Financial inclusion in India: An axiomatic approach

In this paper we first develop an axiomatic measure of financial inclusion. This measure is readily implementable and useful to determine policy priorities to promote financial inclusion. Next, we demonstrate that supply side data on banking services can be usefully employed to measure financial inclusion. Third, we examine the effects of major banking policies on financial inclusion across states in India during 1972–2009, using panel data econometrics techniques. We find that the social-banking policy has played crucial role to foster financial inclusion across states in India during 1977–1990. Thereafter, the move toward pro-market financial sector reform has adversely affected the pace of financial inclusion. This paper identifies geographic penetration of banks and credit availability as two policy targets to foster financial inclusion in India.     

Estimation of smooth regression functions in monotone response models

We consider the estimation of smooth regression functions in a class of conditionally parametric co-variate-response models. Independent and identically distributed observations are available from the distribution of (Z,X)$(Z,X)$, where Z is a real-valued co-variate with some unknown distribution, and the response X conditional on Z   is distributed according to the density p(·,ψ(Z))$p(·,\psi (Z))$, where p(·,θ)$p(·,\theta )$ is a one-parameter exponential family. The function ψ$\psi$ is a smooth monotone function. Under this formulation, the regression function E(X|Z)$E(X|Z)$ is monotone in the co-variate Z   (and can be expressed as a one–one function of ψ$\psi$); hence the term “monotone response model”. Using a penalized least squares approach that incorporates both monotonicity and smoothness, we develop a scheme for producing smooth monotone estimates of the regression function and also the function ψ$\psi$ across this entire class of models. Point-wise asymptotic normality of this estimator is established, with the rate of convergence depending on the smoothing parameter. This enables construction of Wald-type (point-wise) as well as pivotal confidence sets for ψ$\psi$ and also the regression function. The methodology is extended to the general heteroscedastic model, and its asymptotic properties are discussed.     

Decision-theoretic estimation of generalized variance and generalized precision

Consider a random data matrix X=(X₁,...,X_k):pXk with independent columns [sathik] and an independent p X p Wishart matrix [sathik]. Estimators dominating the best affine equivariant estimators of [sathik] are obtained under four types of loss functions. Improved estimators (Testimators) of generalized variance and generalized precision are also considered under convex entropy loss (CEL).     

Estimation of location parameters of several exponential distributions

In this paper we address the problem of simultaneous estimation of location parameters of several exponential distributions assuming that the scale parameters are unknown and possibly unequal. From a decision theoretic point of view it is shown that the standard estimators are inadmissible and the improved estimators are obtained when p, the number of populations, is more than one.     

Unbiasedly estimating the total of a stigmatizing variable from a complex survey on permitting options for direct or randomized responses

Following the approach of Mangat and Singh (in J Ind Statist Assoc 32(3): 71–75, 1994) we consider estimating the population total of a sensitive variable like earning through gambling, amount of tax evaded etc. on generating sample responses allowing options for direct or randomized responses according to a specified device. Gathering two independent responses from each individual chosen according to any general sampling scheme we derive unbiased estimators for the total as well as for the variances of these estimators.     

Hypothesis testing on the common location parameter of several shifted exponential distributions: A note

This note deals with hypothesis testing on the common location parameter of several shifted exponential distributions with unknown and possibly unequal scale parameters. No exact test is available for the above mentioned problem; and one does not have the luxury of applying the asymptotic Chi-square test for the likelihood ratio test statistic since the distributions do not satisfy the usual regularity conditions. Therefore, we have proposed a few approximate tests based on the parametric bootstrap method which appear to work well even for small samples in terms of attaining the level. Powers of the proposed tests have been provided along with a recommendation of their usage.