Search results for: T.N. Sriram

Items from 1 to 14 out of 14 results

article

Robust multivariate association and dimension reduction using density divergences

Ross Iaci, T.N. Sriram

Journal of Multivariate Analysis > 2013 > 117 > Complete > 281-295

In this article, we introduce two new families of multivariate association measures based on power divergence and alpha divergence that recover both linear and nonlinear dependence relationships between multiple sets of random vectors. Importantly, this novel approach not only characterizes independence, but also provides a smooth bridge between well-known distances that are inherently robust against...

article

Multivariate Association and Dimension Reduction: A Generalization of Canonical Correlation Analysis

Ross Iaci, T.N. Sriram, Xiangrong Yin

Biometrics > 66 > 4 > 1107 - 1118

Summary In this article, we propose a new generalized index to recover relationships between two sets of random vectors by finding the vector projections that minimize an L ₂ distance between each projected vector and an unknown function of the other. The unknown functions are estimated using the Nadaraya–Watson smoother. Extensions to multiple sets and groups of multiple sets are also discussed,...

article

L2E estimation of mixture complexity for count data

T. Umashanger, T.N. Sriram

Computational Statistics and Data Analysis > 2009 > 53 > 12 > 4243-4254

For count data, robust estimation of the number of mixture components in finite mixtures is revisited using L2 distance. An information criterion based on L2 distance is shown to yield an estimator, which is also shown to be strongly consistent. Monte Carlo simulations show that our estimator is competitive with other procedures in correctly determining the number of components when the data comes...

article

Estimation of the offspring mean in a controlled branching process with a random control function

T.N. Sriram, A. Bhattacharya, M. González, R. Martínez, more

Stochastic Processes and their Applications > 2007 > 117 > 7 > 928-946

Controlled branching processes (CBP) with a random control function provide a useful way to model generation sizes in population dynamics studies, where control on the growth of the population size is necessary at each generation. An important special case of this process is the well known branching process with immigration. Motivated by the work of Wei and Winnicki [C.Z. Wei, J. Winnicki, Estimation...

article

Robust estimation of mixture complexity for count data

Mi-Ja Woo, T.N. Sriram

Computational Statistics and Data Analysis > 2007 > 51 > 9 > 4379-4392

For finite mixtures, consistent estimation of unknown number of components, called mixture complexity, is considered based on a random sample of counts, when the exact form of component probability mass functions are unknown but are postulated to belong to some parametric family. Following a recent approach of Woo and Sriram [2006. Robust estimation of mixture complexity. J. Amer. Statist. Assoc.,...

article

Fixed-width confidence interval based on a minimum Hellinger distance estimator

Sangyeol Lee, T.N. Sriram, Xinyu Wei

Journal of Statistical Planning and Inference > 2006 > 136 > 12 > 4276-4292

In the context of discrete data, a sequential fixed-width confidence interval for an unknown parameter in a parametric model is constructed using a minimum Hellinger distance estimator (MHD) as the center of the interval. It is shown that our sequential procedure is asymptotically consistent and efficient, when the assumed parametric model is correct. These results, in addition to being exactly same...

article

Rates of convergence of an adaptive kernel density estimator for finite mixture models

R.J. Karunamuni, T.N. Sriram, J. Wu

Statistics and Probability Letters > 2006 > 76 > 3 > 221-230

Kernel smoothing methods are widely used in many areas of statistics with great success. In particular, minimum distance procedures heavily depend on kernel density estimators. It has been argued that when estimating mixture parameters in finite mixture models, adaptive kernel density estimators are preferable over nonadaptive kernel density estimators. Cutler and Cordero-Braña [1996, J. Amer. Statist...

article

Asymptotic normality of an adaptive kernel density estimator for finite mixture models

R.J. Karunamuni, T.N. Sriram, J. Wu

Statistics and Probability Letters > 2006 > 76 > 2 > 211-220

Choice of an appropriate kernel density estimator is a difficult one in minimum distance estimation based on density functions. Particularly, for mixture models, the choice of bandwidth is very crucial because the component densities may have different scale parameters, which in turn necessitate varying amount of smoothing. Adaptive kernel density estimators use different bandwidths for different...

article

Fixed size confidence regions for parameters of threshold AR(1) models

T.N. Sriram

Journal of Statistical Planning and Inference > 2001 > 97 > 2 > 293-304

For parameters of single and multiple threshold autoregressive models of order one, sequential procedures are proposed for constructing fixed size confidence ellipsoids. Sequential procedures are also proposed for constructing fixed proportional accuracy confidence ellipsoids and fixed width confidence intervals for linear combination of parameters. The confidence ellipsoids and intervals are shown...

article

Minimum Hellinger distance estimation for supercritical Galton-Watson processes

T.N. Sriram, A.N. Vidyashankar

Statistics and Probability Letters > 2000 > 50 > 4 > 331-342

This paper studies the asymptotic behavior of the minimum Hellinger distance estimator of the underlying parameter in a supercritical branching process whose offspring distribution is known to belong to a parametric family. This estimator is shown to be asymptotically normal, efficient at the true model and robust against gross errors. These extend the results of Beran (Ann. Statist. 5, 445-463 (1977))...

article

L _p Convergence of reciprocals of sample means with applications to sequential estimation in linear regression

N. Etemadi, T.N. Sriram, A.N. Vidyashankar

Journal of Statistical Planning and Inference > 1997 > 65 > 1 > 1-15

Let {Z _n ; n 1} be a stationary sequence of non-negative random variables with finite first moment. It is known that the sample average Z _n converges to a random variable Z with probability one. In this paper we have tw objectives: First, we obtain a necessary and sufficient condition for the L _p (p > 0) convergence of Z ^- ¹ _n to Z ^- ¹ . ...

article

Estimation for an adaptive allocation design

William F. Rosenberger, T.N. Sriram

Journal of Statistical Planning and Inference > 1997 > 59 > 2 > 309-319

The generalized Polya urn model has been proposed as a class of adaptive allocation rules. Under a simple population model, maximum likelihood estimators can be derived. Previous work has shown them to be jointly asymptotically normal. We prove some additional results, including strong consistency of the estimators and a law of the iterated logarithm. We then derive the exact Fisher's information...

article

A modified bootstrap for autoregression without stationarity

Somnath Datta, T.N. Sriram

Journal of Statistical Planning and Inference > 1997 > 59 > 1 > 19-30

In this paper, we consider a bootstrap approximation to the distribution of the least squares estimator of the autoregressive parameter β in a first-order autoregressive process which may or may not have a stationary solution. Our bootstrap procedure is a modification of the standard bootstrap and employs a data based shrinkage towards the critical values β = ±1.The error in estimation of the sampling...

article

A modified bootstrap for branching processes with immigration

Somnath Datta, T.N. Sriram

Stochastic Processes and their Applications > 1995 > 56 > 2 > 275-294

In this paper we consider bootstrap approximation to the sampling distribution of an estimator of the offspring mean m in a branching process with immigration. A modification of the standard parametric bootstrap procedure is shown to eliminate the invalidity of the standard bootstrap for the case m = 1, as reported in Sriram (1994). Furthermore, the modified bootstrap is shown to provide valid approximations...

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