Past Seminars

Finding efficient biomarker is critically important for disease detection. Furthermore, rigorous evaluation of biomarkers is essential to guarantee that the tests that are developed are sufficiently accurate and beneficial to the patient. Here we propose a Bayesian predictive approach for determining sample size to compare efficiencies of two binary biomarkers. The operational criteria include classification accuracy, sensitivity, and specificity. In the frequentist approach, one usually estimates the operational criterion from the training data for each marker and using the estimate as the `true' value to select the sample size corresponding to a desirable power, say 80%. However, due to uncertainty to the training data estimates, the designed study could be underpowered when the estimates are treated as true. This may result in a substantially underpowered study while the sample size for the training data is small. In the Bayesian predictive approach the sample size is determined taking into account the uncertainty of the training data estimates. Through simulation studies, we show the effectiveness of the proposed approach.

A series of 4 lectures on the following topics:
1. Urn Models
2. Random Walk
3. Brownian Motion
4. Martingales

A Ferrers graph is a bipartite graph whose edges are in direct correspondence with the boxes in a Ferrers diagram. Ehrenborg and van Willigenburg proved an attractive formula for the number of spanning trees in a Ferrers graph. Several proofs of the formula are known. We give yet another proof based on resistance distance. The main tool is a result which gives necessary and sufficient conditions under which the removal of an edge in a graph does not affect the resistance distance between the end-vertices of another edge. A related conjecture of Ehrenborg on an upper bound for the number of spanning trees in an arbitrary bipartite graph is also discussed.

Unlike the real line, the d-dimensional space Rd, for d >= 2, is not canonically ordered. As a consequence, such fundamental and strongly order-related univariate concepts as quantile and distribution functions, and their empirical counterparts, involving ranks and signs, do not canonically extend to the multivariate context. Palliating that lack of a canonical ordering has remained an open problem for more than half a century, and has generated an abundant literature, motivating, among others, the development of statistical depth and copula-based methods. We show here that, unlike the many de nitions that have been proposed in the literature, the measure transportation-based ones introduced in Chernozhukov et al. (2017) enjoy all the properties (distribution-freeness and preservation of semiparametric e ciency) that make univariate quantiles and ranks successful tools for semiparametric statistical inference. We therefore propose a new center-outward de nition of multivariate distribution and quantile functions, along with their empirical counterparts, for which we establish a Glivenko-Cantelli result. Our approach, based on results by McCann (1995), is geometric rather than analytical and, contrary to the Monge-Kantorovich one in Chernozhukov et al. (2017) (which assumes compactly supported distributions), does not require any moment assumptions. The resulting ranks and signs are shown to be strictly distribution-free, and maximal invariant under the action of transformations (namely, the gradients of convex functions, which thus are playing the role of order-preserving transformations) generating the family of absolutely continuous distributions; this, in view of a general result by Hallin and Werker (2003), implies preservation of semiparametric e ciency. The resulting quantiles are equivariant under the same transformations, which con rms the order-preserving nature of gradients of convex function.

A series of 3 lectures on the following topics:
1. Basics of EM algorithm
2. Statistics: Some caveats
3. p-value conundrum

A series of 3 lectures on the following topics:
1. Basics of EM algorithm
2. Statistics: Some caveats
3. p-value conundrum

Experimental detection of entanglement of an arbitrary state of a given bipartite quantum system is crucial for exploring many areas of quantum information, and even to judge the quality of the entanglement-producing source. Unfortunately, in a realistic scenario, neither we can completely certify the source which produces the entangled state nor can we rely completely on the measuring devices (required for detecting entanglement), usually supplied by a third party. In order to overcome this challenge, we combine here the ideas of Branciard et al.'s measurement device independent entanglement witness protocol [Phys. Rev. Lett. vol. 110, pp. 060405 (2013)] and Augusiak et al.'s universal entanglement witness scheme for twoqubit case [ Phys. Rev. A. 77, 030301 (2008)], and thereby provide a universal entanglement witnessing scheme for any state of two two-level quantum systems in a measurement device independent way. We then provide a set of universal witness operators to check NPT-ness (negative under partial transpose) of states of two d-level quantum systems in a measurement device independent way. We conjecture that no such universal entanglement witness exists for PPT (positive under partial transpose) entangled states. As a verification of measurement device independence of entanglement witnessing process, we analyse the robustness of the concerned entanglement witnessing process in the presence of noise in the inputs as well as in the measurement operators.
Reference: Arindam Mallick and Sibasish Ghosh, Phys. Rev. A, vol. 96, pp. 052323 (2017)

In this paper, we are interested in looking at the changes in female labor supply in a context of rising poverty, and study India's trade liberalization in the 1990s, which lead to increased poverty in rural areas (Topalova 2007, 2010). We study whether female labor supply was used by households to cope with the negative income effects of liberalization. We find that in the poorest 50% of districts, tariff cuts indeed increased labor supply. Yet among the very poorest quartile of districts this is driven by men employed in public works. Since the public works programs in the 1990s were mostly targeted to the lowest income quartile (Dutt et al 2008), this option was not available to household in less poor districts. Indeed, in the second-poorest quartile of districts women increased participation in unpaid agricultural work, and are less likely to primarily engage in domestic duties. Since most of the increase occurs among women who are less educated and belong to lower social status, we conclude that their labor supply is used as an insurance against negative income shocks.

A series of 4 lectures on the following topics:
1. Urn Models
2. Random Walk
3. Brownian Motion
4. Martingales

A series of 2 lectures on the following topics:
1. Basics of EM algorithm
2. Statistics: Some caveats

A series of 4 lectures on the following topics:
1. Urn Models
2. Random Walk
3. Brownian Motion
4. Martingales

A series of 2 lectures on the following topics:
1. Basics of EM algorithm
2. Statistics: Some caveats

In this article, we considered the problem of sea ice cover is melting. Considering the ‘satellite passive microwave remote sensing data’ as functional data, we studied daily observation of sea ice cover of each year as a smooth continuous function of time. We investigated the mean function for the sea ice area for following decades and computed the corresponding 95% bootstrap confidence interval for the both Arctic and Antarctic Oceans. We found the mean function for the sea ice area dropped statistically significantly in recent decades for the Arctic Ocean. However, no such statistical evidence was found for the Antarctic ocean. Essentially, the mean function for sea ice area in the Antarctic Ocean is unchanged. Additional evidence of the melting of sea ice area in the Arctic Ocean is provided by three types of phase curve (namely, Area vs. Velocity, Area vs. Acceleration, and Velocity Vs. Acceleration). In the Arctic Ocean, during the summer, the current decades is observing the size of the sea ice area about 30% less, than what it used to be during the first decade. In this article, we have taken a distribution-free approach for our analysis, except the data generating process, belongs to the Hilbert space.

In this study, the estimation of the Integrated Covariance matrix for high dimensional stock price process is considered. In one-dimension, Integrated variance over a fixed interval can be consistently estimated by Realized variance provided the data is observed at sufficiently high frequency. However, when extended to multi-dimension Realized Covariance becomes a biased estimator because of the underlying assumption that the price movements of different stocks are observed in a synchronous manner- which does not hold in practice. Hayashi and Yoshida proposed an alternative to Realized covariance that does not involve force synchronization of financial data. Although works well with low dimension this estimator becomes inconsistent and unreliable for high dimensional data. One possible way out is to study the bulk spectrum of this matrix and to see how it is connected to the true covariance matrix. In this paper the limiting spectral distribution of high dimensional Hayashi’s estimator has been established when the dimension to sample size ratio tends to 0.

Spectral risk measures proposed by Acerbi (2002, 2004) belong to the family of coherent risk measures and hence inherit the properties of such measures. SRM is a weighted avarage of the quantiles of a loss distribution, the weights of which depend on the user’s risk aversion. A natural estimator for the class of spectral risk measures (SRMs) has the form of L-statistics. In the literature, properties of the estimator of SRMareobtained using the empirical distribution function. We try to investigate the large sample properties of general L-statistics based on i.i.d cases and apply them to our kernel based estimator of SRM. We prove that the estimator is strongly consistent.