This paper extends the nonconcave penalized likelihood approach to handle situations where the number of parameters tends to infinity as the sample size increases. The authors establish asymptotic properties of the penalized likelihood estimators, including an oracle property and asymptotic normality, under regularity conditions. They also demonstrate the consistency of the sandwich formula for the covariance matrix and derive the asymptotic distribution of the penalized likelihood ratio statistic under the null hypothesis. The theoretical results are supported by a simulation study and an application to a real-world data set involving a court case on sexual discrimination in salary. The methodology is shown to be effective in variable selection and parameter estimation, even when the number of parameters is large and grows with the sample size.This paper extends the nonconcave penalized likelihood approach to handle situations where the number of parameters tends to infinity as the sample size increases. The authors establish asymptotic properties of the penalized likelihood estimators, including an oracle property and asymptotic normality, under regularity conditions. They also demonstrate the consistency of the sandwich formula for the covariance matrix and derive the asymptotic distribution of the penalized likelihood ratio statistic under the null hypothesis. The theoretical results are supported by a simulation study and an application to a real-world data set involving a court case on sexual discrimination in salary. The methodology is shown to be effective in variable selection and parameter estimation, even when the number of parameters is large and grows with the sample size.