Numbers of near bivariate record-concomitant observations

Let be independent and identically distributed random vectors with continuous distribution. Let L(n) and X(n) denote the nth record time and the nth record value obtained from the sequence of Xs. Let Y(n) denote the concomitant of the nth record value, which relates to the sequence of Ys. We call a near bivariate nth record-concomitant observation if belongs to the open rectangle (X(n)-a,X(n))×(Y(n)-b1,Y(n)+b2), where a,b1,b2>0 and L(n)<i<L(n+1). Asymptotic properties of the numbers of near bivariate record-concomitant observations are discussed in the present work. New techniques for generating bivariate record-concomitants, the numbers of near record observations and the numbers of near bivariate record-concomitant observations are also proposed.