Matrix Differential Calculus with Applications in Statistics and Econometrics.

Magnus, Jan R.; Neudecker, Heinz

doi:10.2307/2531754

Cited by 1,195 publications

(530 citation statements)

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“…The sensitivities and elasticities of each index to age-specific mortality were derived using matrix calculus (Magnus and Neudecker 1988). These techniques are given extensive treatment in recent papers by Caswell, using most of the same notation that we have here (Caswell 2008;.…”

Section: Sensitivity and Elasticity Analysismentioning

confidence: 99%

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Perturbation Analysis of Indices of Lifespan Variability

2013

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A number of indices exist to calculate lifespan variation, each with different underlying properties. Here we present new formulae for the response of seven of these indices to changes in the underlying mortality schedule (life disparity, the Gini coefficient, the standard deviation, the variance, Theil's index, the mean logarithmic deviation, and the inter-quartile range). We derive each of these indices from an absorbing Markov chain formulation of the life table, and use matrix calculus to obtain the sensitivity and the elasticity (i.e., the proportional sensitivity) to changes in age-specific mortality. Using empirical French and Russian male data we compare the underlying sensitivities to mortality change under different mortality regimes in order to test under which conditions the indices might differ in their conclusions about the magnitude of lifespan variation. Finally, we demonstrate how the sensitivities can be used to decompose temporal changes in the indices into contributions of age-specific mortality changes. The result is an easily computable method for calculating the properties of this important class of longevity indices.

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Section: Sensitivity and Elasticity Analysismentioning

confidence: 99%

“…More details on matrix calculus can be found in Magnus and Neudecker (1988). A good mathematical introduction is in Abadir and Magnus (2005), and demographic discussions appear in Caswell (2007;.…”

Section: Matrix Calculus Preliminariesmentioning

confidence: 99%

Perturbation Analysis of Indices of Lifespan Variability

2013

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“…We perform a second derivative test on the local minima found by the SQP algorithm. In the case of constrained optimization the second-order sufficient condition for a minimum can be expressed in a determinant form of the bordered Hessian [20,36]. We report the details of this analysis for the concave impact case when we choose a discretization N = 100.…”

Section: Characterization Of the Cost Landscapementioning

confidence: 99%

Optimal execution with non-linear transient market impact

Curato

Gatheral

Lillo

2016

Quantitative Finance

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We study the problem of the optimal execution of a large trade in the presence of nonlinear transient impact. We propose an approach based on homotopy analysis, whereby a well behaved initial strategy is continuously deformed to lower the expected execution cost. We find that the optimal solution is front loaded for concave impact and that its expected cost is significantly lower than that of conventional strategies. We then consider brute force numerical optimization of the cost functional; we find that the optimal solution for a buy program typically features a few short intense buying periods separated by long periods of weak selling. Indeed, in some cases we find negative expected cost. We show that this undesirable characteristic of the nonlinear transient impact model may be mitigated either by introducing a bid-ask spread cost or by imposing convexity of the instantaneous market impact function for large trading rates.

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“…We will localize the parameter around the 'truth', so that 6 = 9 {n) = 9o + -^^^^' J' =^(n) = 'I'o + :y=f *: and a = a (n) s ao + -^o-Let h = (a, 6 + (^^^(nl^ooiE"^"2i)) (*®(/-0-')vecp) + (vec(?2))' (*®(/-6')"^( "''H^~E"''*0 (^-^')~l^e cf^i). (20) In other words, the sequence (P",/, : h E H) is asymptotically normal.…”

Section: B Proof Of Theoremmentioning

confidence: 99%

Asymptotically Unbiased Inference for a Dynamic Panel Model with Fixed Effects when Both n and T Are Large

2002

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We consider a dynamic panel AR(1) model with fixed effects when both n and T are large. Under the "T fixed n large" asymptotic approximation, the maximum likelihood estimator is known to be inconsistent due to the well-known incidental peirameter problem. We consider an alternative asymptotic approximation where n and T grow at the same rate. It is shown that, although the MLE is asymptotically biased, a relatively simple fix to the MLE results in an asymptotically unbiased estimator. The bias corrected MLE is shown to be asymptotically efficient by a Hajek type convolution theorem.

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Matrix Differential Calculus with Applications in Statistics and Econometrics.

Cited by 1,195 publications

References 0 publications

Perturbation Analysis of Indices of Lifespan Variability

Perturbation Analysis of Indices of Lifespan Variability

Optimal execution with non-linear transient market impact

Asymptotically Unbiased Inference for a Dynamic Panel Model with Fixed Effects when Both n and T Are Large

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