Penalized empirical likelihood estimation of semiparametric models

We propose an empirical likelihood-based estimation method for conditional estimating equations containing unknown functions, which can be applied for various semiparametric models. The proposed method is based on the methods of conditional empirical likelihood and penalization. Thus, our estimator is called the penalized empirical likelihood (PEL) estimator. For the whole parameter including infinite-dimensional unknown functions, we derive the consistency and a convergence rate of the PEL estimator. Furthermore, for the finite-dimensional parametric component, we show the asymptotic normality and efficiency of the PEL estimator. We illustrate the theory by three examples. Simulation results show reasonable finite sample properties of our estimator.     

Metal-Containing Initiator Systems. XXIX. Selective Initiation of Vinyl Polymerizations with Cobaltocene

The polymerizations of acrylonitrile (AN), acrolein (AL), butadiene (BD), and isobutyl vinyl ether (EBVE) with cobaltocene were investigated. It was found that both AN and AL could polymerize in dimethyl sulfoxide through a coordination mechanism, but AN and BD polymerized by a radical mechanism in the presence of some organic halides, such as carbon tetrachloride, benzyl bromide, and allyl bromide. The initiator system of cobaltocene and organic halide also induced cationic polymerization of IBVE. On the basis of the results obtained, a mechanism for the selective initiation of polymerization is proposed and discussed.     

Preparations and Polymerizations of p-Substituted Phenyl Vinyl Sulfides. Vinyl Polymerization 168

Abstract

p-Substituted phenyl vinyl sulfides (PVS) were prepared and their radical polymerizations were investigated dilatometrically to determine some kinetic constants and to deduce the influences of the sulfur atom and p-substituents of PVS. It was found that PVS could be easily homopolymerized by ordinary radical polymerization mechanisms in the presence of 2,2′-azobisisobutyronitrile, contrary to the case of phenyl vinyl ethers, which do not homopolymerize.

From the rates of polymerization (R_p H) of PVS and those of p-substituted PVS (R_p X) under the same conditions, the plot of log (R_p H/R_p X) against the Hammett's equation was found to give a parabola curve. When these results were plotted by the modified Hammett's equation [log (k_p X/k_p H) = ρσ + γE_R ], however, a straight line with γ = ?4.5 and ρ = 0.35 was obtained. From these results it was concluded that the 3d orbital resonance was important in the transition state of the polymerization of these monomers.     

Graft Copolymerization of Methyl Methacrylate on Poly(phenyl Vinyl Sulfide)

Graft copolymer of poly(phenyl vinyl sulfide) and methyl methacrylate was obtained. The isolation of graft copolymer was carried out by the fractional precipitation method. The isolated polymer was confirmed to be a graft copolymer by IR spectra and T determinations. Graft copolymerizations of poly(phenyl vinyl sulfide) with vinyl acetate, acrylonitrile, acrylamide, and acrylic acid were also carried out, but the separation of graft copolymer in these cases was difficult, and satisfactory results could not be obtained.     

Copolymerization and Charge-Transfer Interaction of Methyl Isopropenyl Ketone Cyclodimer with Maleic Anhydride and Maleimide

The copolymerizations of methyl isopropenyl ketone cyclodimer(MIPKD: 2-acetyl-2,5,6-trimethyl-2,3-dihydropyran) with maleic anhydride (MAn) and with maleimide (MI) in the presence of α,α′-azobisisobutyronitrile were investigated at 60 and 80°C. It was found that the copolymerizations were performed in both systems to give rather low molecular weight copolymers consisting of less than 50% MIPKD units. It was also observed from IR and NMR spectral determinations of the systems of MIPKD with MAn and with MI that 1:1 charge-transfer complexes with a small equilibrium constant were formed. Formation of these complexes seemed to affect the copolymerizations. Finally, the copolymerization of MIPKD with MAn was studied kinetically. The mechanism of copolymerization is discussed.     

Cationic Polymerization Behavior of Some Vinyl Ketone Cyclodimers

Cationic polymerizations of 2,3-dihydropyran derivatives, methyl isopropenyl ketone cyclodimer (MIPKD), chloromethyl vinyl ketone cyclodimer (CMVKD), and methyl isopropenyl ketone-chloromethyl vinyl ketone cyclocodimer, D(MIPK-CMVK), were investigated in the presence of various Lewis acids at 0°C. These monomers were found to undergo cationic polymerization to give low molecular weight polymer which consisted mainly of a vinylene structure. However, the ring-opening polymerization was found to occur to a minor extent in cationic polymerizations of MIPKD and D(MIPK-CMVK) cyclodimer.     

Polymerization of Vinyl Monomers with Binary Initiator System of N-Chlorosuccinimide and Lewis Acids

The polymerization of vinyl monomers with a binary system composed of N-chlorosuccinimide (NCS) and some Lewis acids was investigated by means of kinetic and spectral determinations. It was found that the NCS-ZnCl₂ system was the most effective as an initiator of radical polymerization of methyl methacrylate, and this polymerization was initiated by a radical produced via the reaction of NCS and ZnCl₂, and terminated bimolecularly. By applying a spin trapping technique to the reaction of NCS with ZnCl₂, it was shown that the initiating radical was N-succinimidyl radical which was obtained through a homolysis at the N-Cl bond.     

Generalized Neyman–Pearson optimality of empirical likelihood for testing parameter hypotheses

This paper studies the Generalized Neyman–Pearson (GNP) optimality of empirical likelihood-based tests for parameter hypotheses. The GNP optimality focuses on the large deviation errors of tests, i.e., the convergence rates of the type I and II error probabilities under fixed alternatives. We derive (i) the GNP optimality of the empirical likelihood criterion (ELC) test against all alternatives, and (ii) a necessary and a sufficient condition for the GNP optimality of the empirical likelihood ratio (ELR) test against each alternative.