Classes of orderings of measures and related correlation inequalities. I. Multivariate totally positive distributions

Karlin, Samuel; Rinott, Yosef

doi:10.1016/0047-259x(80)90065-2

Cited by 577 publications

(402 citation statements)

References 33 publications

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“…finite-dimensional distributions for 1/t are totally positive of order two as defined by Karlin andRinott (1980), or Whitt (1982). The weaker condition given in (2.lb) becomes equivalent to total positivity if the stochastic process generating { 1lt} conditional on a 0E0 is a first order Markov process.…”

Section: The Modelmentioning

confidence: 99%

Empirical Implications of Alternative Models of Firm Dynamics

Pakes

Ericson

1998

Journal of Economic Theory

396

137

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Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in AbstractThis paper considers two models for analyzing the dynamics of firm behavior that allow for heterogeneity among firms, idiosyncratic (or firm specific) sources of uncertainty, and discrete events (exit and entry). Models with these characteristics are needed for empirical analysis of the causes and effects of the dispersion in the distribution of outcome paths among firms, and for correcting for the self-selection induced by liquidation in the empirical analysis of firms responses to alternative policy and environmental changes. It is shown that the two models have different nonparametric implications, and that these are rich enough to enable the construction of both testing, and selection correction, procedures that are both, fully consistent with the theoretical model, and easy to implement. The paper concludes by checking for the implications of the two models on an eight year panel of Wisconsin firms. We find one model to be consistent with the data on manufacturing, and the other to be consistent with the data for retail trade.

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Section: The Modelmentioning

confidence: 99%

Empirical Implications of Alternative Models of Firm Dynamics

Pakes

Ericson

1998

Journal of Economic Theory

396

137

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“…Numerous examples of TP2 matrices satisfying (A3) can be found in Karlin and Rinott (1980). Examples of TP2 observation kernels include Gaussian, Exponential, Binomial and Poisson distributions.…”

Section: Krishnamurthy: Myopic Bounds For Pomdpsmentioning

confidence: 99%

Myopic Bounds for Optimal Policy of POMDPs: An Extension of Lovejoy’s Structural Results

Krishnamurthy

Pareek

2015

Operations Research

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This paper provides a relaxation of the sufficient conditions, and also an extension of the structural results for Partially Observed Markov Decision Processes (POMDPs) given in Lovejoy (1987). Sufficient conditions are provided so that the optimal policy can be upper and lower bounded by judiciously chosen myopic policies. These myopic policy bounds are constructed to maximize the volume of belief states where they coincide with the optimal policy. Numerical examples illustrate these myopic bounds for both continuous and discrete observation sets.

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“…Indeed it is well known that in finite dimensional case Gauss distribution generate the measure, satisfying (4) if r i,j ≤ 0, i = j, where W = ||w i,j || n i,j=1 is the matrix inverse to the correlation matrix R [2]. In the case of Wiener process R = ||t i t j || n i,j=1 , t i > t j , i > j and the inverse matrix W has nonzero elements only on the diagonal and also elements in the strip above and belong the diagonal w p,p+1 = w p+1,p = (t p − t p+1 ) −1 , p = 1, 2, .…”

Section: ν(A)ν(b) ≤ ν(A B)ν(a B) a B ∈ B(c)mentioning

confidence: 99%

“…That proof was simplified in [2] via induction on dimension n suggested in [3], [7] , [8]. The question we consider here is how the problem can be viewed in the case of not arbitrary measure ν on R T , when possibly T = [0, 1]?…”

mentioning

confidence: 99%