A power approximation for the Kenward and Roger Wald test in the linear mixed model

We derive a noncentral F power approximation for the Kenward and Roger test. We use a method of moments approach to form an approximate distribution for the Kenward and Roger scaled Wald statistic, under the alternative. The result depends on the approximate moments of the unscaled Wald statistic. Via Monte Carlo simulation, we demonstrate that the new power approximation is accurate for cluster randomized trials and longitudinal study designs. The method retains accuracy for small sample sizes, even in the presence of missing data. We illustrate the method with a power calculation for an unbalanced group-randomized trial in oral cancer prevention.

Meta Distribution and Secrecy of Partial Non-Orthogonal Multiple Access (NOMA) in Poisson Networks

<div>This work studies the meta distribution in a partial-NOMA network to obtain fine-grained information about the network performance. As the meta distribution is approximated using the beta distribution via moment matching of the first two moments, reduced integral expressions are derived for the first two moments of the meta distribution. Accurate approximate moments are also proposed to further simplify the calculation. Security is an issue in partial-NOMA because the strong user may decode the weak user’s message in the process of decoding its own message using flexible successive interference cancellation (FSIC). Therefore, a measure of secrecy is defined in this context and the secrecy probability is derived for the case of: 1) a malicious strong user that prioritizes eavesdropping, 2) an innocent strong user that decodes the weak user’s message only when it is required to do so. The obtained results highlight the superiority of partial-NOMA over traditional NOMA in terms of secrecy. They also show that receive filtering and FSIC have a significant positive impact on the secrecy of partial- OMA. Furthermore, partial-NOMA with a small overlap of the resource-block can secure the network from the additional deterioration a malicious eavesdropper may cause.</div>

Meta Distribution and Secrecy of Partial Non-Orthogonal Multiple Access (NOMA) in Poisson Networks

<div>This work studies the meta distribution in a partial-NOMA network to obtain fine-grained information about the network performance. As the meta distribution is approximated using the beta distribution via moment matching of the first two moments, reduced integral expressions are derived for the first two moments of the meta distribution. Accurate approximate moments are also proposed to further simplify the calculation. Security is an issue in partial-NOMA because the strong user may decode the weak user’s message in the process of decoding its own message using flexible successive interference cancellation (FSIC). Therefore, a measure of secrecy is defined in this context and the secrecy probability is derived for the case of: 1) a malicious strong user that prioritizes eavesdropping, 2) an innocent strong user that decodes the weak user’s message only when it is required to do so. The obtained results highlight the superiority of partial-NOMA over traditional NOMA in terms of secrecy. They also show that receive filtering and FSIC have a significant positive impact on the secrecy of partial- OMA. Furthermore, partial-NOMA with a small overlap of the resource-block can secure the network from the additional deterioration a malicious eavesdropper may cause.</div>

MOMENT APPROXIMATIONS OF DISPLACED FORWARD-LIBOR RATES WITH APPLICATION TO SWAPTIONS

We present an algorithm to approximate moments for forward rates under a displaced lognormal forward-LIBOR model (DLFM). Since the joint distribution of rates is unknown, we use a multi-dimensional full weak order 2.0 Ito–Taylor expansion in combination with a second-order Delta method. This more accurately accounts for state dependence in the drift terms, improving upon previous approaches. To verify this improvement we conduct quasi-Monte Carlo simulations. We use the new mean approximation to provide an improved swaption volatility approximation, and compare this to the approaches of Rebonato, Hull–White and Kawai, adapted to price swaptions under the DLFM. Rebonato and Hull–White are found to be the least accurate. While Kawai is the most accurate, it is computationally inefficient. Numerical results show that our approach strikes a balance between accuracy and efficiency.

Fiscal Policy and Debt Management with Incomplete Markets*

A Ramsey planner chooses a distorting tax on labor and manages a portfolio of securities in an economy with incomplete markets. We develop a method that uses second order approximations of Ramsey policies to obtain formulas for conditional and unconditional moments of government debt and taxes that include means and variances of the invariant distribution as well as speeds of mean reversion. The asymptotic mean of the planner's portfolio minimizes a measure of fiscal risk. We obtain analytic expressions that approximate moments of the invariant distribution and apply them to data on a primary government deficit, aggregate consumption, and returns on traded securities. For U.S. data, we find that the optimal target debt level is negative but close to zero, the invariant distribution of debt is very dispersed, and mean reversion is slow.