Risk-Efficient Sequential Estimation of the Number of Multinomial Cells Hokwon Cho 1, * and Z. Govindarajulu 2 1 Department of Mathematical Sciences, University of Nevada, Las Vegas, Nevada, USA 2 Department of Statistics, University of Kentucky, Lexington, Kentucky, USA ABSTRACT We consider risk-efficient sequential estimation under squared error loss of the number of classes which are equally probable to occur in a given multinomial population. It is assumed that the sampling cost per observation is constant. Large-sample properties of the sequen- tial estimator are studied. Finally, Monte Carlo simulation is carried out in order to investigate its finite sample behavior. The proposed sequential procedure performs better (in the sense of reducing aver- age stopping time and risk) than the one based on the estimator K n , the number of distinct cells observed in a sample of size n. *Correspondence: Hokwon Cho, Department of Mathematical Sciences, Univer- sity of Nevada, 4505 Maryland Parkway, Box 454020, Las Vegas, NV 89154- 4050, USA; E-mail: cho@unlv.nevada.edu. 2159 DOI: 10.1081/STA-200026590 0361-0926 (Print); 1532-415X (Online) Copyright # 2004 by Marcel Dekker, Inc. www.dekker.com 200026590_LSTA33_09_R3_091704 COMMUNICATIONS IN STATISTICS Theory and Methods Vol. 33, No. 9, pp. 2159–2174, 2004