiple Knapsack Problem

This paper presents an Attribute Grammar with Lookahead (AG+LA) approach, a technique to solve heavily constrained Multiple Knapsack Problem. This approach incorporates a form of lookahead into the mapping process of Grammatical Evolution (GE) using Attribute Grammar (AG) to focus only on feasible solutions, thereby avoiding issues such as repeated remapping and introns, both of which are limitations of previous approaches based on AG. We also present AG+LAE (AG+LA with an efficiency measure to bias the search towards the most efficient, i.e., best value, objects), the successor of AG+LA where a biasing process is incorporated using problem specific knowledge to significantly improve the performance of its predecessor, both in terms of the number of evaluations required and the quality of solutions obtained. Degenerate code, as used in DNA, is code that uses redundancy, so that different codons can represent the same thing. Many developmental systems, such as GE, use a degenerate encoding to help promote neutral mutations, that is, minor genetic changes that do not result in a phenotypic change. While early work in GE suggested that some level of degeneracy was important, it does come at the cost of increasing the size of the search space. Duplicate Elimination techniques, as opposed to degenerate encoding, are employed in decoder-based Evolutionary Algorithms to ensure that the newly generated solutions are not already contained in the current population. The results and analysis show that it is crucial to incorporate duplicate elimination to improve the performance of both approaches, while the reduced level of degeneracy is crucial only for AG+LA.     

Bias of estimator of change point detected by a CUSUM procedure

For independent observations from a standard one-parameter exponential family, the estimator of change point after being detected by a CUSUM procedure is defined as the last zero point of the CUSUM process before the alarm time. By assuming that the change occurs far away from beginning and the control limit is large, an explicit form for the bias of estimator is derived conditioning on the change being detected. By further assuming that the change magnitude and its reference value approach zero at the same order, the local second order expansion of the bias is obtained for numerical evaluation. It is found that, surprisingly, even in the normal distribution case, the bias is non-zero when the change magnitude equals to its reference value, in contrast to the continuous time analog and the fixed sample size case. Numerical results show that the approximations are quite satisfactory.     

Unbounded growth in the Neoclassical growth model with non-constant discounting

For a Neoclassical growth model, the literature highlights that exponential discounting is observationally equivalent to quasi-hyperbolic discounting, if the instantaneous discount rate decreases asymptotically towards a positive value. Conversely, in this paper a zero long-run value allows a solution without stagnation. We prove that a less than exponential but unbounded growth can be attained, even without technological progress. The growth rate of consumption decreases asymptotically towards zero, although so slowly that consumption grows unboundedly. The asymptotic convergence towards a non-hyperbolic steady-state which saving rate matches the intertemporal elasticity of substitution and the speed of convergence towards this equilibrium are analyzed.     

The superiority of “optimal control” over simulation in policy analysis

The simulation approach to policy analysis usually concentrates on policy multipliers as a measure of the thrust of economic policy. However, this measure is inadequate for one branch of economic policy, namely, fiscal policy. The reason is that the effectiveness of fiscal policy depends, via the government budget constraint, on the method of finance. It is argued in this paper that for this very reason the conventional way of calculating simulation-based dynamic multipliers introduces a bias towards the no-crowding-out thesis. This bias arises even in models of monetarist persuasion. Furthermore, it is shown that this bias can be removed by utilizing multipliers based on optimal control. We illustrate this proposition by providing numerical results using a large-scale U.K. econometric model of international monetarist persuasion (the London Business School model, LBS). Section 1 builds up a framework through which policy optimization can be compared and evaluated to policy simulations. In Section 2 we derive and compare policy multipliers obtained through policy simulations and optimal control. Section 3 provides a numerical example with the findings being summarized in Section 4.     

欧式看涨期权价格折现值的研究

在金融活动中 ,投资者对资金流的现值的了解是很重要的 .为此本文引入期权价格折现值的概念 .讨论了当利率是常数时 ,欧式看涨期权价格折现值所满足的微分方程 .     

Mixed integer programming models for dispatching vehicles at a container terminal

This paper presents scheduling models for dispatching vehicles to accomplish a sequence of container jobs at the container terminal, in which the starting times as well as the order of vehicles for carrying out these jobs need to be determined. To deal with this scheduling problem, three mixed 0–1 integer programming models, Model I, Model II and Model III are provided. We present interesting techniques to reformulate the two mixed integer programming models, Model I and Model II, as pure 0–1 integer programming problems with simple constraint sets and present a lower bound for the optimal value of Model I. Model III is a complicated mixed integer programming model because it involves a set of non-smooth constraints, but it can be proved that its solutions may be obtained by the so-called greedy algorithm. We present numerical results showing that Model III is the best among these three models and the greedy algorithm is capable of solving large scale problems.     

The first moment of Salié sums

The main objective of this article is to study the asymptotic behavior of Salié sums over arithmetic progressions. We deduce from our asymptotic formula that Salié sums possess a bias towards being positive. The method we use is based on the Kuznetsov formula for modular forms of half-integral weight. Moreover, in order to develop an explicit formula, we are led to determine an explicit orthogonal basis of the space of modular forms of half-integral weight.     

Adaptive Filtering: a Theoretical and Simulation Study of the Convergence of the Parameter Estimates

The existence of bias in the final parameter estimates using adaptive filtering is demonstrated theoretically. For observations generated by an autoregressive model of order one, an approximate theoretical expression for the bias is derived which is valid for long series of observations. The validity of the expression is investigated by simulation and comparing the theoretical bias with the simulated bias at the end of one major iteration. By carrying out a number of major iterations, it is shown that the bias reaches a stable value which is a function of the learning constant. The magnitude of the stable bias may be made as small as desired by taking smaller values for the learning constant. However, as the learning constant decreases, the number of major iterations required to achieve stability increases. By means of simulation experiments, the existence of bias in the final parameter estimates is demonstrated for shorter series of observations generated by an AR(1) model, and for long series of observations generated by an AR(2) model. Again the bias appears to increase with the magnitude of the learning constant. It is argued that the presence of this bias need not be a drawback in the practical application of the method since, by systematic reduction of the training constant between major iterations, the bias may also be reduced, while reasonably rapid convergence can still be maintained.     

The Capital-Investment Appraisal of New Technology: Problems,Misconceptions and Research Directions

The application of traditional techniques of capital-investment appraisal to new technology has been criticized for its bias towards short-term gains and the consequent favour of the status quo. This paper considers four classes of criticisms. They relate to the use of payback and discounted cash-flow methods, the assumptions made about the future, benefits of new technology which are ignored, and issues related to management control. The paper rehearses the criticisms and discusses their validity. The overall conclusion is that the biases in capital-investment appraisal are avoidable. The criticisms are not valid with regard to the overall approach of capital-investment appraisal, and the apparent bias is due to misapplication of the techniques.     

On the Bias of the Generalized Regression Estimator in Survey Sampling

It is well known that the generalized regression (GREG) estimator of the finite population total is asymptotically unbiased. Consequently, bias is negligible when the sample size is large. But the magnitude of the bias is not known, if we are estimating small areas or operating with small samples. Furthermore, beside the sample size, the bias depends on the auxiliary variables, on their relation to the study variable and on the sampling design. In small samples it is important to know sources of the bias and in some cases to use a bias-corrected regression estimator. The aim of the present paper is to derive approximate bias expressions of the GREG estimator under different population models and different sampling designs to study the magnitude of the bias.      

THE INSURANCE VALUE OF BIODIVERSITY IN THE PROVISION OF ECOSYSTEM SERVICES

ABSTRACT. Biodiversity provides insurance against the uncertain provision of ecosystem services which are being used by risk‐averse economic agents. I present a conceptual ecological‐economic model that combines (i) current results from ecology about the relationships between biodiversity, ecosystem functioning, and the provision of ecosystem services with (ii) economic methods to study decision‐making under uncertainty. In this framework I (1) determine the insurance value of biodiversity, (2) study the optimal allocation of funds in the trade‐off between investing into biodiversity protection and the purchase of financial insurance, and (3) analyze the effect of different institutional regimes in the market for financial insurance on biodiversity protection. I conclude that biodiversity acts as a form of natural insurance for risk‐averse ecosystem managers against the over‐ or under‐provision with ecosystem services. Therefore, biodiversity has an insurance value, which is a value component in addition to the usual value arguments, such as direct or indirect use or non‐use values. In this respect, biodiversity and financial insurance are substitutes. Hence, the availability, and exact institutional design, of financial insurance influence the level of biodiversity protection.     

An efficient shrinkage bootstrap bias estimator for smooth functions of sample means

Summary  Since it is not always possible to calculate bootstrap estimators, they are usually approximated by simulation. In this article, we propose a bootstrap bias estimator for smooth functions of sample means that has less mean squared error, due to the simulation process, than the ordinary bootstrap. The estimator is based on shrinking the bootstrap mean towards the original sample mean. It can easily be implemented while demanding almost no additional computational effort.