Asymptotic bias in the linear mixed effects model under non-ignorable missing data mechanisms

Summary.  In longitudinal studies, missingness of data is often an unavoidable problem. Estimators from the linear mixed effects model assume that missing data are missing at random. However, estimators are biased when this assumption is not met. In the paper, theoretical results for the asymptotic bias are established under non-ignorable drop-out, drop-in and other missing data patterns. The asymptotic bias is large when the drop-out subjects have only one or no observation, especially for slope-related parameters of the linear mixed effects model. In the drop-in case, intercept-related parameter estimators show substantial asymptotic bias when subjects enter late in the study. Eight other missing data patterns are considered and these produce asymptotic biases of a variety of magnitudes.     

Protecting the economic health of the poor in India: Are health mutuals the right medicine?

In addition to government‐sponsored health insurance schemes (GSHIS), many microfinance institutions (MFIs) and community‐based organizations (CBOs) in India have started microinsurance health insurance schemes. These include health mutuals for the benefit of their members. This article explores these as an alternative health‐financing model in India. A literature search produced 926 relevant publications. After applying advanced search options and removing duplicates, abstracts of 324 papers were read and then 47 papers reviewed, and finally 29 were included in this review. Five key themes emerged: (1) “Health for all” arguments and opportunities in favour of micro health insurance schemes; (2) micro health insurance products; (3) impact of micro health insurance schemes; (4) systematic irregularities and regulatory framework; and (5) innovation. We also look at the emerging market patterns that will define micro health insurance products. Health mutuals can effectively provide mass health protection to the poor and not so poor through efficient business models, bespoke benefit packages and multiple payment plans. They can reduce financial vulnerability and improve health outcomes. While GSHIS can cover a substantial tranche of expected health‐related costs, the balance can be supplemented through innovative financial products that reduce financial risk.     

The immigration issue in Assam and conflicts around it

Assam, the northeastern state of India, has experienced strong anti-outsider sentiment for more than half a century now. What makes the Assam case unique is that it has faced both internal as well as illegal international migration in massive scales giving rise to intense existential fear and apprehension among its smaller indigenous communities. Their lack of the required political authority and the indifferent attitude of the Indian Union government in addressing the issue have only multiplied its magnitude. The article explicates the politico-economic dynamics of the immigration issue in Assam and the social tension and conflicts around it in a historical perspective and suggests that a multi-pronged approach backed by strong political will is imperative to negotiate the challenges of immigration in the state in an effective manner.     

India's demand for international reserve and monetary disequilibrium: Reserve adequacy under floating regime

The main aim of this study is to investigate India's demand for international reserve by focusing on the role of national monetary disequilibrium and to present new benchmarks for assessing the adequacy of international reserves. We assessed India's position in terms of reserve adequacy and found that India is well placed and has sufficient stock of international reserves to meet the minimum adequacy requirements. Also, the results reveal that the central bank is holding substantial excess reserves and the related opportunity cost (1.5% of GDP) appears to be quite considerable. Further, the estimates of reserve demand function suggest that scale of foreign trade, uncertainty and profitability considerations play significant role in determining India's long-term reserve demand policies. More importantly, validating the monetary approach to balance of payment, our results show that national monetary disequilibrium does play a crucial role in short-run reserve movements. An excess of money demand (supply) induces an inflow (outflow) of international reserves with an elasticity of 0.56 which also implies that Reserve Bank of India responds to correct the domestic money market disequilibrium; and did not just leave it completely on the mercy of reserve inflows.     

Vocational education,self‐employment and burnout among Australian workers

We examine the relationship between vocational education and occupational burnout among workers in different forms of employment. Although the self‐employed enjoy higher levels of job autonomy and work‐related satisfaction, we do not know whether they experience lower rates of occupational burnout, and whether vocational education plays a role in this relationship. This latter consideration is important, given that vocational qualifications often lead to self‐employment and prior research demonstrated that formal training may reduce burnout. However, formal education was previously measured in years of schooling, without considering the distinction between academically‐oriented and vocational courses. Therefore, using data from a 2001 national survey of working Australians, we first establish that the self‐employed are significantly less likely to experience burnout. We then demonstrate that some resilience to burnout can be attributed to the attainment of skilled vocational training, net of employment characteristics which are also very important.     

Protection of privacy in efficient application of randomized response techniques

In estimating the proportion of people bearing a sensitive attribute A, say, in a given community, following Warner’s (J Am Stat Assoc 60:63–69, 1965) pioneering work, certain randomized response (RR) techniques are available for application. These are intended to ensure efficient and unbiased estimation protecting a respondent’s privacy when it touches a person’s socially stigmatizing feature like rash driving, tax evasion, induced abortion, testing HIV positive, etc. Lanke (Int Stat Rev 44:197–203, 1976), Leysieffer and Warner (J Am Stat Assoc 71:649–656, 1976), Anderson (Int Stat Rev 44:213–217, 1976, Scand J Stat 4:11–19, 1977) and Nayak (Commun Stat Theor Method 23:3303–3321, 1994) among others have discussed how maintenance of efficiency is in conflict with protection of privacy. In their RR-related activities the sample selection is traditionally by simple random sampling (SRS) with replacement (WR). In this paper, an extension of an essential similarity in case of general unequal probability sample selection even without replacement is reported. Large scale surveys overwhelmingly employ complex designs other than SRSWR. So extension of RR techniques to complex designs is essential and hence this paper principally refers to them. New jeopardy measures to protect revelation of secrecy presented here are needed as modifications of those in the literature covering SRSWR alone. Observing that multiple responses are feasible in addressing such a dichotomous situation especially with Kuk’s (Biometrika 77:436–438, 1990) and Christofides’ (Metrika 57:195–200, 2003) RR devices, an average of the response-specific jeopardizing measures is proposed. This measure which is device dependent, could be regarded as a technical characteristic of the device and it should be made known to the participants before they agree to use the randomization device. The views expressed are the authors’, not of the organizations they work for. Prof Chaudhuri’s research is partially supported by CSIR Grant No. 21(0539)/02/EMR-II.     

An infinite class of PBIB designs

In this paper, an infinite class of partially balanced incomplete block (PBIB) designs of m+1 associate classes is constructed through the use of a series of row-orthogonal matrices known as partially balanced orthogonal designs (PBOD) of m-associate classes. For the purpose, a series of PBOD is obtained through a method described herein. An infinite class of regular GD designs is also reported.     

Cell-to-switch level planning in mobile wireless networks for efficient management of radio resources

A major step in effectively managing radio resources in a cellular network is to design an appropriate scheme for assigning cells to a location area (LA), serviced by a switch, and allocate resources for individual switches. However, this assignment is already proven in the literature to be an NP-hard problem [Merchant A, Sengupta B. Assignment of cells to switches in PCS networks. IEEE/ACM Transactions on Networking 3(5) (1995) 521–6] that requires efficient heuristic search techniques for obtaining real-time solutions. This work presents a state-space search technique, which is a variant of best first search heuristic technique. The algorithm called the block depth first search (BDFS), allocates cells to switches during switch level resource planning. Under various simulated performance criteria, we compare the performance of the proposed technique with other similar procedures in the literature. Our results indicate that the BDFS outperforms the meta-heuristic procedures in terms of both efficiency and quality of solutions. Hence, we conclude that our proposed technique can be effectively used for switch level planning leading to an efficient management of scarce radio resource in cellular networks.     

Pointwise and uniform convergence of multivariate kernel density estimators using random bandwidths

We obtain the rates of pointwise and uniform convergence of multivariate kernel density estimators using a random bandwidth vector obtained by some data-based algorithm. We are able to obtain faster rate for pointwise convergence. The uniform convergence rate is obtained under some moment condition on the marginal distribution. The rates are obtained under i.i.d. and strongly mixing type dependence assumptions.     

On the equivalence of two approaches to simplicity in the analysis of block designs and some related results

Two seemingly different approaches to simplicity in the analysis of connected block designs, and their relationship to the concepts of balance are discussed.