Approximations for non-symmetric truncated sequential and repeated significance tests

Abstract

Let X₁, X₂…X_N be a random sample from a N(μ, l) population. Using the B-value process {B(t); 0 ≤ t ≤ 1} introduced by Lan and Wittes (1988) one ran design a sequential test for H₀ : μ = μ₀ versus H₁ : μ > μ₀ for some functions γ1(t) > γ2(t): if B(t) > γ₁(t) stop and reject H₀ , if B(t) < γ2(t) stop and do not reject H₀ , otherwise take one more observation. When t = 1, stop anyway rejecting H₀ if B(1) > γ1(1). We suggest some approximations which are usually upper bounds for the significance level, power of the tests and lower bounds for the expected stopping time. Simulations show that the approximations get better as N → ∞ and/or μ → ∞. The exact values are difficult to obtain while the suggested approximations are very easy to compute in the case of linear and RST type boundaries and simulation results show that they are quite reasonable in several cases, even for moderate N.

Keywords:

• B-value
• Brownian motion
• Simulation
• Stopping time

^∗Address: [email protected] and [email protected]. Departmento de Estatistica, IMECC

^∗Address: [email protected] and [email protected]. Departmento de Estatistica, IMECC

Notes

^∗Address: [email protected] and [email protected]. Departmento de Estatistica, IMECC

Additional information

Notes on contributors

Ronaldo Dias

Nancy Lopes Garcia