Searcharxiv⌕ Search

arXiv subjects

Abhik Ghosh

Publications and source records attributed to Abhik Ghosh.

At least 109 records · Page 6Linked to original sources
arXiv2015

Predictions for the 21cm-galaxy cross-power spectrum observable with LOFAR and Subaru

The 21cm-galaxy cross-power spectrum is expected to be one of the promising probes of the Epoch of Reionization (EoR), as it could offer information about the progress of reionization and the typical scale of ionized regions at different redshifts. With upcoming observations of 21cm emission from the EoR with the Low Frequency Array (LOFAR), and of high redshift Lyalpha emitters (LAEs) with Subaru's Hyper Suprime Cam (HSC), we investigate the observability of such cross-power spectrum with these two instruments, which are both planning to observe the ELAIS-N1 field at z=6.6. In this paper we use N-body + radiative transfer (both for continuum and Lyalpha photons) simulations at redshift 6.68, 7.06 and 7.3 to compute the 3D theoretical 21cm-galaxy cross-power spectrum, as well as to predict the 2D 21cm-galaxy cross-power spectrum expected to be observed by LOFAR and HSC. Once noise and projection effects are accounted for, our predictions of the 21cm-galaxy cross-power spectrum show clear anti-correlation on scales larger than ~ 60 h$^{-1}$ Mpc (corresponding to k ~ 0.1 h Mpc$^{-1}$), with levels of significance p=0.04 at z=6.6 and p=0.048 at z=7.3. On smaller scales, instead, the signal is completely contaminated.

astro-ph.CO↗
arXiv2015

A Bayesian analysis of redshifted 21-cm HI signal and foregrounds: Simulations for LOFAR

Observations of the EoR with the 21-cm hyperfine emission of neutral hydrogen (HI) promise to open an entirely new window onto the formation of the first stars, galaxies and accreting black holes. In order to characterize the weak 21-cm signal, we need to develop imaging techniques which can reconstruct the extended emission very precisely. Here, we present an inversion technique for LOFAR baselines at NCP, based on a Bayesian formalism with optimal spatial regularization, which is used to reconstruct the diffuse foreground map directly from the simulated visibility data. We notice the spatial regularization de-noises the images to a large extent, allowing one to recover the 21-cm power-spectrum over a considerable $k_{\perp}-k_{\para}$ space in the range of $0.03\,{\rm Mpc^{-1}}<k_{\perp}<0.19\,{\rm Mpc^{-1}}$ and $0.14\,{\rm Mpc^{-1}}<k_{\para}<0.35\,{\rm Mpc^{-1}}$ without subtracting the noise power-spectrum. We find that, in combination with using the GMCA, a non-parametric foreground removal technique, we can mostly recover the spherically average power-spectrum within $2σ$ statistical fluctuations for an input Gaussian random rms noise level of $60 \, {\rm mK}$ in the maps after 600 hrs of integration over a $10 \, {\rm MHz}$ bandwidth.

astro-ph.CO↗
arXiv2015

Testing Composite Null Hypothesis Based on $S$-Divergences

We present a robust test for composite null hypothesis based on the general $S$-divergence family. This requires a non-trivial extension of the results of Ghosh et al.~(2015). We derive the asymptotic and theoretical robustness properties of the resulting test along with the properties of the minimum $S$-divergence estimators under parameter restrictions imposed by the null hypothesis. An illustration in the context of the normal model is also presented.

math.ST↗
arXiv2014

The Minimum S-Divergence Estimator under Continuous Models: The Basu-Lindsay Approach

Robust inference based on the minimization of statistical divergences has proved to be a useful alternative to the classical maximum likelihood based techniques. Recently Ghosh et al. (2013) proposed a general class of divergence measures for robust statistical inference, named the S-Divergence Family. Ghosh (2014) discussed its asymptotic properties for the discrete model of densities. In the present paper, we develop the asymptotic properties of the proposed minimum S-Divergence estimators under continuous models. Here we use the Basu-Lindsay approach (1994) of smoothing the model densities that, unlike previous approaches, avoids much of the complications of the kernel bandwidth selection. Illustrations are presented to support the performance of the resulting estimators both in terms of efficiency and robustness through extensive simulation studies and real data examples.

math.ST↗
arXiv2014

Estimation of Multivariate Location and Covariance using the S -Hellinger Distance

This paper describes a generalization of the Hellinger distance which we call the S -Hellinger distance; this general family connects the Hellinger distance smoothly with the $L_2$-divergence by a tuning parameter $α$ and is indeed a subfamily of the S -Divergence family of Ghosh et al. (2013 a, b). We use this general divergence in the context of estimating the location and covariances under (continuous) multivariate models and show that the proposed minimum S -Hellinger distance estimator is affine equivariant, asymptotically consistent and have high breakdown point under suitable conditions. We also illustrate its performance through an extensive simulation study which show that the proposed estimators give more robust estimator than the minimum Hellinger distance estimator for the location and correlation parameters under different types of contamination with the contamination proportion being as high as 20%.

stat.ME↗
arXiv2014

On the Robustness of a Divergence based Test of Simple Statistical Hypotheses

The most popular hypothesis testing procedure, the likelihood ratio test, is known to be highly non-robust in many real situations. Basu et al. (2013a) provided an alternative robust procedure of hypothesis testing based on the density power divergence; however, although the robustness properties of the latter test were intuitively argued for by the authors together with extensive empirical substantiation of the same, no theoretical robustness properties were presented in this work. In the present paper we will consider a more general class of tests which form a superfamily of the procedures described by Basu et al. (2013a). This superfamily derives from the class of $S$-divergences recently proposed by Basu et al. (2013a). In this context we theoretically prove several robustness results of the new class of tests and illustrate them in the normal model. All the theoretical robustness properties of the Basu et al. (2013a) proposal follows as special cases of our results.

math.ST↗
arXiv2014

Visibility based angular power spectrum estimation in low frequency radio interferometric observations

We present two estimators to quantify the angular power spectrum of the sky signal directly from the visibilities measured in radio interferometric observations. This is relevant for both the foregrounds and the cosmological 21-cm signal buried therein. The discussion here is restricted to the Galactic synchrotron radiation, the most dominant foreground component after point source removal. Our theoretical analysis is validated using simulations at 150 MHz, mainly for GMRT and also briefly for LOFAR. The Bare Estimator uses pairwise correlations of the measured visibilities, while the Tapered Gridded Estimator uses the visibilities after gridding in the uv plane. The former is very precise, but computationally expensive for large data. The latter has a lower precision, but takes less computation time which is proportional to the data volume. The latter also allows tapering of the sky response leading to sidelobe suppression, an useful ingredient for foreground removal. Both estimators avoid the positive bias that arises due to the system noise. We consider amplitude and phase errors of the gain, and the w-term as possible sources of errors . We find that the estimated angular power spectrum is exponentially sensitive to the variance of the phase errors but insensitive to amplitude errors. The statistical uncertainties of the estimators are affected by both amplitude and phase errors. The w-term does not have a significant effect at the angular scales of our interest. We propose the Tapered Gridded Estimator as an effective tool to observationally quantify both foregrounds and the cosmological 21-cm signal.

astro-ph.CO↗
arXiv2014

The Logarithmic Super Divergence and its use in Statistical Inference

This paper introduces a new superfamily of divergences that is similar in spirit to the S-divergence family introduced by Ghosh et al. (2013). This new family serves as an umbrella that contains the logarithmic power divergence family (Renyi, 1961; Maji, Chakraborty and Basu 2014) and the logarithmic density power divergence family (Jones et al., 2001) as special cases. Various properties of this new family and the corresponding minimum distance procedures are discussed with particular emphasis on the robustness issue; these properties are demonstrated through simulation studies. In particular the method demonstrates the limitation of the first order influence function in assessing the robustness of the corresponding minimum distance procedures.

stat.ME↗
arXiv2014

Robust Estimation of Bivariate Tail Dependence Coefficient

The problem of estimating the coefficient of bivariate tail dependence is considered here from the robustness point of view; it combines two apparently contradictory theories of robust statistics and extreme value statistics. The usual maximum likelihood based or the moment type estimators of tail dependence coefficient are highly sensitive to the presence of outlying observations in data. This paper proposes some alternative robust estimators obtained by minimizing the density power divergence with suitable model assumptions; their robustness properties are examined through the classical influence function analysis. The performance of the proposed estimators is illustrated through an extensive empirical study considering several important bivariate extreme value distributions.

stat.AP↗
arXiv2014

Asymptotic Properties of Minimum S-Divergence Estimator for Discrete Models

Robust inference based on the minimization of statistical divergences has proved to be a useful alternative to the classical techniques based on maximum likelihood and related methods. Recently Ghosh et al. (2013) proposed a general class of divergence measures, namely the S-Divergence Family and discussed its usefulness in robust parametric estimation through some numerical illustrations. In this present paper, we develop the asymptotic properties of the proposed minimum S-Divergence estimators under discrete models.

stat.ME↗
arXiv2014

Constraining the epoch of reionization with the variance statistic: simulations of the LOFAR case

Several experiments are underway to detect the cosmic redshifted 21-cm signal from neutral hydrogen from the Epoch of Reionization (EoR). Due to their very low signal-to-noise ratio, these observations aim for a statistical detection of the signal by measuring its power spectrum. We investigate the extraction of the variance of the signal as a first step towards detecting and constraining the global history of the EoR. Signal variance is the integral of the signal's power spectrum, and it is expected to be measured with a high significance. We demonstrate this through results from a simulation and parameter estimation pipeline developed for the Low Frequency Array (LOFAR)-EoR experiment. We show that LOFAR should be able to detect the EoR in 600 hours of integration using the variance statistic. Additionally, the redshift ($z_r$) and duration ($Δz$) of reionization can be constrained assuming a parametrization. We use an EoR simulation of $z_r = 7.68$ and $Δz = 0.43$ to test the pipeline. We are able to detect the simulated signal with a significance of 4 standard deviations and extract the EoR parameters as $z_r = 7.72^{+0.37}_{-0.18}$ and $Δz = 0.53^{+0.12}_{-0.23}$ in 600 hours, assuming that systematic errors can be adequately controlled. We further show that the significance of detection and constraints on EoR parameters can be improved by measuring the cross-variance of the signal by cross-correlating consecutive redshift bins.

astro-ph.CO↗
arXiv2014

The Logarithmic Super Divergence and Statistical Inference : Asymptotic Properties

Statistical inference based on divergence measures have a long history. Recently, Maji, Ghosh and Basu (2014) have introduced a general family of divergences called the logarithmic super divergence (LSD) family. This family acts as a superfamily for both of the logarithmic power divergence (LPD) family (eg. Renyi, 1961) and the logarithmic density power divergence (LDPD)family introduced by Jones et al. (2001). In this paper we describe the asymptotic properties of the inference procedures resulting from this divergence in discrete models. The properties are well supported by real data examples.

math.ST↗
arXiv2014

Robust Estimation in Generalised Linear Models : The Density Power Divergence Approach

The generalised linear model (GLM) is a very important tool for analysing real data in biology, sociology, agriculture, engineering and many other application domain where the relationship between the response and explanatory variables may not be linear or the distributions may not be normal in all the cases. However, quite often such real data contain a significant number of outliers in relation to the standard parametric model used in the analysis; in such cases the classical maximum likelihood estimator may fail to produce reasonable estimators and related inference could be unreliable. In this paper, we develop a robust estimation procedure for the generalised linear models that can generate robust estimators with little loss in efficiency. We will also explore two particular cases of the generalised linear model in details -- Poisson regression for count data and logistic regression for binary data -- which are widely applied in real life experiments. We will also illustrate the performance of the proposed estimators through several interesting data examples

stat.ME↗
arXiv2014

Influence Function Analysis of the Restricted Minimum Divergence Estimators : A General Form

The minimum divergence estimators have proved to be useful tools in the area of robust inference. The robustness of such estimators are measured using the classical Influence functions. However, in many complex situations like testing a composite hypothesis using divergence require the estimators to be restricted into some subspace of the parameter space. The robustness of these restricted minimum divergence estimators are very important in order to have overall robust inference. In this paper we provide a comprehensive description of the robustness of such restricted estimators in terms of their Influence Function for a general class of density based divergences along with their unrestricted versions. In particular, the robustness of some popular minimum divergence estimators are also demonstrated under certain usual restrictions. Thus this paper provides a general framework for the influence function analysis of a large class of minimum divergence estimators with or without restrictions on the parameters.

math.ST↗
arXiv2013

Estimating Copula and Test of Independence based on a generalized framework of all rank-based Statistics in Bivariate Sample

Copulas are mathematical objects that fully capture the dependence structure among random variables and hence, offer a great flexibility in building multivariate stochastic models. In statistics, a copula is used as a general way of formulating a multivariate distribution in such a way that various general types of dependence can be represented. In case of bivariate sample, the notion of estimating copula is closely related to that of testing independence in a bivariate sample, as when the components of the bivariate sample are independent the copula becomes simply product of two uniform distributions. So apart from non-parametric estimation of copulas we also considered it relevant to introduce some non-parametric tests to better understand the very essence of copula in the explanation of association between the components. In fact we will develop a general multivariate statistics that gives rise to a much larger class of non-parametric rank based statistics. This class of statistics can be used in estimation and testing for the association present in the bivariate sample. We choose some representative statistics from that class and compared their power in testing independence using simulation as an attempt to choose the best candidate in that class.

stat.ME↗
arXiv2012

Characterizing Foreground for redshifted 21-cm radiation: 150 MHz GMRT observations

Foreground removal is a major challenge for detecting the redshifted 21-cm neutral hydrogen (HI) signal from the Epoch of Reionization (EoR). We have used 150 MHz GMRT observations to characterize the statistical properties of the foregrounds in four different fields of view. The measured multi-frequency angular power spectrum C_l(Delta nu) is found to have values in the range 10^4 mK^2 to 2 x 10^4 mK^2 across 700 <= l <= 2 x 10^4 and Delta nu <= 2.5 MHz, which is consistent with model predictions where point sources are the most dominant foreground component. The measured C_l(Delta nu) does not show a smooth Delta nu dependence, which poses a severe difficulty for foreground removal using polynomial fitting. The observational data was used to assess point source subtraction. Considering the brightest source (~ 1 Jy) in each field, we find that the residual artifacts are less than 1.5% in the most sensitive field (FIELD I). We have used FIELD I, which has a rms noise of 1.3 mJy/Beam, to study the properties of the radio source population to a limiting flux of 9 mJy. The differential source count is well fitted with a single power law of slope -1.6. We find there is no evidence for flattening of the source counts towards lower flux densities which suggests that source population is dominated by the classical radio-loud Active Galactic Nucleus (AGN). The diffuse Galactic emission is revealed after the point sources are subtracted out from FIELD I . We find C_l \propto l^{-2.34} for 253 <= l <= 800 which is characteristic of the Galactic synchrotron radiation measured at higher frequencies and larger angular scales. We estimate the fluctuations in the Galactic synchrotron emission to be sqrt{l(l+1)C_l/2 pi} ~ 10 K at l=800 (theta > 10'). The measured C_l is dominated by the residual point sources and artifacts at smaller angular scales where C_l ~ 10^3 mK^2 for l > 800.

astro-ph.CO↗
arXiv2011

Improved foreground removal in GMRT 610 MHz observations towards redshifted 21-cm tomography

Foreground removal is a challenge for 21-cm tomography of the high redshift Universe. We use archival GMRT data (obtained for completely different astronomical goals) to estimate the foregrounds at a redshift ~ 1. The statistic we use is the cross power spectrum between two frequencies separated by Δν at the angular multipole l, or equivalently the multi-frequency angular power spectrum C_l(Δν). An earlier measurement of C_l(Δν) using this data had revealed the presence of oscillatory patterns along Δν, which turned out to be a severe impediment for foreground removal (Ghosh et al. 2011). Using the same data, in this paper we show that it is possible to considerably reduce these oscillations by suppressing the sidelobe response of the primary antenna elements. The suppression works best at the angular multipoles l for which there is a dense sampling of the u-v plane. For three angular multipoles l = 1405, 1602 and 1876, this sidelobe suppression along with a low order polynomial fitting completely results in residuals of (\leq 0.02 mK^2), consistent with the noise at the 3σ level. Since the polynomial fitting is done after estimation of the power spectrum it can be ensured that the estimation of the HI signal is not biased. The corresponding 99% upper limit on the HI signal is xHI b \leq 2.9, where xHI is the mean neutral fraction and b is the bias.

astro-ph.CO↗