In this paper we develop a method for estimating varying coefficients on effects of covariates without modeling the shape of the spatial-temporal baseline trend. We consider the situation where primary interest is in the effects of covariates and the spatial-temporal baseline trend, though non-negligible, is of secondary interest. This is similar to the situation with the Coxproportional hazards model in survival analysis. Basis functions are used to model the shapes of the varying coefficients, but no particular shape is assumed for the spatial-temporal baseline trend. After the effects of covariates are evaluated, estimates of the spatial-temporal baseline trend can be obtained nonparametrically.

The paper considers the problem of volatility co-movement, namely as to whether two financial returns have perfectly correlated common volatility process, in the framework of multivariate stochastic volatility models and proposes a test which checks the volatility co-movement. The proposed test is a stochastic volatility version of the co-movement test proposed by Engle and Susmel (1993), who investigated whether international equity markets have volatility co-movement using the framework of the ARCH model.

In empirical analysis we found that volatility co-movement exists among closely-linked stock markets and that volatility co-movement of the exchange rate markets tends to be found when the overall volatility level is low, which is contrasting to the often-cited finding in the financial contagion literature that financial returns have co-movement in the level during the financial crisis.

Diallel cross designs in the framework of random effects model are considered for the estimation of ratio of variance components, viz. heritability of crosses of inbred lines. New methods for construction of partial diallel cross (PDC) design sunder unblocked and blocked set up are proposed. The resulting designs of these methods are capable of minimizing variance of the estimator of heritability. Consistency of the estimator is also established. One of the practical advantage of the proposed series of designs is attributed to its ability to reduce number of distinct crosses over those for complete diallel cross (CDC) to an extent of 10 to 20 percent. Another heartening aspect of the proposed methods is that the blocks of these designs are incomplete and have smaller block sizes up to one-third than those of complete block designs. Note that, the variance-minimization criterion for optimality reduces to MS-optimality criterion of PDC designs defined in the context of fixed effects model. Further, the newly constructed designs are proved to be asymptotically universally optimal under fixed effects model. Since construction of these designs under blocked set up is quite involved, therefore a computer program is written in C++ for generating these designs which is provided in the Appendix.

The Dantzig selector for a special parametric model of diffusion processes is studied in this paper. In our model, the diffusion coefficient is given as the exponential of the linear combination of other processes which are regarded as covariates. We propose an estimation procedure which is an adaptation of the Dantzig selector for linear regression models and prove the l_q consistencyof the estimator for all q ∈ [1,∞].