In sample surveys, research is going on in the following areas:
- Adaptive and Network Sampling especially with constrained sample-size
- Derivation of appropriate unbiased estimation in multi-stage sampling when the initially selected samples are to be curtailed at the survey-stages
- Application of bootstrap in two-stage sampling with unequal probabilities
- Randomized Response and related techniques of indirect questioning.
In Symmetric Cryptography, the Klimov-Shamir T-functions have been analyzed and their weakness as stand-alone pseudo-random generators were shown; Boolean functions with some kind of provable resistance to algebraic attacks have been constructed.
In Asymmetric Cryptography, research is going on to develop new protocols for hybrid encryption, implementation of Tate pairing and provably secure authenticated key agreement protocol.
In the area of Hash functions, research is going on in the field of Constructions and theoretical properties of UOWHFs and the Construction of hash functions with a good rate.
In Visual cryptography research is going on to develop new constructions for the visual threshold scheme using combinatorial designs.
In the area of Steganography & Digital watermarking, the Primarily cryptanalysis of some existing schemes has been done.
Some new robustness techniques based on minimum distance ideas have been developed. In the context of multinomial goodness-of-fit tests, some results have been derived which lead to generally more powerful tests under the composite `not equal to’ alternative. Some new correlation inequalities have been constructed under the Gaussian set up, and some existing results have been extended in this context. In the area of longitudinal growth curve models, goodness-of-fit tests have been developed for the exponential and Gompertz models. Currently attempts are going on to extend them to other growth curve models.
Given paired data from two populations, the problem of classification between the populations was considered. A nonparametric classification rule based on a set of incomplete and complete pairs of data was devised and its large sample properties explored. The classifier has applications in Medical Statistics and Biometry. Admissibility and Bahadur optimality of the LRT for Generalized Variance has been established. The theory and applications of Generalized Canonical Variables have been reviewed. Dependency properties of certain multivariate distributions have been studied in terms of their parameters.
The problem of predicting the extent of the wear of cutting tools in various machining operations is important for preventing tool breakage and ensuring optimal usage of tools with uninterrupted operation. A novel technique of predicting tool wear from electrical signals of the spindle motor in a face-milling operation was developed. Electrical sensors are less invasive in comparison to other sensors (e.g., of cutting force, acoustic emission, vibration), and relatively cheaper. Further, the robustness of the method from environmental disturbance makes it an attractive option.
Directional Data Analysis
Probability distributions on r-manifolds (r >=3) have been constructed through maxent and conditional specification characterizations. Constructions of and optimal inference for axial distributions have been obtained. Constructions and inference for asymmetric circular distributions and processes have been explored. Dependency analysis for distributions on the torus and cylinder for some parametric families have been pursued. Directional regression analysis for some real-life data has been conducted. The importance and usefulness of circular statistics in Bioinformatics have been investigated.
Reliability Inference and Survival Analysis
New models and tests for Accelerated Life Testing have been proposed. Parametric and non-parametric inference in models with concomitants of order statistics has been studied. Online and retrospective change-point optimal tests for several parametric linear and circular families of distributions have been derived. Parametric analysis of Quality Adjusted Lifetime data has been analyzed to estimate the corresponding survival distribution.
A unified and conveniently implementable approach to Bayesian inference for probability models on the torus with implicitly defined normalizing constants has been obtained. Full bayesian change point analysis with some circular parametric models has been proposed.
A general adaptive design was formulated to deal with continuous responses in the presence of covariates in phase III clinical trial set up. Properties of the design was studied in details. Some research on adaptive designs for survival data and adaptive designs under crossover set up was also carried out. A general optimal adaptive design was studied which maximized utility.
Categorical Data Analysis
A general model was obtained for longitudinal categorical data set up and some related inference was carried out. Odds ratio in 2×2 contingency table was theoretically studied under some situations where the usual assumptions do not hold.
The genetic effect in a study of twins was statistically formulated and investigated.