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## Nonparametric tests for conditional independence using conditional distributions

Bouezmarni, Taoufik; Taamouti, Abderrahim
Tipo: info:eu-repo/semantics/draft; info:eu-repo/semantics/workingPaper Formato: text/plain; application/pdf
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The concept of causality is naturally defined in terms of conditional distribution, however almost all the empirical works focus on causality in mean. This paper aim to propose a nonparametric statistic to test the conditional independence and Granger non-causality between two variables conditionally on another one. The test statistic is based on the comparison of conditional distribution functions using an L2 metric. We use Nadaraya-Watson method to estimate the conditional distribution functions. We establish the asymptotic size and power properties of the test statistic and we motivate the validity of the local bootstrap. Further, we ran a simulation experiment to investigate the finite sample properties of the test and we illustrate its practical relevance by examining the Granger non-causality between S&P 500 Index returns and VIX volatility index. Contrary to the conventional t-test, which is based on a linear mean-regression model, we find that VIX index predicts excess returns both at short and long horizons.; Financial support from the Natural Sciences and Engineering Research Council of Canada and from the Spanish Ministry of Education through grants SEJ 2007-63098 are also acknowledged

## Efficient estimation using the characteristic function : theory and applications with high frequency data

Kotchoni, Rachidi
Fonte: Université de Montréal Publicador: Université de Montréal
Tipo: Thèse ou Mémoire numérique / Electronic Thesis or Dissertation
Português
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Nous abordons deux sujets distincts dans cette thèse: l'estimation de la volatilité des prix d'actifs financiers à partir des données à haute fréquence, et l'estimation des paramétres d'un processus aléatoire à partir de sa fonction caractéristique. Le chapitre 1 s'intéresse à l'estimation de la volatilité des prix d'actifs. Nous supposons que les données à haute fréquence disponibles sont entachées de bruit de microstructure. Les propriétés que l'on prête au bruit sont déterminantes dans le choix de l'estimateur de la volatilité. Dans ce chapitre, nous spécifions un nouveau modèle dynamique pour le bruit de microstructure qui intègre trois propriétés importantes: (i) le bruit peut être autocorrélé, (ii) le retard maximal au delà duquel l'autocorrélation est nulle peut être une fonction croissante de la fréquence journalière d'observations; (iii) le bruit peut avoir une composante correlée avec le rendement efficient. Cette dernière composante est alors dite endogène. Ce modèle se différencie de ceux existant en ceci qu'il implique que l'autocorrélation d'ordre 1 du bruit converge vers 1 lorsque la fréquence journalière d'observation tend vers l'infini. Nous utilisons le cadre semi-paramétrique ainsi défini pour dériver un nouvel estimateur de la volatilité intégrée baptisée "estimateur shrinkage". Cet estimateur se présente sous la forme d'une combinaison linéaire optimale de deux estimateurs aux propriétés différentes...

## Constraining Galaxy Formation and Cosmology with the Conditional Luminosity Function of Galaxies

Yang, Xiaohu; Mo, H. J.; Bosch, Frank C. van den
Tipo: Artigo de Revista Científica
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45.84%
We use the conditional luminosity function (CLF), which gives the number of galaxies with luminosities in the range [L, L+dL] that reside in a halo of mass M, to link the distribution of galaxies to that of dark matter haloes. We seek the CLF that reproduces the galaxy luminosity function and the luminosity dependence of the galaxy clustering strength and test the models by comparing the resulting mass-to-light ratios (M/L) with constraints from the Tully-Fisher (TF) relation. We obtain a number of stringent constraints on both galaxy formation and cosmology. In particular, this method can break the degeneracy between Omega_0 and the power-spectrum normalization sigma_8, inherent in current weak-lensing and cluster-abundance studies. For flat LCDM cosmogonies with sigma_8 normalized by recent weak lensing observations, the best results are obtained for Omega_0~0.3; Omega_0 < 0.2 leads to too large galaxy correlation lengths, while Omega_0 > 0.4 gives too high M/L. The best-fit model for the LCDM concordance cosmology (Omega_0=0.3) predicts M/L that are slightly too high. We discuss a number of possible effects that might remedy this problem, including small modification of cosmological parameters, warm in stead of cold dark matter...

## Magnitude Gap Statistics and the Conditional Luminosity Function

More, Surhud
Tipo: Artigo de Revista Científica
Português
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45.92%
In a recent preprint, Hearin et al. (2012,H12) suggest that the halo mass-richness calibration of clusters can be improved by using the difference in the magnitude of the brightest and the second brightest galaxy (magnitude gap) as an additional observable. They claim that their results are at odds with the results from Paranjape & Sheth (2012, PS12) who show that the magnitude distribution of the brightest and second brightest galaxies can be explained based on order statistics of luminosities randomly sampled from the total galaxy luminosity function. We find that a conditional luminosity function (CLF) for galaxies which varies with halo mass, in a manner which is consistent with existing observations, naturally leads to a magnitude gap distribution which changes as a function of halo mass at fixed richness, in qualitative agreement with H12. We show that, in general, the luminosity distribution of the brightest and the second brightest galaxy depends upon whether the luminosities of galaxies are drawn from the CLF or the global luminosity function. However, we also show that the difference between the two cases is small enough to evade detection in the small sample investigated by PS12. This shows that the luminosity distribution is not the appropriate statistic to distinguish between the two cases...

## Uniform limit laws of the logarithm for nonparametric estimators of the regression function in presence of censored data

Maillot, Bertrand; Viallon, Vivian
Tipo: Artigo de Revista Científica
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45.83%
In this paper, we establish uniform-in-bandwidth limit laws of the logarithm for nonparametric Inverse Probability of Censoring Weighted (I.P.C.W.) estimators of the multivariate regression function under random censorship. A similar result is deduced for estimators of the conditional distribution function. The uniform-in-bandwidth consistency for estimators of the conditional density and the conditional hazard rate functions are also derived from our main result. Moreover, the logarithm laws we establish are shown to yield almost sure simultaneous asymptotic confidence bands for the functions we consider. Examples of confidence bands obtained from simulated data are displayed.; Comment: 34 pages, 4 figures

## Random time with differentiable conditional distribution function

Song, Shiqi
Tipo: Artigo de Revista Científica
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55.82%
Given a stochastic structure with a filtration $\mathbb{F}$, the class of all random times whose conditional distribution functions are differentiable with respect to some $\mathbb{F}$ adapted non decreasing processes is considered. The main property of a random time in this class is that it can be isomorphically implanted into an auxiliary model which is absolutely continuous with respect to a Cox model. Three formulas are established: the conditional expectation formula, the optional splitting formula, and the enlargement of filtration formula. This study is particularly useful for models which are not defined directly with Cox models, such as the dynamic one-default model developed recently.

## Approximating conditional distribution functions using dimension reduction

Hall, Peter; Yao, Qiwei
Tipo: Artigo de Revista Científica
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55.92%
Motivated by applications to prediction and forecasting, we suggest methods for approximating the conditional distribution function of a random variable Y given a dependent random d-vector X. The idea is to estimate not the distribution of Y|X, but that of Y|\theta^TX, where the unit vector \theta is selected so that the approximation is optimal under a least-squares criterion. We show that \theta may be estimated root-n consistently. Furthermore, estimation of the conditional distribution function of Y, given \theta^TX, has the same first-order asymptotic properties that it would enjoy if \theta were known. The proposed method is illustrated using both simulated and real-data examples, showing its effectiveness for both independent datasets and data from time series. Numerical work corroborates the theoretical result that \theta can be estimated particularly accurately.; Comment: Published at http://dx.doi.org/10.1214/009053604000001282 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)

## A Conditional Luminosity Function Model of the Cosmic Far-Infrared Background Anisotropy Power Spectrum

De Bernardis, Francesco; Cooray, Asantha
Tipo: Artigo de Revista Científica
Português
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45.89%
The cosmic far-infrared background (CFIRB) is expected to be generated by faint, dusty star-forming galaxies during the peak epoch of galaxy formation. The anisotropy power spectrum of the CFIRB captures the spatial distribution of these galaxies in dark matter halos and the spatial distribution of dark matter halos in the large-scale structure. Existing halo models of CFIRB anisotropy power spectrum are either incomplete or lead to halo model parameters that are inconsistent with the galaxy distribution selected at other wavelengths. Here we present a conditional luminosity function approach to describe the far-IR bright galaxies. We model the 250 um luminosity function and its evolution with redshift and model-fit the CFIRB power spectrum at 250 um measured by the Herschel Space Observatory. We introduce a redshift dependent duty-cycle parameter so that we are able to estimate the typical duration of the dusty star formation process in the dark matter halos as a function of redshifts. We find the duty cycle of galaxies contributing to the far-IR background is 0.3 to 0.5 with a dusty star-formation phase lasting for \sim0.3-1.6 Gyrs. This result confirms the general expectation that the far-IR background is dominated by star-forming galaxies in an extended phases...

## Inference on a Distribution Function from Ranked Set Samples

Tipo: Artigo de Revista Científica
Português
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45.94%
Consider independent observations (X_1,R_1), (X_2,R_2), ..., (X_n,R_n) with random or fixed ranks R_i in {1,2,...,k}, while conditional on R_i = r, the random variable X_i has the same distribution as the r-th order statistic within a random sample of size k from an unknown continuous distribution function F. Such observation schemes are utilized in situations in which ranking observations is much easier than obtaining their precise values. Two wellknown special cases are ranked set sampling (McIntyre 1952) with k = n and R_i = i, and judgement post-stratification (MacEachern et al. 2004} with R_i being uniformly distributed on {1,2,...,k}. Within a rather general setting we analyze and compare the asymptotic distribution of three different estimators of the distribution function F. The asymptotics are for fixed number k and n tending to infinity. The three estimators under consideration are the stratified estimator of Stokes and Sager (1988), a new moment-based estimator, and the nonparametric maximum-likelihood estimator of Kvam and Samaniego (1994). Our results on the latter estimator generalize and refine the analysis of Huang (1997). It turns out that it is asymptotically more efficient than the former two estimators. The efficiency gain over the new estimator is typically rather small...

## Distribution of energy dissipated by a driven two-level system

Wollfarth, Philip; Shnirman, Alexander; Utsumi, Yasuhiro
Tipo: Artigo de Revista Científica
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In the context of fluctuation relations, we study the distribution of energy dissipated by a driven two-level system. Incorporating an energy counting field into the well known spin-boson model enables us to calculate the distribution function of the amount of energy exchanged between the system and the bath. We also derive the conditional distribution functions of the energy exchanged with the bath for particular initial and/or final states of the two-level system. We confirm the symmetry of the conditional distribution function expected from the theory of fluctuation relations. We also find that the conditional distribution functions acquire considerable quantum corrections at times shorter or of the order of the dephasing time. Our findings can be tested using solid-state qubits.; Comment: 5 pages, 4 figures

## A comparison of the accuracy of saddlepoint conditional cumulative distribution function approximations

Zhang, Juan; Kolassa, John E.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
45.94%
Consider a model parameterized by a scalar parameter of interest and a nuisance parameter vector. Inference about the parameter of interest may be based on the signed root of the likelihood ratio statistic R. The standard normal approximation to the conditional distribution of R typically has error of order O(n^{-1/2}), where n is the sample size. There are several modifications for R, which reduce the order of error in the approximations. In this paper, we mainly investigate Barndorff-Nielsen's modified directed likelihood ratio statistic, Severini's empirical adjustment, and DiCiccio and Martin's two modifications, involving the Bayesian approach and the conditional likelihood ratio statistic. For each modification, two formats were employed to approximate the conditional cumulative distribution function; these are Barndorff-Nielson formats and the Lugannani and Rice formats. All approximations were applied to inference on the ratio of means for two independent exponential random variables. We constructed one and two-sided hypotheses tests and used the actual sizes of the tests as the measurements of accuracy to compare those approximations.; Comment: Published at http://dx.doi.org/10.1214/074921707000000193 in the IMS Lecture Notes Monograph Series (http://www.imstat.org/publications/lecnotes.htm) by the Institute of Mathematical Statistics (http://www.imstat.org)

## A prescription for the conditional mass function of dark matter haloes

Rubino-Martin, J. A.; Betancort-Rijo, J.; Patiri, S.
Tipo: Artigo de Revista Científica
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45.85%
[ABRIDGED] The unconditional mass function (UMF) of dark matter haloes has been determined accurately in the literature, showing excellent agreement with high resolution numerical simulations. However, this is not the case for the conditional mass function (CMF). We propose a simple analytical procedure to derive the CMF by rescaling the UMF to the constrained environment using the appropriate mean and variance of the density field at the constrained point. This method introduces two major modifications with respect to the standard re-scaling procedure. First of all, rather than using in the scaling procedure the properties of the environment averaged over all the conditioning region, we implement the re-scaling locally. We show that for high masses this modification may lead to substantially different results. Secondly, we modify the (local) standard re-scaling procedure in such a manner as to force normalisation, in the sense that when one integrates the CMF over all possible values of the constraint multiplied by their corresponding probability distribution, the UMF is recovered. In practise, we do this by replacing in the standard procedure the value delta_c (the linear density contrast for collapse) by certain adjustable effective parameter delta_eff. In order to test the method...

## Conditional Limit Results for Type I Polar Distributions

Hashorva, Enkelejd
Tipo: Artigo de Revista Científica
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45.9%
Let (S_1,S_2)=(R \cos(\Theta), R \sin (\Theta)) be a bivariate random vector with associated random radius R which has distribution function $F$ being further independent of the random angle \Theta. In this paper we investigate the asymptotic behaviour of the conditional survivor probability \Psi_{\rho,u}(y):=\pk{\rho S_1+ \sqrt{1- \rho^2} S_2> y \lvert S_1> u}, \rho \in (-1,1),\in R when u approaches the upper endpoint of F. On the density function of \Theta we require a certain local asymptotic behaviour at 0, whereas for F we require that it belongs to the Gumbel max-domain of attraction. The main result of this contribution is an asymptotic expansion of \Psi_{\rho,u}, which is then utilised to construct two estimators for the conditional distribution function 1- \Psi_{\rho,u}. Further, we allow \Theta to depend on u.; Comment: 14 pages, paper submitted to Extremes in 2007

## Certainty bands for the conditional cumulative distribution function and applications

Ferrigno, Sandie; Foliguet, Bernard; Maumy-Bertrand, Myriam; Muller-Gueudin, Aurélie
Tipo: Artigo de Revista Científica
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45.86%
In this paper, we establish uniform asymptotic certainty bands for the conditional cumulative distribution function. To this aim, we give exact rate of strong uniform consistency for the local linear estimator of this function. The corollaries of this result are the asymptotic certainty bands for the quantiles and the regression function. We illustrate our results with simulations and an application on fetopathologic data.; Comment: 25 pages

## Modelling consumer credit risk via survival analysis

Cao, R.; Vilar, J. M.; Devía, A.
Tipo: Artigo de Revista Científica Formato: application/pdf
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55.9%
Credit risk models are used by financial companies to evaluate in advance the insolvency risk caused by credits that enter into default. Many models for credit risk have been developed over the past few decades. In this paper, we focus on those models that can be formulated in terms of the probability of default by using survival analysis techniques. With this objective three different mechanisms are proposed based on the key idea of writing the default probability in terms of the conditional distribution function of the time to default. The first method is based on a Cox’s regression model, the second approach uses generalized linear models under censoring and the third one is based on nonparametric kernel estimation, using the product-limit conditional distribution function estimator by Beran. The resulting nonparametric estimator of the default probability is proved to be consistent and asymptotically normal. An empirical study, based on modified real data, illustrates the three methods.

## Time series models with an EGB2 conditional distribution

Caivano, Michele; Harvey, Andrew
Tipo: Article; accepted version
Português
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This version is the author accepted manuscript. The final version is available from Wiley at http://onlinelibrary.wiley.com/doi/10.1111/jtsa.12081/full.; A time series model in which the signal is buried in noise that is non-Gaussian may throw up observations that, when judged by the Gaussian yardstick, are outliers. We describe an observation driven model, based on an exponential generalized beta distribution of the second kind (EGB2), in which the signal is a linear function of past values of the score of the conditional distribution. This specification produces a model that is not only easy to implement, but which also facilitates the development of a comprehensive and relatively straight forward theory for the asymptotic distribution of the maximum likelihood estimator. Score driven models of this kind can also be based on conditional t-distributions, but whereas these models carry out what, in the robustness literature, is called a soft form of trimming, the EGB2 distribution leads to a soft form of Winsorizing. An EGARCH model based on the EGB2 distribution is also developed. This model complements the score driven EGARCH model with a conditional t-distribution. Finally dynamic location and scale models are combined and applied to data on the UK rate of inflation.

## Time series models with an EGB2 conditional distribution

Harvey, Andrew; Caivano, Michele
Fonte: Faculty of Economics, University of Cambridge Publicador: Faculty of Economics, University of Cambridge
Tipo: Working Paper; not applicable
Português
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A time series model in which the signal is buried in noise that is non-Gaussian may throw up observations that, when judged by the Gaussian yardstick, are outliers. We describe an observation driven model, based on an exponential generalized beta distribution of the second kind (EGB2), in which the signal is a linear function of past values of the score of the conditional distribution. This specification produces a model that is not only easy to implement, but which also facilitates the development of a comprehensive and relatively straight-forward theory for the asymptotic distribution of the maximum likelihood estimator. The model is fitted to US macroeconomic time series and compared with Gaussian and Student-t models. A theory is then developed for an EGARCH model based on the EGB2 distribution and the model is fitted to exchange rate data. Finally dynamic location and scale models are combined and applied to data on the UK rate of inflation.

## Methods for estimating a conditional distribution function

Hall, Peter; Wolff, Rodney; Yao, Qiwei
Fonte: American Statistical Association Publicador: American Statistical Association
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
75.89%
Motivated by the problem of setting prediction intervals in time series analysis, we suggest two new methods for conditional distribution estimation. The first method is based on locally fitting a logistic model and is in the spirit of recent work on locally parametric techniques in density estimation. It produces distribution estimators that may be of arbitrarily high order but nevertheless always lie between 0 and 1. The second method involves an adjusted form of the Nadaraya-Watson estimator. It preserves the bias and variance properties of a class of second-order estimators introduced by Yu and Jones but has the added advantage of always being a distribution itself. Our methods also have application outside the time series setting; for example, to quantile estimation for independent data. This problem motivated the work of Yu and Jones.

## Order-preserving nonparametric regression, with applications to conditional distribution and quantile function estimation

Hall, Peter; Mueller, Hans-Georg
Fonte: American Statistical Association Publicador: American Statistical Association
Tipo: Artigo de Revista Científica
Português
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In some regression problems we observe a "response" Y ti to level t of a "treatment" applied to an individual with level Xi of a given characteristic, where it has been established that response is monotone increasing in the level of the treatment. A related problem arises when estimating conditional distributions, where the raw data are typically independent and identically distributed pairs (X i, Zi), and Yti denotes the proportion of Zi's that do not exceed t. We expect the regression means g t(x) = E(YtiXi = x) to enjoy the same order relation as the responses, that is, gt ≤ gs whenever s ≤ t. This requirement is necessary to obtain bona fide conditional distribution functions, for example. If we estimate gt by passing a linear smoother through each dataset Χt = {(Xi, Y ti) : 1 ≤ i ≤ n}, then the order-preserving property is guaranteed if and only if the smoother has nonnegative weights. However, in such cases the estimators generally have high levels of boundary bias. On the other hand, the order-preserving property usually fails for linear estimators with low boundary bias, such as local linear estimators, or kernel estimators employing boundary kernels. This failure is generally most serious at boundaries of the distribution of the explanatory variables...

## Methods for estimating a conditional distribution function

Hall, Peter; Wolff, Rodney C. L.; Yao, Qiwei
Fonte: American Statistical Association Publicador: American Statistical Association
Tipo: Article; PeerReviewed Formato: application/pdf