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Bounded function

About: Bounded function is a research topic. Over the lifetime, 77295 publications have been published within this topic receiving 1321552 citations.


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Journal ArticleDOI
TL;DR: In this paper, the authors develop attractive functional forms and simple quasi-likelihood estimation methods for regression models with a fractional dependent variable, and apply these methods to a data set of employee participation rates in 401 (k) pension plans.
Abstract: SUMMARY We develop attractive functional forms and simple quasi-likelihood estimation methods for regression models with a fractional dependent variable. Compared with log-odds type procedures, there is no difficulty in recovering the regression function for the fractional variable, and there is no need to use ad hoc transformations to handle data at the extreme values of zero and one. We also offer some new, robust specification tests by nesting the logit or probit function in a more general functional form. We apply these methods to a data set of employee participation rates in 401 (k) pension plans. I. INTRODUCTION Fractional response variables arise naturally in many economic settings. The fraction of total weekly hours spent working, the proportion of income spent on charitable contributions, and participation rates in voluntary pension plans are just a few examples of economic variables bounded between zero and one. The bounded nature of such variables and the possibility of observing values at the boundaries raise interesting functional form and inference issues. In this paper we specify and analyse a class of functional forms with satisfying econometric properties. We also synthesize and expand on the generalized linear models (GLM) literature from statistics and the quasi-likelihood literature from econometrics to obtain robust methods for estimation and inference with fractional response variables. We apply the methods to estimate a model of employee participation rates in 401 (k) pension plans. The key explanatory variable of interest is the plan's 'match rate,' the rate at which a firm matches a dollar of employee contributions. The empirical work extends that of Papke (1995), who studied this problem using linear spline methods. Spline methods are fiexible, but they do not ensure that predicted values lie in the unit interval. To illustrate the methodological issues that arise with fractional dependent variables, suppose that a variable y, O^y^l, is to be explained by a 1 x/^ vector of explanatory variables \ = {Xi,X2 XK), with the convention that Xi = l. The population model

2,933 citations

Journal ArticleDOI
TL;DR: In this paper, the authors show that positive solutions of second order elliptic equations are symmetric about the limiting plane, and that the solution is symmetric in bounded domains and in the entire space.
Abstract: We prove symmetry, and some related properties, of positive solutions of second order elliptic equations. Our methods employ various forms of the maximum principle, and a device of moving parallel planes to a critical position, and then showing that the solution is symmetric about the limiting plane. We treat solutions in bounded domains and in the entire space.

2,792 citations

Book ChapterDOI
01 Mar 2003
TL;DR: In this paper, the authors investigate the use of data-dependent estimates of the complexity of a function class, called Rademacher and Gaussian complexities, in a decision theoretic setting and prove general risk bounds in terms of these complexities.
Abstract: We investigate the use of certain data-dependent estimates of the complexity of a function class, called Rademacher and Gaussian complexities. In a decision theoretic setting, we prove general risk bounds in terms of these complexities. We consider function classes that can be expressed as combinations of functions from basis classes and show how the Rademacher and Gaussian complexities of such a function class can be bounded in terms of the complexity of the basis classes. We give examples of the application of these techniques in finding data-dependent risk bounds for decision trees, neural networks and support vector machines.

2,535 citations

Journal ArticleDOI
TL;DR: In this paper, it was shown that coprime right factorizations exist for the input-to-state mapping of a continuous-time nonlinear system provided that the smooth feedback stabilization problem is solvable for this system.
Abstract: It is shown that coprime right factorizations exist for the input-to-state mapping of a continuous-time nonlinear system provided that the smooth feedback stabilization problem is solvable for this system. It follows that feedback linearizable systems admit such fabrications. In order to establish the result, a Lyapunov-theoretic definition is proposed for bounded-input-bounded-output stability. The notion of stability studied in the state-space nonlinear control literature is related to a notion of stability under bounded control perturbations analogous to those studied in operator-theoretic approaches to systems; in particular it is proved that smooth stabilization implies smooth input-to-state stabilization. >

2,504 citations

Book ChapterDOI
22 Mar 1999
TL;DR: This paper shows how boolean decision procedures, like Stalmarck's Method or the Davis & Putnam Procedure, can replace BDDs, and introduces a bounded model checking procedure for LTL which reduces model checking to propositional satisfiability.
Abstract: Symbolic Model Checking [3, 14] has proven to be a powerful technique for the verification of reactive systems. BDDs [2] have traditionally been used as a symbolic representation of the system. In this paper we show how boolean decision procedures, like Stalmarck's Method [16] or the Davis & Putnam Procedure [7], can replace BDDs. This new technique avoids the space blow up of BDDs, generates counterexamples much faster, and sometimes speeds up the verification. In addition, it produces counterexamples of minimal length. We introduce a bounded model checking procedure for LTL which reduces model checking to propositional satisfiability. We show that bounded LTL model checking can be done without a tableau construction. We have implemented a model checker BMC, based on bounded model checking, and preliminary results are presented.

2,424 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20243
20234,319
20229,421
20214,210
20204,423
20194,004